WO2016168280A1

WO2016168280A1 - Generating an accurate model of noise and subtracting it from seismic data

Info

Publication number: WO2016168280A1
Application number: PCT/US2016/027261
Authority: WO
Inventors: Massimiliano Vassallo; Paul RAS; Ali Ozbek; Nihed EL ALLOUCHE; Yousif Izzeldin Kamil Amin
Original assignee: Schlumberger Technology Corporation; Schlumberger Canada Limited; Services Petroliers Schlumberger; Geoquest Systems B.V.
Priority date: 2015-04-14
Filing date: 2016-04-13
Publication date: 2016-10-20

Abstract

A method includes obtaining seismic data including measurements of a seismic wavefield and obtaining at least one component of a spatial gradient of the measurements of the seismic wavefield. The method includes determining a representation of the seismic data based at partially on the measurements and the at least one component of the spatial gradient and identifying a signal of interest and noise in the representation of the seismic data based at least partially on different characteristics of the signal of interest and the noise in a domain of the representation. The method includes calculating at least one of a signal model or a noise model from the signal of interest and noise identified in the representation of the seismic data and determining a noise attenuated signal for the seismic data based at least partially on the at least one of the signal model or the noise model.

Description

GENERATING AN ACCURATE MODEL OF NOISE AND SUBTRACTING IT FROM

SEISMIC DATA

Cross-Reference to Related Application

[0001] This application claims priority to U. S. Provisional Patent Application having Serial No. 62/147,087, filed on April 14, 2015. The entirety of this priority provisional patent application is incorporated by reference herein.

Background

[0002] In seismic acquisition, land or marine, noise may propagate more slowly than a signal of interest, resulting in a broader spatial bandwidth. For this reason, seismic acquisition technologies based on the measurement of data at discrete locations may choose between either oversampling the signal and sampling the noise, or sampling the signal and under-sampling the noise. The former results in a larger number of receivers to acquire the signal of interest, which results in increased cost. The latter may result in a reduced cost acquisition system but may increase a risk of data being compromised by aliased noise, which may be challenging to attenuate during processing processes.

[0003] In land measurements, near surface effects generate strong waves that propagate slowly and approximately horizontal in aerated layers, resulting in an apparent velocity in the seismic gathers that is lower than the seismic events reflected from the subsurface. In towed marine measurements, typically swell effects also generate slow waves, affecting the pressure measurements, especially at the low end of the spectrum. In acquisition systems located on the ocean floor, similar challenges as on land-based seismic acquisition systems are faced.

[0004] In multi-sensor towed marine measurements, vibration noise propagating along the cable is dominant on the accelerometer measurements. This noise propagates along the cable more slowly than seismic events reflected from the subsurface. Other sources of noise also affect accelerometers, also propagating slowly along the cable. Examples of such noise sources are torsional noise, weather related noise, noise associated to positioning equipment, currents, and noise generated by external sources of perturbation, such as barnacles on the cables.

[0005] In the cases above, because the noise is much stronger in amplitude than some of the reflected seismic signals, fine sampling (and hence high acquisition costs) may used to safely remove the noise with a time-space filter during processing. If the noise is not sampled properly, often due to cost efficiency reasons, spatial alias may compromise the usable signal and may be challenging to attenuate during processing, due to both sampling limitations and high dynamic range.

Summary

[0006] Embodiments of the disclosure may provide a method for noise mitigation. The method may include obtaining seismic data including measurements of a seismic wavefield for at least one subsurface volume. The method may also include obtaining at least one component of a spatial gradient of the measurements of the seismic wavefield. Additionally, the method may include determining a representation of the seismic data based at partially on the measurements of the seismic wavefield and the at least one component of the spatial gradient. Further, the method may include identifying a signal of interest and noise in the representation of the seismic data based at least partially on different characteristics of the signal of interest and the noise in a domain of the representation. The method may include calculating at least one of a signal model or a noise model from the signal of interest and noise identified in the representation of the seismic data. The method may also include determining a noise attenuated signal for the seismic data based at least partially on the at least one of the signal model or the noise model.

[0007] In an embodiment, obtaining the measurements of the seismic wavefield may include receiving acoustic signals collected for the at least one subsurface volume. Obtaining the at least one component of the spatial gradient of the measurement may include determining the at least one component of the spatial gradient from the acoustic signals. Determining the representation of the seismic data may include processing the measurements and the at least one component of the spatial gradient using an analysis process.

[0008] In an embodiment, the analysis process may include at least one of multichannel interpolation by matching pursuit, generalized matching pursuit, an extended generalized matching pursuit, a finite difference multichannel interpolation by matching pursuit, or a greedy algorithm.

[0009] In an embodiment, calculating the at least one of the signal model or the noise model may include removing the signal of interest from the representation of the seismic data to form the noise model. Determining the noise attenuated signal for the seismic data may include subtracting the noise model from the measurements of the seismic wavefield. [0010] In an embodiment, determining the noise attenuated signal for the seismic data may include selecting the signal of interest from the representation of the seismic data as the noise attenuated signal.

[0011] In an embodiment, obtaining the measurements of the seismic wavefield may include receiving acoustic signals collected for the at least one subsurface volume. Obtaining the at least one component of the spatial gradient of the measurements may include receiving the at least one component of the spatial gradient collected for the at least one subsurface volume. Determining the reconstructed wavefield for the seismic data may include processing the measurements and the at least one component of the spatial gradient using an analysis process.

[0012] In an embodiment, the analysis process may include at least one of multichannel interpolation by matching pursuit, generalized matching pursuit, an extended generalized matching pursuit, a finite difference multichannel interpolation by matching pursuit, or a greedy algorithm.

[0013] In an embodiment, calculating the at least one of the signal model or the noise model may include removing the signal of interest from the representation of the seismic data to form the noise model. Determining the noise attenuated signal for the seismic data may include subtracting the noise model from the measurements of the seismic wavefield.

[0014] In an embodiment, determining the noise attenuated signal for the seismic data may include selecting the signal of interest from the representation of the seismic data as the noise attenuated signal.

[0015] Embodiments of the disclosure may provide a non-transitory computer-readable medium storing instructions. The instructions, when executed by one or more processors of a computing system, may cause the computing system to perform a method. The method may include obtaining seismic data including measurements of a seismic wavefield for at least one subsurface volume. The method may also include obtaining at least one component of a spatial gradient of the measurements of the seismic wavefield. Additionally, the method may include determining a representation of the seismic data based at partially on the measurements of the seismic wavefield and the at least one component of the spatial gradient. Further, the method may include identifying a signal of interest and noise in the representation of the seismic data based at least partially on different characteristics of the signal of interest and the noise in a domain of the representation. The method may include calculating at least one of a signal model or a noise model from the signal of interest and noise identified in the representation of the seismic data. The method may also include determining a noise attenuated signal for the seismic data based at least partially on the at least one of the signal model or the noise model.

[0016] Embodiments of the disclosure may provide a computing system. The computing system may include one or more processors and a memory system including one or more non-transitory computer-readable media storing instructions. The instructions, when executed by one or more processors, may cause the computing system to perform a method. The method may include obtaining seismic data including measurements of a seismic wavefield for at least one subsurface volume. The method may also include obtaining at least one component of a spatial gradient of the measurements of the seismic wavefield. Additionally, the method may include determining a representation of the seismic data based at partially on the measurements of the seismic wavefield and the at least one component of the spatial gradient. Further, the method may include identifying a signal of interest and noise in the representation of the seismic data based at least partially on different characteristics of the signal of interest and the noise in a domain of the representation. The method may include calculating at least one of a signal model or a noise model from the signal of interest and noise identified in the representation of the seismic data. The method may also include determining a noise attenuated signal for the seismic data based at least partially on the at least one of the signal model or the noise model.

Brief Description of the Drawings

[0017] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the present teachings and together with the description, serve to explain the principles of the present teachings.

[0018] Figures 1 A, IB, 1C, ID, 2, and 3 illustrate simplified, schematic views of an oilfield and its operation, according to an embodiment.

[0019] Figure 4 illustrates a flowchart of an example of a method for noise attenuation, according to an embodiments.

[0020] Figures 5 A and 5B illustrate plots of traces used as input to an embodiment of a method of the present disclosure, according to an embodiment.

[0021] Figures 5C and 5D illustrate plots of traces after employing an embodiment of the method of the present disclosure, according to an embodiment. [0022] Figures 6, 7, 8, 9, 10, 11, 12, 13, and 14 illustrate flowcharts of different examples of methods for noise attenuation, according to various embodiments.

[0023] Figures 15A and 15B illustrate another flowchart of an example of another method for noise attenuation, according to an embodiment.

[0024] Figure 16 illustrates a schematic view of a computing or processor system for performing the method, according to an embodiment.

Detailed Description

[0025] Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings and figures. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be apparent to one of ordinary skill in the art that the embodiments of the present disclosure may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments.

[0026] It will also be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are used to distinguish one element from another. For example, a first object or step could be termed a second object or step, and, similarly, a second object or step could be termed a first object or step, without departing from the scope of the present disclosure. The first object or step, and the second object or step, are both, objects or steps, respectively, but they are not to be considered the same object or step.

[0027] The terminology used in the description of the present disclosure herein is for the purpose of describing particular embodiments and is not intended to be limiting of the present disclosure. As used in the description and the appended claims, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term "and/or" as used herein refers to and encompasses any possible combinations of one or more of the associated listed items. It will be further understood that the terms "includes," "including," "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Further, as used herein, the term "if may be construed to mean "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context.

[0028] Attention is now directed to processing procedures, methods, techniques and workflows that are in accordance with some embodiments. Some operations in the processing procedures, methods, techniques and workflows disclosed herein may be combined and/or the order of some operations may be changed.

[0029] Figures 1 A- ID illustrate simplified, schematic views of oilfield 100 having subterranean one or more geological formations 102 containing reservoir 104 therein in accordance with implementations of various technologies and techniques described herein. Figure 1 A illustrates a survey operation being performed by a survey tool, such as seismic truck 106.1, to measure properties of the subterranean formation. The survey operation may be a seismic survey operation for producing sound vibrations. In Figure 1 A, one such sound vibration, e.g., sound vibration 1 12 generated by source 1 10, reflects off horizons 1 14 in earth formation 1 16. A set of sound vibrations may be received by sensors, such as geophone-receivers 1 18, situated on the earth's surface. The data received 120 may be provided as input data to a computer system, for example, a computer 122.1 of a seismic truck 106.1, and responsive to the input data, computer 122.1 generates seismic data output 124. This seismic data output may be stored, transmitted or further processed as desired, for example, by data analysis, data reduction, and the like.

[0030] Figure IB illustrates a drilling operation being performed by drilling tools 106.2 suspended by rig 128 and advanced into subterranean formations 102 to form wellbore 136. Mud pit 130 may be used to draw drilling mud into the drilling tools via flow line 132 for circulating drilling mud down through the drilling tools, then up wellbore 136 and back to the surface. The drilling mud may be filtered and returned to the mud pit. A circulating system may be used for storing, controlling, or filtering the flowing drilling mud. The drilling tools may be advanced into subterranean formations 102 to reach reservoir 104. Each well may target one or more reservoirs. The drilling tools may be adapted for measuring downhole properties using logging while drilling tools. The logging while drilling tools may also be adapted for taking core sample 133 as shown.

[0031] Computer facilities may be positioned at various locations about the oilfield 100 (e.g., the surface unit 134) and/or at remote locations. Surface unit 134 may be used to communicate with the drilling tools and/or offsite operations, as well as with other surface or downhole sensors. Surface unit 134 may be capable of communicating with the drilling tools to send commands to the drilling tools, and to receive data therefrom. Surface unit 134 may also collect data generated during the drilling operation and produce data output 135, which may then be stored or transmitted.

[0032] Sensors (S), such as gauges, may be positioned about oilfield 100 to collect data relating to various oilfield operations as described previously. As shown, sensor (S) may be positioned in one or more locations in the drilling tools and/or at rig 128 to measure drilling parameters, such as weight on bit, torque on bit, pressures, temperatures, flow rates, compositions, rotary speed, and/or other parameters of the field operation. Sensors (S) may also be positioned in one or more locations in the circulating system.

[0033] Drilling tools 106.2 may include a bottom hole assembly (BHA) (not shown), generally referenced, near the drill bit (e.g. , within several drill collar lengths from the drill bit). The bottom hole assembly may include capabilities for measuring, processing, and storing information, as well as communicating with surface unit 134. The bottom hole assembly may further include drill collars for performing various other measurement functions.

[0034] The bottom hole assembly may include a communication subassembly that communicates with surface unit 134. The communication subassembly may be adapted to send signals to and receive signals from the surface using a communications channel such as mud pulse telemetry, electro-magnetic telemetry, or wired drill pipe communications. The communication subassembly may include, for example, a transmitter that generates a signal, such as an acoustic or electromagnetic signal, which is representative of the measured drilling parameters. It will be appreciated by one of skill in the art that a variety of telemetry systems may be employed, such as wired drill pipe, electromagnetic or other known telemetry systems.

[0035] Typically, the wellbore may be drilled according to a drilling plan that is established prior to drilling. The drilling plan may set forth equipment, pressures, trajectories and/or other parameters that define the drilling process for the wellsite. The drilling operation may then be performed according to the drilling plan. As information is gathered, the drilling operation may deviate from the drilling plan. Additionally, as drilling or other operations are performed, the subsurface conditions may change. The earth model may also be adjusted as information is collected

[0036] The data gathered by sensors (S) may be collected by surface unit 134 and/or other data collection sources for analysis or other processing. The data collected by sensors (S) may be used alone or in combination with other data. The data may be collected in one or more databases and/or transmitted on or offsite. The data may be historical data, real time data, or combinations thereof. The real time data may be used in real time, or stored for later use. The data may also be combined with historical data or other inputs for further analysis. The data may be stored in separate databases, or combined into a single database.

[0037] Surface unit 134 may include transceiver 137 to allow communications between surface unit 134 and various portions of the oilfield 100 or other locations. Surface unit 134 may also be provided with or functionally connected to one or more controllers (not shown) for actuating mechanisms at oilfield 100. Surface unit 134 may then send command signals to oilfield 100 in response to data received. Surface unit 134 may receive commands via transceiver 137 or may itself execute commands to the controller. A processor may be provided to analyze the data (locally or remotely), make the decisions and/or actuate the controller. In this manner, oilfield 100 may be selectively adjusted based on the data collected. This technique may be used to optimize (or improve) portions of the field operation, such as controlling drilling, weight on bit, pump rates, or other parameters. These adjustments may be made automatically based on computer protocol, and/or manually by an operator. In some cases, well plans may be adjusted to select optimum (or improved) operating conditions, or to avoid problems.

[0038] Figure 1C illustrates a wireline operation being performed by wireline tool 106.3 suspended by rig 128 and into wellbore 136 of Figure IB. Wireline tool 106.3 may be adapted for deployment into wellbore 136 for generating well logs, performing downhole tests and/or collecting samples. Wireline tool 106.3 may be used to provide another method and apparatus for performing a seismic survey operation. Wireline tool 106.3 may, for example, have an explosive, radioactive, electrical, or acoustic energy source 144 that sends and/or receives electrical signals to surrounding subterranean formations 102 and fluids therein.

[0039] Wireline tool 106.3 may be operatively connected to, for example, geophones 1 18 and a computer 122.1 of a seismic truck 106.1 of Figure 1A. Wireline tool 106.3 may also provide data to surface unit 134. Surface unit 134 may collect data generated during the wireline operation and may produce data output 135 that may be stored or transmitted. Wireline tool 106.3 may be positioned at various depths in the wellbore 136 to provide a survey or other information relating to the subterranean formation 102. [0040] Sensors (S), such as gauges, may be positioned about oilfield 100 to collect data relating to various field operations as described previously. As shown, sensor S may be positioned in wireline tool 106.3 to measure downhole parameters which relate to, for example porosity, permeability, fluid composition and/or other parameters of the field operation.

[0041] Figure ID illustrates a production operation being performed by production tool 106.4 deployed from a production unit or Christmas tree 129 and into completed wellbore 136 for drawing fluid from the downhole reservoirs into surface facilities 142. The fluid flows from reservoir 104 through perforations in the casing (not shown) and into production tool 106.4 in wellbore 136 and to surface facilities 142 via gathering network 146.

[0042] Sensors (S), such as gauges, may be positioned about oilfield 100 to collect data relating to various field operations as described previously. As shown, the sensor (S) may be positioned in production tool 106.4 or associated equipment, such as Christmas tree 129, gathering network 146, surface facility 142, and/or the production facility, to measure fluid parameters, such as fluid composition, flow rates, pressures, temperatures, and/or other parameters of the production operation.

[0043] Production may also include injection wells for added recovery. One or more gathering facilities may be operatively connected to one or more of the wellsites for selectively collecting downhole fluids from the wellsite(s).

[0044] While Figures 1 A-1D illustrate tools used to measure properties of an oilfield, it will be appreciated that the tools may be used in connection with non-oilfield operations, such as gas fields, mines, aquifers, storage or other subterranean facilities. Also, while certain data acquisition tools are depicted, it will be appreciated that various measurement tools capable of sensing parameters, such as seismic two-way travel time, density, resistivity, production rate, etc., of the subterranean formation and/or its geological formations may be used. Various sensors (S) may be located at various positions along the wellbore and/or the monitoring tools to collect and/or monitor the desired data. Other sources of data may also be provided from offsite locations.

[0045] The field configurations of Figures 1 A-1D are intended to provide a brief description of an example of a field usable with oilfield application frameworks. Part of, or the entirety, of oilfield 100 may be on land, water and/or sea, as further discussed below. Also, while a single field measured at a single location is depicted, oilfield applications may be utilized with any combination of one or more oilfields, one or more processing facilities and one or more wellsites. [0046] Figure 2 illustrates another schematic view, partially in cross section of oilfield 200 having data acquisition tools 202.1, 202.2, 202.3 and 202.4 positioned at various locations along oilfield 200 for collecting data of subterranean formation 204 in accordance with implementations of various technologies and techniques described herein. Data acquisition tools 202.1-202.4 may be the same as data acquisition tools 106.1-106.4 of Figures 1A-1D, respectively, or others not depicted. As shown, data acquisition tools 202.1-202.4 may generate data plots or measurements 208.1-208.4, respectively. These data plots are depicted along oilfield 200 to demonstrate the data generated by the various operations.

[0047] Data plots 208.1-208.3 are examples of static data plots that may be generated by data acquisition tools 202.1-202.3, respectively; however, it should be understood that data plots 208.1- 208.3 may also be data plots that are updated in real time. These measurements may be analyzed to better define the properties of the formation(s) and/or determine the accuracy of the measurements and/or for checking for errors. The plots of each of the respective measurements may be aligned and scaled for comparison and verification of the properties.

[0048] Static data plot 208.1 may be a seismic two-way response over a period of time. Static plot 208.2 may be core sample data measured from a core sample of the formation 204. The core sample may be used to provide data, such as a graph of the density, porosity, permeability, or some other physical property of the core sample over the length of the core. Tests for density and viscosity may be performed on the fluids in the core at varying pressures and temperatures. Static data plot 208.3 may be a logging trace that typically provides a resistivity or other measurement of the formation at various depths.

[0049] A production decline curve or graph 208.4 may be a dynamic data plot of the fluid flow rate over time. The production decline curve may provide the production rate as a function of time. As the fluid flows through the wellbore, measurements may be taken of fluid properties, such as flow rates, pressures, composition, etc.

[0050] Other data may also be collected, such as historical data, user inputs, economic information, and/or other measurement data and other parameters of interest. As described below, the static and dynamic measurements may be analyzed and used to generate models of the subterranean geological formation to determine characteristics thereof. Similar measurements may also be used to measure changes in geological formation aspects over time. [0051] The subterranean structure 204 may have a plurality of geological formations 206.1- 206.4. As shown, this structure may have several formations or layers, including a shale layer 206.1, a carbonate layer 206.2, a shale layer 206.3 and a sand layer 206.4. A fault 207 may extend through the shale layer 206.1 and the carbonate layer 206.2. The static data acquisition tools may be adapted to take measurements and detect characteristics of the formations.

[0052] While a specific subterranean formation with specific geological structures is depicted, it will be appreciated that oilfield 200 may contain a variety of geological structures and/or formations, sometimes being complex. In some locations, typically below the water line, fluid may occupy pore spaces of the formations. Each of the measurement devices may be used to measure properties of the formations and/or its geological features. While each acquisition tool is shown as being in specific locations in oilfield 200, it will be appreciated that one or more types of measurement may be taken at one or more locations across one or more fields or other locations for comparison and/or analysis.

[0053] The data collected from various sources, such as the data acquisition tools of Figure 2, may then be processed and/or evaluated. Typically, seismic data displayed in static data plot 208.1 from data acquisition tool 202.1 may be used by a geophysicist to determine characteristics of the subterranean formations and features. Additionally, the seismic data may be processed and analyzed to aid in the evaluation of the seismic data, as described herein. The core data shown in static plot 208.2 and/or log data from well log 208.3 may be used by a geologist to determine various characteristics of the subterranean formation. The production data from graph 208.4 may be used by the reservoir engineer to determine fluid flow reservoir characteristics. The data analyzed by the geologist, geophysicist and the reservoir engineer may be analyzed using modeling techniques.

[0054] Figure 3 illustrates a side view of a marine-based survey 360 of a subterranean geological subsurface 362 in accordance with one or more implementations of various techniques described herein. Subsurface 362 may include seafloor surface 364. Seismic sources 366 may include marine sources such as vibroseis or airguns, which may propagate seismic waves 368 (e.g., energy signals) into the Earth over an extended period of time or at a nearly instantaneous energy provided by impulsive sources. The seismic waves may be propagated by marine sources as a frequency sweep signal. For example, marine sources of the vibroseis type may initially emit a seismic wave at a low frequency (e.g., 5 Hz) and increase the seismic wave to a high frequency (e.g., 80-90Hz) over time.

[0055] The component(s) of the seismic waves 368 may be reflected and converted by seafloor surface 364 (i.e., reflector), and seismic wave reflections 370 may be received by a plurality of seismic receivers 372. Seismic receivers 372 may be disposed on a plurality of streamers (i.e., streamer array 374). The seismic receivers 372 may generate electrical signals representative of the received seismic wave reflections 370. The electrical signals may be embedded with information regarding the subsurface 362 and captured as a record of seismic data.

[0056] In one implementation, each streamer may include streamer steering devices such as a bird, a deflector, a tail buoy and the like, which are not illustrated in this application. The streamer steering devices may be used to control the position of the streamers in accordance with the techniques described herein.

[0057] In one implementation, seismic wave reflections 370 may travel upward and reach the water/air interface at the water surface 376, a portion of reflections 370 may then reflect downward again (i.e., sea-surface ghost waves 378) and be received by the plurality of seismic receivers 372. The sea-surface ghost waves 378 may be referred to as surface multiples. The point on the water surface 376 at which the wave may be reflected downward is generally referred to as the downward reflection point.

[0058] The electrical signals may be transmitted to a vessel 380 via transmission cables, wireless communication or the like. The vessel 380 may then transmit the electrical signals to a data processing center. In other embodiments, the vessel 380 may include an onboard computer capable of processing the electrical signals (i.e., seismic data). Those skilled in the art having the benefit of this disclosure will appreciate that this illustration is highly idealized. For instance, surveys may be of formations deep beneath the surface. The formations may typically include multiple reflectors, some of which may include dipping events, and may generate multiple reflections (including wave conversion) for receipt by the seismic receivers 372. In one implementation, the seismic data may be processed to generate a seismic image of the subsurface 362.

[0059] Marine seismic acquisition systems tow each streamer in streamer array 374 at the same depth (e.g., 5-10m). However, marine based survey 360 may tow the streamers in streamer array 374 at different depths such that seismic data may be acquired and processed in a manner that avoids the effects of destructive interference due to sea-surface ghost waves. For instance, marine- based survey 360 of Figure 3 illustrates eight streamers towed by vessel 380 at eight different depths. The depth of each streamer may be controlled and maintained using the birds disposed on each streamer.

[0060] Variable-depth single-streamer marine streamer deghosting decomposes the upgoing wavefield in terms of its wavenumber along a single horizontal coordinate. This may be done on a frequency-by-frequency basis. A linear system may then be built that models the ghost operator, assuming that there is no propagation orthogonal to this coordinate axis. The upgoing wavefield may then be estimated by inverting this linear system. If the out-of-plane propagation is large, the inverse of the linear system may become unstable, and damping may be applied.

[0061] According to an embodiment of the present disclosure, seismic data including seismic measurements of at least one subsurface volume may be processed to remove or reduce the noise contained in the seismic data. In some embodiments, seismic data including seismic measurements of the at least one subsurface volume may be analyzed using a multi -component interpolation technology, or multi-component spectral analysis, to create an accurate model of the noise present on seismic measurements. The estimated model of noise may be accurate enough to allow its direct subtraction from the seismic measurement without an adaptive filter, although such an adaptive filter may be used. In some embodiments, the multi-component interpolation technology, or multi-component spectral analysis, may be used for attenuation of noise that has a slower propagation velocity than the signal, in the case it is aliased during the sampling process, which may make it difficult to attenuate from the measured data. Noise such as "ground roll" in land acquisition or "vibration noise" in multi-sensor marine measurements may be targets of the present methods. The methods include data sampled by receivers that are able to measure either a signal and its directional gradient along the direction of propagation of the noise, or groups of at least two receivers deployed at close distance, to allow a usable estimate of the gradient with finite different methods (or others).

[0062] In some embodiments, the process of analyzing the seismic data may utilize dynamic range effects, when the noise is much stronger than the signal of interest. In some embodiments, this may enable an effective and signal safe attenuation of the noise that is outside of the theoretical bandwidth of signal. The noise targeted by the analysis can be either coherent or incoherent without particular distinction. The analysis may allow separating the near surface noise from the deeper seismic reflections. Incoherent ambient noise may also be reduced when using the analysis process.

[0063] In some embodiments, the process of analyzing the seismic data may be applied to seismic data sampled by receivers able to measure either, a signal and its directional gradient along the direction of propagation of the noise, or groups of at least two receivers deployed at close distance, to allow a usable estimate of the gradient with finite difference methods.

[0064] Figure 4 illustrates an example of a method 400 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 400 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 400 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A-ID, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B.

[0065] After the method 400 begins, in 402, seismic data including measurements of at least one subsurface volume may be received. The seismic data may be received by one or more computer systems, for examples, any of the computer systems described herein.

[0066] In some embodiments, the seismic data may include measurements measured directly by seismic survey tools. For example, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, direct particle motion measurements, direct measurement of sensor locations, and the like. In some embodiments, the seismic data may include measurements generated by processing the measurements measured directly by seismic survey tools. For example, the direct sensor measurements may be processed to generate an estimated measurement for a group of two or more sensors. Likewise, for example, the direct particle motion measurements may be processed to covert the measurements to a spatial gradient. For example, measurement of a group of two or more sensors may be processed to estimate the spatial gradient of the particular motion measurement, e.g., a finite difference operator or other difference operators may be used to estimate the gradients.

[0067] For example, Figure 5 A illustrates a plot showing seismic data, i.e., input traces sampled at 50m spacing, and Figure 5B illustrates the representation in the frequency- wavenumber (FK) domain of a portion of these data. In Figure 5A, the vertical axis is time, measured in seconds, and the horizontal is space, in meters. In Figure 5B, the vertical axis represents frequency, in Hz, and the horizontal the wavenumber, in 1/m units. In this case, the seismic data was obtained by averaging measurements of couples of receivers at short distance. In some embodiments, these may be direct measurements of single sensors, eventually processed. The severe alias of the near surface noise is recognizable, especially in the FK plot at low frequencies.

[0068] In some embodiments, the seismic data may include data that was collected using any type and/or configuration of seismic acquisition system, for example, survey tools as described above. In some embodiments, the seismic data may be collected by any kind of seismic acquisition system that allows one to measure or to estimate a spatial gradient of a measured wavefield, either at the source or receiver side, or combination of both.

[0069] For example, the seismic survey tool may include single or multi-sensor marine acquisition systems that include receivers spaced along the cables. The marine acquisition systems may also include a coarse set of accelerometers along the cable with a layout, for example, as a sparse series of couples. In marine acquisition systems, nodes may contain a number of few seismic receivers in a small space, allowing the estimate of the gradient of the wavefield of interest. In marine acquisition systems, the noise to be separated from the reflection signal may include near surface events, as well as incoherent ambient noise. In one example, for marine acquisition systems, spatial gradient may be estimated along the cable direction, by combining couples or groups of consecutive sensors. This may allow the attenuation of noise propagating along the inline direction, such as near surface noise. This may also be applied to multi-measurement streamers to estimate the inline gradient of the acceleration measurements, hence allowing attenuation of the slow and strong vibration and torsional noise from the acceleration measurements. In other examples, the marine acquisition systems may include a design for seismic streamers, containing a smaller number of receivers that offer another noise attenuation strategy, not requiring dense sampling along the cable. In another example, for marine acquisition systems, the spatial gradient may be computed across cables, at low frequencies where the wavefield would not be aliased.

[0070] Likewise, for example, the seismic survey tool may include a land acquisition system that includes a single or a group of two or more receivers deployed at sampling positions. In land acquisition system, for example, the seismic data may include measurements from traditional sensors that positioned in a way that facilitates groups of seismic traces to be processed so that an estimate of the gradient can be computed by applying finite difference operators. In one example, the positioning may include couples of receivers at short distance, each couple being at wide distance from the next couple of receivers. Additionally, for example, the land acquisition systems may include sticks or sensor technologies that measure directly a spatial gradient of the wavefield.

[0071] Further, the seismic survey tool may include ocean bottom nodes (OBN) acquisition systems. In OBN acquisition systems, nodes may contain one or more seismic receivers in a small space, allowing the estimate of the gradient of the wavefield of interest. In OBN acquisition systems, the noise to be separated from the reflection signal may include near surface events, as well as incoherent ambient noise. In one example, for OBN acquisition systems, spatial gradient may be estimated along the cable direction, by combining couples or groups of consecutive sensors. This would allow the attenuation of noise propagating along the inline direction, such as near surface noise. This could also be applied to multi-measurements streamer to estimate the inline gradient of the acceleration measurements, hence allowing attenuation of the slow and strong vibration and torsional noise from the acceleration measurements. In another example, the OBN acquisition systems may include a design for seismic streamers, containing a smaller number of receivers that offer a noise attenuation strategy, not requiring dense sampling along the cable. In another example, for OBN acquisition systems, spatial gradient may be computed across cables, at low frequencies where the wavefield would not be aliased.

[0072] In some embodiments, any of the seismic acquisition systems may include seismic source devices that allow spatial gradients to be measured or estimated on the source side. For example, marine acquisition systems or OBN acquisition systems may include marine vibrators that would enable the generation of a source gradient wavefield. In any seismic acquisition systems, the source device may allow the estimate the source gradient. Once the source gradient is available, the seismic data can be used to further attenuate noise outside of the theoretical bandwidth of the signal. In addition, the combination of source and receiver gradients, either measured or estimated, may allow the use of the seismic data in a variety of domains, such as, the offset-azimuth-midpoint.

[0073] Returning to Figure 4, in 404, a reconstructed wavefield may be determined for the seismic data based at least partially on the measurements and spatial gradient data associated with the seismic data. In some embodiments, the seismic data may be analyzed using multi-channel interpolation and/or spatial analysis techniques. The analysis may include using the measured wavefield, an estimate of the measured wavefield, and the spatial gradient (estimated or measured), or combination thereof to determine the wavefield components, e.g., a signal of interest and noise signal, of the seismic data.

[0074] When seismic data including a spatial gradient along a particular direction is collected, multi-channel interpolation may allow the reconstruction of the measured signal on a fine grid of receivers even when its original spatial sampling may be too coarse to allow such reconstruction on the fine grid in theory. The multi-channel interpolation techniques may process the gradient measurements, which provide additional information.

[0075] In some embodiments, Multichannel Interpolation by Matching Pursuit (MIMAP) may be used to analyze the seismic data and determine the components of the wavefield. MIMAP is an analysis technique based at least partially on spectral estimation of the seismic data. In MIMAP, the spectral estimate may enable the computation of the interpolated wavefield. MIMAP can include an analysis technique that uses pressure and gradients to interpolate the pressure wavefield. MIMAP may allow reconstruction of wavefield affected by severe spatial aliasing. MIMAP may estimate a reconstructed wavefield by iteratively matching the input measurements until these are fully explained by a set of basis functions. For example, MFMAP may match iteratively the input measurements by trying to estimate their spatial spectrum and determine iteratively which basis functions are likely components of the wavefield. In practice, MFMAP may achieve reconstruction by estimating the spectrum of the data iteratively until a stop condition, such as the norm of the error being below a predetermined value, is reached. MFMAP may also be utilized to determine the components of the wavefield where spatial gradient is not directly measured, but an estimated spatial gradient is available or determined. For example, an estimated spatial gradient may be generated by a finite difference operator on the measurements of a group of receivers. MFMAP may treat the estimated spatial gradient as if it was an actual spatial gradient for the analysis.

[0076] In some embodiments, Generalized Matching Pursuit (GMP) may be used to analyze the seismic data and determine the components of the wavefield. GMP is a generalization of MFMAP. GMP may process the pressure wavefield as well as horizontal and/or vertical components of the gradient of the pressure measured by multi-sensor seismic acquisition system. GMP may achieve joint interpolation and deghosting of the pressure wavefield. GMP may estimate a reconstructed wavefield by matching iteratively the input measurements until these are fully explained by a set of basis functions. For example, the GMP may match iteratively the input measurements by trying to estimate their spatial spectrum and determine iteratively which basis functions are likely components of the wavefield. In practice, GMP may achieve reconstruction by estimating the spectrum of the data iteratively until a stop condition, such as the norm of the error being below a predetermined value. GMP may also be utilized to determine the components of the wavefield where spatial gradient is not directly measured, but an estimated spatial gradient is available or determined. For example, an estimated spatial gradient may be generated by a finite difference operator on the measurements of a group of receivers. GMP may treat the estimated spatial gradient as if it was an actual spatial gradient for the analysis.

[0077] In some embodiments, Extended Generalized Matching Pursuit (E-GMP) may be used to analyze the seismic data and determine the components of the wavefield. E-GMP may estimate a reconstructed wavefield by matching iteratively the input measurements until these are fully explained by a set of basis functions. For example, the E-GMP may match iteratively the input measurements by trying to estimate their spatial spectrum and determine iteratively which basis functions are likely components of the wavefield. In practice, E-GMP may achieve reconstruction by estimating the spectrum of the data iteratively until a stop condition is reached. E-GMP may process a more generic set of data, provided that the relation between the input measurements and the desired output is known. For instance, E-GMP may determine the components of the wavefield where spatial gradient is not directly measured, but an estimated spatial gradient is available or determined. For example, an estimated spatial gradient may be generated by a finite difference operator on the measurements of a group of receivers. E-GMP may consider the actual model used to generate the estimated gradient, and may matches the data respecting such model. E-GMP may use this estimated gradient for interpolation purposes without suffering of the approximation error in estimating the gradient. E-GMP may use the finite different operator to model the relation between a signal of interest and its estimated spatial gradient. In E-GMP, the use of an actual operator used to estimate the spatial gradient may provide an improved match than the use of the ideal gradient operator that would be used within GMP.

[0078] In some embodiments, finite difference MFMAP (FD-MFMAP) may be used to analyze the seismic data and determine the components of the wavefield. FD-MFMAP is a particular realization of E-GMP that generalizes MFMAP, i.e., extends MFMAP to the finite difference gradient. For example, an estimated spatial gradient may be generated by a finite difference operator on the measurements of a group of receivers. FD-MFMAP may treat the estimated spatial gradient as if it were an actual spatial gradient for the analysis. [0079] MFMAP, GMP, E-GMP, and FD-MEVIAP are techniques based on spectral estimation of the input data: in these cases, the spectral estimate supports the computation of the interpolated wavefield. In these examples, the spectral estimation performed by these (and other) techniques may produce a signal of interest, without any interpolated data being generated.

[0080] In some embodiments, other types of non-matching point algorithms may be utilized to determine wavefield components. For example, greedy algorithms may be utilized to determine the components of the wavefield. A greedy algorithm may be an algorithm that follows the problem solving heuristic of making the locally optimal choice at each process with the hope of finding a global optimum. A greedy heuristic may yield locally optimal solutions that approximate a global optimal solution in a reasonable time. For example, a greedy strategy for the traveling salesman problem (which is of a high computational complexity) may be the following heuristic: "At each process visit an unvisited city nearest to the current city." This heuristic may not find an exhaustive solution, but terminate in a reasonable number of iterations; finding a globally optimal solution typically may include a large number of iterations, and may thus be impractical. In mathematical optimization, greedy algorithms solve combinatorial problems having the properties of matroids. Greedy algorithms may have five components: a candidate set, from which a solution is created; a selection function, which chooses the candidate to be added to the solution; a feasibility function, that is used to determine if a candidate can be used to contribute to a solution; an objective function, which assigns a value to a solution, or a partial solution, and a solution function, which will indicate when a complete solution is discovered.

[0081] The use of MTMAP, GMP, E-GMP, and FD-MFMAP as reconstruction techniques or as spectral estimate techniques may utilize the measurements or estimates of a measured seismic signal and its spatial gradient. In some embodiments, any combination of multichannel data that can support an effective spectral estimate from aliased input, and that may return in output even a processed version of the input. For example, by applying GMP using measured Y and Z gradients in addition to the pressure as the input, a deghosted version of the input pressure maybe returned in output, resulting in the noise attenuation effect described above.

[0082] In some embodiments, the spectral estimate and/or reconstruction of seismic wavefield are possible also if gradient measurements are not available. In the embodiments and examples described above, the noise attenuation may be achieved by the separation of noisy components from signal components in the estimation, e.g., rather by the technique of estimating the spectrum. In some embodiments, spectral estimate and/or reconstruction may be achieved without processing gradient measurements.

[0083] Returning to Figure 4, in 406, a signal of interest and a noise signal may be identified in the reconstructed wavefield, based at least partially on different spectral characteristics of the signal of interest and the noise signal. In 408, the signal of interest may be removed from the reconstructed wavefield. In some embodiments, the multi-channel interpolation and/or spatial analysis techniques can provide an identification of the one or more of the wavefield components associated with a signal of interest in the seismic data, which can be used to identify and remove the signal of interest. Once the signal of interest is identified and removed, at the measurement positions, what remains is a representation of the measured near surface noise which forms the noise model.

[0084] In some embodiments, if the gradient measurements are used directly as a noise model, adaptive filters may be utilized to subtract the noise model from the seismic data. In this example, the spatial gradient may be used to allow multi-channel interpolation and/or spatial analysis techniques to distinguish between what is signal and what is noise on the input measurements. A noise model may be generated from the energy that has been classified as noise in this process. This may not call for an adaptive filter to be used to match the noise model to the noise, and subtract it, as the noise model is already an accurate estimate of the noise.

[0085] In some embodiments, once identified, one or more filters, e.g. directional filters, may be applied during the multi-channel interpolation and/or spatial analysis techniques to identify and remove the signal of interest from the seismic data. For example, near surface noise may be more challenging to interpolate: its reconstruction in between input position may still be subject to residual aliasing. In this example, it may easier to isolate the signal of interest than the near surface noise when filtering the output.

[0086] In some embodiments, the multi-channel interpolation and/or spatial analysis techniques may be based on filtering the reflected signal out of the reconstructed wavefield. In some embodiments, a reconstruction technique to interpolate the data may be performed from a coarse grid to a fine grid.

[0087] In some embodiments, a reconstruction technique to interpolate the data may be performed from a coarse grid to a course grid. For example, the multi-channel interpolation and/or spatial analysis techniques may selecting as output the basis functions that are associated to the noise model to be matched, ignoring the components that are likely describing the signals of interest. This example may produce an output of the model of noise, which can be returned at the input positions, and not call for a fine grid of interpolated traces and a directional filter post- reconstruction.

[0088] In 410, a noise attenuated signal for the seismic data may be determined based at least partially on the signal of interest from the reconstructed wavefield. In some embodiments, the noise model may be directly subtracted from the collected seismic data, at each measurement position, thereby removing the noise and leaving the noise attenuated signal representing the subsurface volume.

[0089] In some embodiments, the subtraction may be optional, for example, the signal of interest in the reconstructed wavefield may be accurately determined by the multi-channel interpolation and/or spatial analysis techniques and used as the output. In this example, the signal of interest from the reconstructed wavefield may be selected as the noise attenuated signal representing the subsurface volume.

[0090] Figures 5C and 5D illustrates a plot showing the seismic data shown in Figures 5A and 5B, after the noise model was subtracted from the measurement. In Figures 5C, the vertical axis is time, measured in seconds, and the horizontal is space, in meters. In Figure 5D, the vertical axis represents frequency, in Hz, and the horizontal represents the wavenumber, in 1/m units.

[0091] After 410, the method 400 can end, repeat, or return to any process.

[0092] Figure 6 illustrates another example of a method 600 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 600 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 600 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A-1D, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B.

[0093] After the method 600 begins, in 602, seismic data including measurements of a wavefield sampled on a course grid and an estimate of a spatial gradient of the wavefield by combining a group of measurements may be received. The seismic data may be received by one or more computer systems, for examples, any of the computer systems described herein. [0094] In this example, the seismic data may include measurements measured directly by seismic survey tools and measurements estimated. For instance, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, and direct measurement of sensor locations. Additionally, for instance, measurements that are estimated may include: input wavefield estimated as the average of two measurements form a couple of two receivers (i.e. pair of receiver); and input gradient estimated by finite difference operator applied to measurements of a couple of two receivers. Figures 5 A and 5B illustrated an example of the seismic data.

[0095] In this example, the seismic data may be generated and collected by using the measurements of couples of receivers in a land seismic acquisition. The couples of receivers may be positioned in a layout of a two-dimensional (2D) line. The couples of receivers may be positioned at a short distance from each other, e.g., approximately 5m or less. Each couple of receivers may be positioned at large distance from the closest ones, e.g., approximately 50m. The average of each couple of traces collected may associated to the mid-position between the couples of receivers, and considered as an estimate of the wavefield there. The normalized difference of each couple of traces was used as an estimate of the gradient of the wavefield at the midpoint between the couples of two receivers.

[0096] In 604, MFMAP/GMP/ FD-MTMAP may be performed to interpolate the seismic data. In some embodiments, MTMAP may be used to interpolate the seismic data. In some embodiments, GMP may be utilized to interpolate the data. In some embodiments, FD-MTMAP may be utilized to interpolate the data.

[0097] For example, both estimated wavefield and gradients may be input to MFMAP to reconstruct the wavefield on a densely spaced grid of virtual receivers. The nominal position of the input traces may be part of the output grid. The nominal position of the input traces may not be used, as long as the information related to these positions is recoverable by processing the data. The seismic wavefield of interest is characterized by seismic reflections perceived with a relatively broad temporal bandwidth and a relatively fast apparent velocity. However, similarly to land seismic acquisition, the available measurements are affected by strong near surface effects, particularly energetic at low frequency, with a slow apparent velocity, hence resulting severely aliased when measured at 50m interval. In this case, MFMAP may reconstruct the aliased near- surface energy. On the output grid, both, seismic signal of interest and near surface noise are finely sampled and can be processed with linear digital filters operating in time and space. Hence, considering the different spectral characteristic of reflected seismic and near surface noise, it is possible to separate the noise from the events reflected in depth by applying a directional filter.

[0098] The property of MTMAP may estimate the reconstructed wavefield by matching iteratively the input measurements until these are fully explained by a set of basis functions. These basis functions are used to reconstruct the wavefield in between the input positions. The match with the measured traces at input positions may provide an accurate reconstruction.

[0099] In this example, the gradient may be used to allow MTMAP to distinguish between what is signal and what is noise on the input measurements, and to generate a noise model from the energy that has been classified as noise in this process. This may not call for an adaptive filter to be used to match the noise model to the noise, and subtract it, as the noise model is already an accurate estimate of the noise.

[0100] In some embodiments, GMP or FD-MFMAP may be utilized. In this example, the relation between the data may be taken into account and finite difference approximations of the signal and gradients may be obtained by processing the measurements.

[0101] In 606, the interpolated data may be filtered to separate signal of interest and noise with different spectral characteristics.

[0102] In this example, once the reflected signal is isolated and removed from the reconstructed traces, what remains is an interpolated version of the near surface noise, possibly still affected by spatial aliasing at the reconstructed positions. However, the match of MEVIAP at the input positions may be accurate: at these positions, once the reflected signal is removed, what remains is an accurate representation of the measured near surface noise.

[0103] On the output grid, both, seismic signal of interest and near surface noise are finely sampled and can hence be processed with linear digital filters operating in time and space. Hence, considering the different spectral characteristic of reflected seismic and near surface noise, it is possible to separate the noise from the events reflected in depth by applying a directional filter or equivalent.

[0104] In 608, a noise model may be formed based on the filtered noise data. For example, the filtered noise data may be decimated at the input locations. In some embodiments, the noise model may be formed by removing the filtered noise at any positions except the input sample positions, e.g., location of the seismic sensors that collected the seismic data. [0105] In 610, the noise model may be subtracted from the measurements. In some embodiments, the noise model may be directly subtracted from the collected seismic data, at each measurement position, thereby removing the noise and leaving the signal of interest representing the subsurface volume. After 610, the method 600 can end, repeat, or return to any process.

[0106] Figures 5C and 5D illustrates a plot showing the seismic data shown in Figures 5A and 5B, after the noise model was subtracted from the measurement. In Figures 5C, the vertical axis is time, measured in seconds, and the horizontal is space, in meters. In Figure 5D, the vertical axis represents frequency, in Hz, and the horizontal represents the wavenumber, in 1/m units.

[0107] Figure 7 illustrates another example of a method 700 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 700 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 700 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A-1D, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B.

[0108] After the method 700 begins, in 702, seismic data including measurements of a wavefield and a spatial gradient of the wavefield sampled on a course grid may be received. The seismic data may be received by one or more computer systems, for example, any of the computer systems described herein.

[0109] In this example, the seismic data may include measurements measured directly by seismic survey tools and measurements estimated. For instance, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, the direct sensor measurements of the spatial gradient, and direct measurement of sensor locations. Additionally, for instance, measurements that are estimated may include: input wavefield estimated as the average of two measurements form a couple of two receivers (i.e. pair of receivers); and input gradient estimated by finite difference operator applied to measurements of a couple of two receivers.

[0110] In 704, the seismic data may be interpolated by processing wavefield and spatial gradient. In some embodiments, MTMAP may be used to interpolate the seismic data. In some embodiments, GMP may be utilized to interpolate the data. In some embodiments, FD-MTMAP may be utilized to interpolate the data. [0111] In this example, MEVIAP, GMP, and FD-MEVIAP may utilize both the directly measured seismic signal and gradient, and the estimated gradient. The property of MEVIAP may estimate the reconstructed wavefield by matching iteratively the input measurements until these are fully explained by a set of basis functions. These basis functions are used to reconstruct the wavefield in between the input positions. The match with the measured traces at input positions may provide an accurate reconstruction.

[0112] In this example, the gradient may be used to allow MEVIAP to distinguish between what is signal and what is noise on the input measurements, and to generate a noise model from the energy that has been classified as noise in this process. This may not call for an adaptive filter to be used to match the noise model to the noise, and subtract it, as the noise model is already an accurate estimate of the noise.

[0113] In some embodiments, GMP or FD-MEVIAP may be utilized. In this example, the relation between the data may be taken into account and finite difference approximations of the signal and gradients may be obtained by processing the measurements.

[0114] In 706, the interpolated data may be filtered to separate signal of interest and noise with different spectral characteristics.

[0115] In this example, once the reflected signal is isolated and removed from the reconstructed traces, what remains is an interpolated version of the near surface noise, possibly still affected by spatial aliasing at the reconstructed positions. However, the match of MEVIAP at the input positions may be accurate: at these positions, once the reflected signal is removed, what remains is an accurate representation of the measured near surface noise.

[0116] On the output grid, both, seismic signal of interest and near surface noise are finely sampled and can hence be processed with linear digital filters operating in time and space. Hence, considering the different spectral characteristic of reflected seismic and near surface noise, it is possible to separate the noise from the events reflected in depth by applying a directional filter or equivalent.

[0117] In 708, a noise model may be formed based on the filtered noise. For example, the filtered noise may be decimated, at the input sample positions, to form the filtered noise. In some embodiments, the noise model may be formed by removing the filtered noise at any positions expect the input sample positions, e.g., location of the seismic sensors that collected the seismic data. [0118] In 710, the noise model may be subtracted from the measurements. In some embodiments, the noise model may be directly subtracted from the collected seismic data, at each measurement position, thereby removing the noise and leaving the signal of interest representing the subsurface volume. After 710, the method 700 can end, repeat, or return to any process.

[0119] Figure 8 illustrates another example of a method 800 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 800 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 800 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A-1D, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B.

[0120] After the method 800 begins, in 802, seismic data including measurements of a wavefield and a spatial gradient of the wavefield sampled on a course grid may be received. The seismic data may be received by one or more computer systems, for examples, any of the computer systems described herein.

[0121] In this example, the seismic data may include measurements measured directly by seismic survey tools and measurements estimated. For instance, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, the direct sensor measurements of the spatial gradient, and direct measurement of sensor locations.

[0122] In 804, MEVIAP/ GMP/FD-MFM AP may be performed to interpolate the seismic data. In some embodiments, MTMAP may be used to interpolate the seismic data. In some embodiments, GMP may be utilized to interpolate the data. In some embodiments, FD-MTMAP may be utilized to interpolate the data.

[0123] In this example, MTMAP, GMP, and FD-MFMAP may utilize both the directly measured seismic signal and gradient. The property of MIMAP may estimate the reconstructed wavefield by matching iteratively the input measurements until these are fully explained by a set of basis functions. These basis functions are used to reconstruct the wavefield in between the input positions. The match with the measured traces at input positions may provide an accurate reconstruction.

[0124] In this example, the gradient may be used to allow MFMAP to distinguish between what is signal and what is noise on the input measurements, and to generate a noise model from the energy that has been classified as noise in this process. This may not call for an adaptive filter to be used to match the noise model to the noise, and subtract it, as the noise model is already an accurate estimate of the noise.

[0125] In 806, the interpolated data may be filtered to separate signal of interest and noise with different spectral characteristics.

[0126] In this example, once the reflected signal is isolated and removed from the reconstructed traces, what remains is an interpolated version of the near surface noise, possibly still affected by spatial aliasing at the reconstructed positions. However, the match of MEVIAP at the input positions may be accurate: at these positions, once the reflected signal is removed, what remains is an accurate representation of the measured near surface noise.

[0127] On the output grid, both, seismic signal of interest and near surface noise are finely sampled and can hence be processed with linear digital filters operating in time and space. Hence, considering the different spectral characteristic of reflected seismic and near surface noise, it is possible to separate the noise from the events reflected in depth by applying a directional filter or equivalent.

[0128] In 808, the filtered noise may be decimated, at the input sample positions, to form a noise model. In some embodiments, the noise model may be formed by removing the filtered noise at any positions expect the input sample positions, e.g., location of the seismic sensors that collected the seismic data.

[0129] In 810, the noise model may be subtracted from the measurements. In some embodiments, the noise model may be directly subtracted from the collected seismic data, at each measurement position, thereby removing the noise and leaving the signal of interest representing the subsurface volume. After 810, the method 800 can end, repeat, or return to any process.

[0130] Figure 9 illustrates another example of a method 900 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 900 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 900 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A-1D, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B. [0131] After the method 900 begins, in 902, seismic data including measurements of a wavefield sampled on a course grid and an estimate of a spatial gradient of the wavefield obtained by combining a group of measurement may be received. The seismic data may be received by one or more computer systems, for examples, any of the computer systems described herein.

[0132] In this example, the seismic data may include measurements measured directly by seismic survey tools and measurements estimated. For instance, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, and direct measurement of sensor locations. Additionally, for instance, measurements that are estimated may include: input wavefield estimated as the average of two measurements form a couple of two receivers (i.e. pair of receivers); and input gradient estimated by finite difference operator applied to measurements of a couple of two receivers. Figures 5A and 5B illustrated an example of the seismic data.

[0133] In this example, the seismic data may be generated and collected by using the measurements of couples of receivers in a land seismic acquisition. The couples of receivers may be positioned in a layout of a two-dimensional (2D) line. The couples of receivers may be positioned at a short distance from each other, e.g., approximately 5m or less. Each couple of receivers may be positioned at large distance from the closest ones, e.g., approximately 50m. The average of each couple of traces collected may associated to the mid-position between the couples of receivers, and considered as an estimate of the wavefield there. The normalized difference of each couple of traces was used as an estimate of the gradient of the wavefield at the midpoint between the couples of two receivers.

[0134] In 904, E-GMP may be performed to interpolate the seismic data. In some embodiments, E-GMP may estimate a reconstructed wavefield by matching iteratively the input measurements until these are fully explained by a set of basis functions. For example, the E-GMP may match iteratively the input measurements by trying to estimate their spatial spectrum and determine iteratively which basis functions are likely components of the wavefield. In practice, E-GMP may achieve reconstruction by estimating the spectrum of the data iteration after iteration. E-GMP may process a more generic set of data, provided that the relation between the input measurements and the desired output is known. For instance, E-GMP may determine the components of the wavefield where spatial gradient is not directly measured, but an estimated spatial gradient is available or determined. For example, an estimated spatial gradient may be generated by a finite difference operator on the measurements of a group of receivers. E-GMP may consider the actual model used to generate the estimated gradient, and may matches the data respecting such model. E-GMP may use this estimated gradient for interpolation purposes without suffering of the approximation error in estimating the gradient. E-GMP may use the finite different operator to model the relation between a signal of interest and its estimated spatial gradient. In E-GMP, the use of an actual operator used to estimate the spatial gradient may provide an improved match than the use of the ideal gradient operator that would be used within GMP.

[0135] In 906, the interpolated data may be filtered to separate signal of interest and noise with different spectral characteristics.

[0136] In this example, once the reflected signal is isolated and removed from the reconstructed traces, what remains is an interpolated version of the near surface noise, possibly still affected by spatial aliasing at the reconstructed positions. However, the match of E-GMP at the input positions may be accurate: at these positions, once the reflected signal is removed, what remains is an accurate representation of the measured near surface noise.

[0137] On the output grid, both, seismic signal of interest and near surface noise are finely sampled and can hence be processed with linear digital filters operating in time and space. Hence, considering the different spectral characteristic of reflected seismic and near surface noise, it is possible to separate the noise from the events reflected in depth by applying a directional filter or equivalent.

[0138] In 908, a noise model may be formed based on the filtered noise. For example, the filtered noise may be decimated, at the input sample positions, to form the noise model. In some embodiments, the noise model may be formed by removing the filtered noise at any positions expect the input sample positions, e.g., location of the seismic sensors that collected the seismic data.

[0139] In 910, the noise model may be subtracted from the measurements. In some embodiments, the noise model may be directly subtracted from the collected seismic data, at each measurement position, thereby removing the noise and leaving the signal of interest representing the subsurface volume. After 910, the method 900 can end, repeat, or return to any process.

[0140] Figure 10 illustrates another example of a method 1000 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 1000 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 1000 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A- ID, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B.

[0141] After the method 1000 begins, in 1002, seismic data including measurements of a wavefield and a spatial gradient of the wavefield sampled on a course grid may be received. The seismic data may be received by one or more computer systems, for examples, any of the computer systems described herein.

[0142] In this example, the seismic data may include measurements measured directly by seismic survey tools and measurements estimated. For instance, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, the direct sensor measurements of the spatial gradient, and direct measurement of sensor locations. Additionally, for instance, measurements that are estimated may include: input wavefield estimated as the average of two measurements form a couple of two receivers (i.e. pair of receiver); and input gradient estimated by finite difference operator applied to measurements of a couple of two receivers.

[0143] In 1004, a spatial spectrum of the seismic data may be estimated based at least partially on the wavefield and spatial gradient. In 1006, spectral components likely containing signal of interest may be separated from spectral components likely containing noise. In 1008, the spectral components of the noise at measurement positions may be evaluated to form a noise model.

[0144] In some embodiments, MTMAP may be used to interpolate the seismic data. In some embodiments, GMP may be utilized to interpolate the data. In some embodiments, FD-MTMAP may be utilized to interpolate the data. In some embodiments, E-GMP may be utilized to interpolate the data.

[0145] In some embodiments, MEVI AP/ GMP/E-GMP/FD-MEVI AP may be performed by selecting as output the basis functions that are associated to the noise model to be matched, ignoring the components that are likely describing reflected signals. In this example, MEVIAP/ GMP/E-GMP/FD-MEVI AP may produce as output the noise model. This can be returned at the input positions, thus avoiding a fine grid of interpolated traces and a directional filter post- reconstruction. [0146] In 1010, the noise model may be subtracted from the measurements. In some embodiments, the noise model may be directly subtracted from the collected seismic data, at each measurement position, thereby removing the noise and leaving the signal of interest representing the subsurface volume.

[0147] After 1010, the method 1000 can end, repeat, or return to any process.

[0148] Figure 1 1 illustrates another example of a method 1100 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 1 100 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 1 100 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A- ID, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B.

[0149] After the method 1100 begins, in 1102, seismic data including measurements of a wavefield and a spatial gradient of the wavefield sampled on a course grid may be received. The seismic data may be received by one or more computer systems, for examples, any of the computer systems described herein.

[0150] In this example, the seismic data may include measurements measured directly by seismic survey tools and measurements estimated. For instance, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, the direct sensor measurements of the spatial gradient, and direct measurement of sensor locations. Additionally, for instance, measurements that are estimated may include: input wavefield estimated as the average of two measurements form a couple of two receivers (i.e. pair of receiver); and input gradient estimated by finite difference operator applied to measurements of a couple of two receivers.

[0151] In 1 104, a spatial spectrum of the seismic data may be estimated using MFMAP/GMP/FD- MFMAP. In 1 106, spectral components likely containing signal of interest may be separated within MFMAP/GMP/FD- MFMAP from spectral components likely containing noise. In 1 108, a noise model at the measurement position may be created while running MFMAP/ GMP/FD-MFM AP . In some embodiments, MFMAP may be used to interpolate the seismic data. In some embodiments, GMP may be utilized to interpolate the data. In some embodiments, FD-MFMAP may be utilized to interpolate the data. [0152] In some embodiments, MIMAP/GMP/FD-MIMAP may be performed by selecting as output the basis functions that are associated to the noise model to be matched, ignoring the components that are likely describing reflected signals. In this example, MIMAP/GMP/FD- MIMAP may produce as output the noise model: this can be returned at the input positions, hence not requiring a fine grid of interpolated traces and a directional filter post-reconstruction.

[0153] In 1 110, the noise model may be subtracted from the measurements. In some embodiments, the noise model may be directly subtracted from the collected seismic data, at each measurement position, thereby removing the noise and leaving the signal of interest representing the subsurface volume. After 1110, the method 1100 can end, repeat, or return to any process.

[0154] Figure 12 illustrates another example of a method 1200 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 1200 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 1200 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A- ID, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B.

[0155] After the method 1200 begins, in 1202, seismic data including measurements of a wavefield sampled on a course grid and an estimate of a spatial gradient of the wavefield obtained by combining a group of measurements may be received. The seismic data may be received by one or more computer systems, for examples, any of the computer systems described herein.

[0156] In this example, the seismic data may include measurements measured directly by seismic survey tools and measurements estimated. For instance, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, the direct sensor measurements of the spatial gradient, and direct measurement of sensor locations. Additionally, for instance, measurements that are estimated may include: input wavefield estimated as the average of two measurements form a couple of two receivers (i.e. pair of receiver); and input gradient estimated by finite difference operator applied to measurements of a couple of two receivers.

[0157] In 1204, spatial spectrum of the seismic data may be estimated using E-GMP. In 1206, spectral components likely containing signal of interest may be separated within E-GMP from spectral components likely containing noise. In 1208, a noise model at the measurement position may be created while running E-GMP.

[0158] In some embodiments, E-GMP may be performed by selecting as output the basis functions that are associated to the noise model to be matched, ignoring the components that are likely describing reflected signals. In this example, E-GMP may produce as output the noise model: this can be returned at the input positions, hence not requiring a fine grid of interpolated traces and a directional filter post-reconstruction.

[0159] In 1210, the noise model may be subtracted from the measurements. In some embodiments, the noise model may be directly subtracted from the collected seismic data, at each measurement position, thereby removing the noise and leaving the signal of interest representing the subsurface volume. After 1210, the method 1200 can end, repeat, or return to any process.

[0160] Figure 13 illustrates another example of a method 1300 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 1300 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 1300 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A- ID, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B.

[0161] After the method 1300 begins, in 1302, seismic data including measurements of a wavefield and a spatial gradient of the wavefield sampled on a course grid may be received. The seismic data may be received by one or more computer systems, for examples, any of the computer systems described herein.

[0162] In this example, the seismic data may include measurements measured directly by seismic survey tools and measurements estimated. For instance, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, the direct sensor measurements of the spatial gradient, and direct measurement of sensor locations. Additionally, for instance, measurements that are estimated may include: input wavefield estimated as the average of two measurements form a couple of two receivers (i.e. pair of receiver); and input gradient estimated by finite difference operator applied to measurements of a couple of two receivers. [0163] In 1304, the seismic data may be interpolated by processing wavefield and spatial gradient. In 1306, the interpolated data may be filtered to separate signal of interest and noise with different spectral characteristics.

[0164] In some embodiments, the one or more of the wavefield components associated with a signal of interest in the seismic data may be accurately determined by the multi-channel interpolation and/or spatial analysis techniques and used as the output. For example, the multichannel interpolation and/or spatial analysis techniques may reconstruct the wavefield for the signal of interest and the noise with different spectral characteristics. Then, the multi-channel interpolation and/or spatial analysis techniques may filter out the noise with different spectral characteristics.

[0165] In some embodiments, MTMAP may be used to interpolate the seismic data. In some embodiments, GMP may be utilized to interpolate the data. In some embodiments, FD-MTMAP may be utilized to interpolate the data. In some embodiments, E-GMP may be utilized to interpolate the data.

[0166] In 1308, an estimated signal of interest may be decimated at the input sample positions. In some embodiments, the estimated signal of interest may be formed by removing the signals of interest at any positions expect the input sample positions, e.g., location of the seismic sensors that collected the seismic data.

[0167] After 1308, the method 1300 can end, repeat, or return to any process.

[0168] Figure 14 illustrates another example of a method 1400 of removing noise from seismic data, according to various embodiments. The illustrated processes of the method 1400 are examples and that any of the illustrated processes can be removed, additional processes may be added, and the order of the illustrated processes may be changed. In some embodiments, any of the illustrated processes of the method 1400 may be performed by one or more computer systems, for example, the computer systems illustrated in Figures 1 A- ID, Figure 2, and Figure 3, described above, and/or the computer systems described below in Figures 15A and 15B.

[0169] After the method 1400 begins, in 1402, seismic data including measurements of a wavefield and a spatial gradient of the wavefield sampled on a course grid may be received. The seismic data may be received by one or more computer systems, for examples, any of the computer systems described herein. [0170] In this example, the seismic data may include measurements measured directly by seismic survey tools and measurements estimated. For instance, the measurements measured directly by seismic survey tools may include direct sensor measurements of acoustic return signal, the direct sensor measurements of the spatial gradient, and direct measurement of sensor locations. Additionally, for instance, measurements that are estimated may include: input wavefield estimated as the average of two measurements form a couple of two receivers (i.e. pair of receiver); and input gradient estimated by finite difference operator applied to measurements of a couple of two receivers.

[0171] In 1404, a spatial spectrum of the seismic data may be estimated based at least partially on the wavefield and spatial gradient. In 1406, spectral components likely containing signal of interest may be separated from spectral components likely containing noise. In 1408, the spectral components of the signal of interest may be evaluated at measurement positions.

[0172] In some embodiments, the one or more of the wavefield components associated with a signal of interest in the seismic data may be accurately determined by the multi-channel interpolation and/or spatial analysis techniques and used as the output. For example, the multichannel interpolation and/or spatial analysis techniques may reconstruct spectral components likely containing signal of interest may be separated from spectral components likely containing noise. Then, the multi-channel interpolation and/or spatial analysis techniques may remove spectral components likely containing noise.

[0173] In some embodiments, MTMAP may be used to interpolate the seismic data. In some embodiments, GMP may be utilized to interpolate the data. In some embodiments, FD-MTMAP may be utilized to interpolate the data. In some embodiments, E-GMP may be utilized to interpolate the data. After 1408, the method 1400 can end, repeat, or return to any process.

[0174] Figures 15A and 15B illustrate another flowchart of an example of a method 1500 for noise attenuation, according to an embodiment. The method 1500 may include obtaining seismic data including measurements of a seismic wavefield for at least one subsurface volume, as at 1502. In some embodiments, for example, obtaining the seismic data may include rreceiving acoustic signals collected for the at least one subsurface volume, as at 1504.

[0175] The method 1500 may include obtaining at least one component of a spatial gradient of the measurements of the seismic wavefield, as at 1506. In some embodiments, for example, obtaining the at least one component of the spatial gradient may include determining the at least one component of the spatial gradient from the acoustic signals, as at 1508. In some embodiments, for example, obtaining the at least one component of the spatial gradient may include receiving the at least one component of the spatial gradient collected for the at least one subsurface volume, as at 1510.

[0176] The method 1500 may include determining a representation of the seismic data based at partially on the measurements of the seismic wavefield and the at least one component of the spatial gradient, as at 1512. In some embodiments, for example, determining the representation of the seismic data may include processing the measurements and the at least one component of the spatial gradient using an analysis process, as at 1514. In some embodiments, for example, the analysis process may include at least one of multichannel interpolation by matching pursuit, generalized matching pursuit, an extended generalized matching pursuit, a finite difference multichannel interpolation by matching pursuit, or a greedy algorithm, as at 1516.

[0177] The method 1500 may include identifying a signal of interest and noise in the representation of the seismic data based at least partially on different characteristics of the signal of interest and the noise in a domain of the representation, as at 1518.

[0178] The method 1500 may include calculating at least one of a signal model or a noise model from the signal of interest and noise identified in the representation of the seismic data, as at 1520. In some embodiments, for example, calculating at least one of the signal model or the noise model may include removing the signal of interest from the representation of the seismic data to form the noise model, as at 1522.

[0179] The method 1500 may include determining a noise attenuated signal for the seismic data based at least partially on the at least one of the signal model or the noise model, as at 1524. In some embodiments, for example, determining the noise attenuated signal for the seismic data may include subtracting the noise model from the measurements of the seismic wavefield, as at 1526. In some embodiments, for example, determining the noise attenuated signal for the seismic data may include selecting the signal of interest from the representation of the seismic data as the noise attenuated signal, as at 1528.

[0180] In some embodiments, the methods of the present disclosure may be executed by a computing system. Figure 16 illustrates an example of such a computing system 1600, in accordance with some embodiments. The computing system 1600 may include a computer or computer system 1601 A, which may be an individual computer system 1601 A or an arrangement of distributed computer systems. The computer system 1601 A includes one or more analysis modules 1602 that are configured to perform various tasks according to some embodiments, such as one or more methods disclosed herein. To perform these various tasks, the analysis module 1602 executes independently, or in coordination with, one or more processors 1604, which is (or are) connected to one or more storage media 1606. The processor(s) 1604 is (or are) also connected to a network interface 1607 to allow the computer system 1601 A to communicate over a data network 1609 with one or more additional computer systems and/or computing systems, such as 160 IB, 1601C, and/or 160 ID (note that computer systems 160 IB, 1601C and/or 160 ID may or may not share the same architecture as computer system 1601A, and may be located in different physical locations, e.g., computer systems 1601 A and 160 IB may be located in a processing facility, while in communication with one or more computer systems such as 1601C and/or 160 ID that are located in one or more data centers, and/or located in varying countries on different continents).

[0181] A processor can include a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device.

[0182] The storage media 1606 can be implemented as one or more computer-readable or machine-readable storage media. Note that while in some example embodiments of Figure 16 storage media 1606 is depicted as within computer system 1601A, in some embodiments, storage media 1606 may be distributed within and/or across multiple internal and/or external enclosures of computing system 1601A and/or additional computing systems. Storage media 1606 may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories, magnetic disks such as fixed, floppy and removable disks, other magnetic media including tape, optical media such as compact disks (CDs) or digital video disks (DVDs), BLUERAY^® disks, or other types of optical storage, or other types of storage devices. Note that the instructions discussed above can be provided on one computer-readable or machine- readable storage medium, or can be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media is (are) considered to be part of an article (or article of manufacture). An article or article of manufacture can refer to any manufactured single component or multiple components. The storage medium or media can be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions can be downloaded over a network for execution.

[0183] In some embodiments, computing system 1600 contains one or more noise mitigation module(s) 1608. In the example of computing system 1600, computer system 1601 A includes the noise mitigation module 1608. In some embodiments, a single noise mitigation module may be used to perform at least some aspects of one or more embodiments of the methods disclosed herein. In some embodiments, a plurality of noise mitigation modules may be used to perform at least some aspects of methods disclosed herein.

[0184] It should be appreciated that computing system 1600 is but one example of a computing system, and that computing system 1600 may have more or fewer components than shown, may combine additional components not depicted in the example embodiment of Figure 16, and/or computing system 1600 may have a different configuration or arrangement of the components depicted in Figure 16. The various components shown in Figure 16 may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits.

[0185] Further, the steps in the processing methods described herein may be implemented by running one or more functional modules in information processing apparatus such as general purpose processors or application specific chips, such as ASICs, FPGAs, PLDs, or other appropriate devices. These modules, combinations of these modules, and/or their combination with general hardware are included within the scope of protection of the present disclosure.

[0186] Geologic interpretations, models and/or other interpretation aids may be refined in an iterative fashion; this concept is applicable to methods as discussed herein. This can include use of feedback loops executed on an algorithmic basis, such as at a computing device (e.g., computing system 1600, Figure 16), and/or through manual control by a user who may make determinations regarding whether a given step, action, template, model, or set of curves has become sufficiently accurate for the evaluation of the subsurface three-dimensional geologic formation under consideration.

[0187] Although the preceding description has been described herein with reference to particular means, materials, and embodiments, it is not intended to be limited to the particular disclosed herein. By way of further example, embodiments may be utilized in conjunction with a handheld system (i.e., a phone, wrist or forearm mounted computer, tablet, or other handheld device), portable system (i.e., a laptop or portable computing system), a fixed computing system (i.e., a desktop, server, cluster, or high performance computing system), or across a network (i.e., a cloud- based system). As such, embodiments extend to all functionally equivalent structures, methods, uses, program products, and compositions as are within the scope of the appended claims.

[0188] The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or to limit the present disclosure to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. Moreover, the order in which the elements of the methods described herein are illustrate and described may be re-arranged, and/or two or more elements may occur simultaneously. The embodiments were chosen and described in order to explain the principals of the present disclosure and its practical applications, to thereby enable others skilled in the art to utilize the present disclosure and various embodiments with various modifications as are suited to the particular use contemplated. Additional information supporting the disclosure is contained in the appendix attached hereto.

Claims

CLAIMS What is claimed is:

1. A method for noise mitigation, comprising:

obtaining seismic data comprising measurements of a seismic wavefield for at least one subsurface volume;

obtaining at least one component of a spatial gradient of the measurements of the seismic wavefield;

determining a representation of the seismic data based at partially on the measurements of the seismic wavefield and the at least one component of the spatial gradient;

identifying a signal of interest and noise in the representation of the seismic data based at least partially on different characteristics of the signal of interest and the noise in a domain of the representation;

calculating at least one of a signal model or a noise model from the signal of interest and noise identified in the representation of the seismic data; and

determining a noise attenuated signal for the seismic data based at least partially on the at least one of the signal model or the noise model.

2. The method of claim 1, wherein:

obtaining the measurements of the seismic wavefield comprises receiving acoustic signals collected for the at least one subsurface volume;

obtaining the at least one component of the spatial gradient of the measurements comprises determining the at least one component of the spatial gradient from the acoustic signals; and determining the representation of the seismic data comprises processing the measurements and the at least one component of the spatial gradient using an analysis process.

3. The method of claim 2, wherein the analysis process comprises at least one of multichannel interpolation by matching pursuit, generalized matching pursuit, an extended generalized matching pursuit, a finite difference multichannel interpolation by matching pursuit, or a greedy algorithm.

4. The method of claim 2, wherein: calculating the at least one of the signal model or the noise model comprises removing the signal of interest from the representation of the seismic data to form the noise model; and

determining the noise attenuated signal for the seismic data comprises subtracting the noise model from the measurements of the seismic wavefield.

5. The method of claim 2, wherein determining the noise attenuated signal for the seismic data comprises selecting the signal of interest from the representation of the seismic data as the noise attenuated signal.

6. The method of claim 1, wherein:

obtaining the at least one component of the spatial gradient of the measurements comprises receiving the at least one component of the spatial gradient collected for the at least one subsurface volume; and

determining the representation for the seismic data comprises processing the measurements and the at least one component of the spatial gradient using an analysis process.

7. The method of claim 6, wherein the analysis process comprises at least one of multichannel interpolation by matching pursuit, generalized matching pursuit, an extended generalized matching pursuit, a finite difference multichannel interpolation by matching pursuit, or a greedy algorithm.

8. The method of claim 6, wherein:

calculating the at least one of the signal model or the noise model comprises removing the signal of interest from the representation of the seismic data to form the noise model; and

9. The method of claim 6, wherein determining the noise attenuated signal for the seismic data comprises selecting the signal of interest from the representation of the seismic data as the noise attenuated signal.

10. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors of a computing system, cause the computing system to perform a method, the method comprising:

11. The non-transitory computer-readable medium of claim 10, wherein

12. The non-transitory computer-readable medium of claim 11, wherein:

13. The non-transitory computer-readable medium of claim 11, wherein determining the noise attenuated signal for the seismic data comprises selecting the signal of interest from the representation of the seismic data as the noise attenuated signal.

14. The non-transitory computer-readable medium of claim 10, wherein:

15. The non-transitory computer-readable medium of claim 14, wherein:

16. The non-transitory computer-readable medium of claim 14, wherein determining the noise attenuated signal for the seismic data comprises selecting the signal of interest from the representation of the seismic data as the noise attenuated signal.

17. A computing system, comprising:

one or more processors; and

a memory system comprising one or more non -transitory computer-readable media storing instructions that, when executed by at least one of the one or more processors, cause the computing system to perform a method, the method comprising:

obtaining seismic data comprising measurements of a seismic wavefield for a at least one subsurface volume; obtaining at least one component of a spatial gradient of the measurements of the seismic wavefield;

18. The computing system of claim 17, wherein:

19. The computing system of claim 18, wherein:

20. The computing system of claim 18, wherein determining the noise attenuated signal for the seismic data comprises selecting the signal of interest from the representation of the seismic data as the noise attenuated signal.