CN113281808B - Anti-dispersion seismic wave forward modeling method, system, device and medium - Google Patents
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- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
- G01V1/30—Analysis
- G01V1/307—Analysis for determining seismic attributes, e.g. amplitude, instantaneous phase or frequency, reflection strength or polarity
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Abstract
The application provides a forward modeling method, a forward modeling system, a forward modeling device and a forward modeling medium for anti-dispersion seismic waves, wherein the forward modeling method comprises the following steps of: acquiring an underground medium velocity field and a forward wavelet dominant frequency, and setting a first projection relation according to the underground medium velocity field and the forward wavelet dominant frequency; resampling in the depth direction according to the first projection relation to generate a second velocity field; according to the second velocity field, forward modeling of the seismic wave field is performed through a wave field propagation equation; the method realizes longitudinal dispersion suppression, can balance efficiency and data quality to perform seismic wave forward modeling, realizes the balance of calculation cost, geologic structure characteristics and better data quality, and can be widely applied to the technical field of seismic exploration.
Description
Technical Field
The application relates to the technical field of seismic exploration, in particular to a forward modeling method, a forward modeling system, a forward modeling device and a storage medium for anti-dispersion seismic waves.
Background
Seismic wave forward modeling is the most basic application tool in the field of seismic exploration, and is an essential basic tool in the analysis of an observation system, the development of a seismic imaging algorithm, the inversion of a seismic waveform and the like. The most mainstream seismic wave forward method at present is a high-order finite difference method, and the method utilizes the high-order finite difference to solve a wave equation so as to obtain a seismic wave field propagated in an underground medium. Solving wave equations by the higher order finite difference method requires balancing the following problems: numerical dispersion problems and calculation amount problems. If the mesh of the subsurface medium is large, strong numerical dispersion exists, and the quality of forward data of the seismic waves is affected. The numerical value dispersion can be reduced by reducing the mesh spacing, and the problem is that the calculated amount is increased rapidly, and particularly when the underground medium speed is low, a small mesh is needed to obtain the seismic data with weak dispersion.
Disclosure of Invention
In view of the above, an objective of the embodiments of the present application is to provide an efficient, accurate and practical forward modeling method of anti-dispersion seismic waves, and a system, a device and a computer-readable storage medium for implementing the method.
In a first aspect, the present application provides a forward modeling method of anti-dispersion seismic waves, which includes the steps of:
acquiring an underground medium velocity field and a forward wavelet dominant frequency, and setting a first projection relation according to the underground medium velocity field and the forward wavelet dominant frequency;
resampling in the depth direction according to the first projection relation to generate a second velocity field;
and according to the second velocity field, performing seismic wave field forward modeling through a wave field propagation equation.
In a possible embodiment of the present application, the step of obtaining the subsurface medium velocity field and the forward wavelet dominant frequency and setting the first projection relation according to the subsurface medium velocity field and the forward wavelet dominant frequency includes:
calculating to obtain the wave length of the seismic waves according to the forward wavelet dominant frequency and the medium speed in the underground medium speed field;
and correlating the seismic wave wavelength with the longitudinal space grid, and determining a first projection relation according to the correlation relation.
In a possible embodiment of the present application, the step of resampling in the depth direction according to the first projection relation and generating a second velocity field includes:
and sampling the seismic wave wavelength according to the first projection relation, and performing variable grid subdivision according to a sampling result to obtain a low-speed area grid and a high-speed area grid.
In a possible embodiment of the solution of the present application, the step of performing forward modeling of the seismic wavefield by a wavefield propagation equation according to the second velocity field includes:
determining a first derivative of the first projection relationship and a second derivative of the first projection relationship;
the wave field propagation equation is:
wherein ,for the first projection relation +.>Is the first derivative of the first projection relation, < +.>For the second derivative of the first projection relationship, u' (t, X) represents the wave field in a variable grid coordinate system, X represents the (X, y, z) spatial coordinates, v represents the velocity of the subsurface medium, and t represents the velocity of the subsurface mediumThe propagation time, γ, is the transverse dispersion suppression coefficient.
In a possible embodiment of the solution of the present application, the transverse dispersion pressing coefficient is determined according to a sampling interval in a horizontal direction, and the transverse dispersion pressing coefficient is in a proportional relationship with the sampling interval in the horizontal direction.
In a possible embodiment of the solution of the present application, when the direction of the variegated propagation is along the depth propagation, the wave field propagation equation is:
where u (t, X) is the wavefield propagating to the t and X points.
In one possible embodiment of the solution according to the application, an attenuation equation is introduced in the transverse spatial grid, by means of which the calculation and the numerical dispersion suppression are balanced.
In a second aspect, the present application further provides an anti-dispersion seismic wave forward modeling system, including:
the parameter determining module is used for acquiring an underground medium speed field and a forward wavelet dominant frequency and setting a first projection relation according to the underground medium speed field and the forward wavelet dominant frequency;
the resampling module is used for resampling in the depth direction according to the first projection relation to generate a second speed field;
and the forward modeling module is used for performing seismic wave field forward modeling through a wave field propagation equation according to the second velocity field.
In a third aspect, the present application further provides an anti-dispersion seismic wave forward modeling apparatus, including:
at least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to perform an anti-scatter seismic forward method of the first aspect.
In a fourth aspect, the present application provides a storage medium having stored therein a processor executable program which when executed by a processor is for running the method of the first aspect.
Advantages and benefits of the application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the application:
according to the technical scheme, a first projection relation is set through an underground medium velocity field and the forward wavelet main frequency, depth direction resampling is carried out according to the first projection relation, and then a seismic wave field forward simulation is carried out through a wave field propagation equation; introducing a wave equation of transverse anti-dispersion, and reducing the numerical dispersion of transverse wave field propagation; and then, a variable grid propagation technology related to the speed is introduced in the longitudinal direction, grid change is converted into equation coefficients, a new equation is derived, longitudinal dispersion pressing is realized, a seismic wave forward modeling method with balanced efficiency and data quality is obtained, and the balance of calculation cost, geological structure characteristics and better data quality is realized.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of the steps of a forward modeling method of anti-dispersion seismic waves according to an embodiment of the present application;
FIG. 2 is a two-dimensional three-layer acoustic media wavefield snapshot of an embodiment employing a coarse grid of wavefield propagation equation (2);
FIG. 3 is a two-dimensional three-layer acoustic media wavefield snapshot using a fine grid of wavefield propagation equation (2) in an embodiment;
FIG. 4 is a coarse grid of wave field propagation equation (1) employed in an embodiment andis a two-dimensional three-layer acoustic medium wave field snapshot of;
FIG. 5 is a two-dimensional three-layer acoustic media wavefield snapshot of an embodiment employing a coarse grid of wavefield propagation equation (1) and γ=0;
FIG. 6 is a two-dimensional three-layer acoustic media wavefield snapshot of an embodiment employing a coarse grid of wavefield propagation equation (1) and lateral fringing;
the embodiment of FIG. 7 uses a two-dimensional three-layer acoustic media wavefield snapshot of a coarse grid of wavefield propagation equation (1) with relatively strong transverse damping.
Detailed Description
Embodiments of the present application are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the application. The step numbers in the following embodiments are set for convenience of illustration only, and the order between the steps is not limited in any way, and the execution order of the steps in the embodiments may be adaptively adjusted according to the understanding of those skilled in the art.
In a first aspect, as shown in fig. 1, the technical solution of the present application provides an embodiment of a forward method of anti-dispersive seismic waves, where the method includes steps S100 to S300:
s100, acquiring an underground medium velocity field and a forward wavelet dominant frequency, and setting a first projection relation according to the underground medium velocity field and the forward wavelet dominant frequency;
wherein, the first projection relation refers to the projection relation from the original grid coordinates to the variable grid coordinates in the embodiment; specifically, according to the characteristic that most of underground structures are layered media and the speed is gradually increased, the embodiment combines the variable grid propagation technology and the high-frequency attenuation equation technology to realize efficient wave field propagation to generate seismic data used for the purposes of observation system design, algorithm inspection and the like. The embodiment firstly sets forward parameters, wherein the forward parameters mainly comprise forward wavelet dominant frequenciesThen determining the velocity field of the underground medium, setting the projection relation from the original grid coordinates to the variable grid coordinates, namely a first projection relation according to the read velocity field and the forward wavelet dominant frequencyWhich is typically selected based on the medium velocity and the main frequency of the wave field.
S200, resampling in the depth direction according to the first projection relation to generate a second velocity field;
in particular, the velocity field is dependent onThe form performs depth direction resampling to generate a velocity field under the new grid, i.e., a second velocity field.
S300, performing seismic wave field forward modeling according to a second velocity field through a wave field propagation equation;
specifically, a wave equation of transverse anti-dispersion is introduced, so that the numerical dispersion of the transverse wave field propagation is reduced; then, a variable grid propagation technology related to the speed is introduced in the longitudinal direction, grid change is converted into equation coefficients, a new equation is derived, longitudinal dispersion suppression is realized, and the seismic wave forward modeling method with efficiency and data quality balance is obtained.
In some possible embodiments, the step S100 of acquiring the subsurface medium velocity field and the forward wavelet dominant frequency and setting the first projection relation according to the subsurface medium velocity field and the forward wavelet dominant frequency may be further subdivided into steps S110-S120:
s110, calculating to obtain the wave length of the seismic waves according to the forward wavelet dominant frequency and the medium speed in the underground medium speed field;
and S120, correlating the seismic wave wavelength with the longitudinal space grid, and determining a first projection relation according to the correlation relation.
In particular, embodiments relate seismic wavelength to longitudinal grid subdivision based on the property that the subsurface medium is mostly a laminar medium and the velocity is generally increasing, the seismic wave wavelength λ being related to the frequency f of the seismic wave and the medium velocity v, which is calculatedThe formula isI.e. the greater the speed, the longer the wavelength, the lower the frequency and the longer the wavelength. With the same simulation accuracy, the longer the wavelength, the larger the split grid can be. Meanwhile, in the embodiment, in order to reduce the complexity of processing and reduce transverse dispersion, an attenuation equation is introduced in the transverse direction, so that the balance of calculated amount and numerical dispersion suppression is achieved.
In some possible embodiments, the depth direction resampling is performed according to the first projection relation, and the second velocity field is generated in step S200, which is more specifically: and sampling the seismic wave wavelength according to the first projection relation, and performing variable mesh subdivision according to a sampling result to obtain a low-speed area mesh and a high-speed area mesh.
Illustratively, the primary frequency wavelength of the earthquake is sampled n times, then byAnd re-splitting the original grid so that the grid splitting meets n sampling conditions. The method has the advantages that the mesh of the low-speed area is smaller, and the mesh of the high-speed area is larger. Embodiments also resample the wavefield at varying grids, with similarly denser low-speed regions and sparse high-speed regions.
In some possible embodiments, the step S300 of forward modeling the seismic wavefield by the wavefield propagation equation according to the second velocity field includes determining a first derivative of the first projection relationshipSecond derivative of the first projection relation +.>Since the spatial dispersion of the analog wave field increases rapidly with increasing spatial grid spacing, a strong dispersion noise is present in the analog wave field, and the higher the dispersion noise frequency, the shorter the wavelength, and the more pronounced. Further in embodiments, consider the subsurfaceThe medium mainly comprises lamellar medium and has the characteristic of gradually increasing speed, and the seismic wave propagated in a certain range with a vertical included angle in the reflection geology is a wave field mainly applied, and the depth variable grid and the horizontal damping technology are combined to form a new wave field propagation equation:
in the wave field propagation equation,for the first projection relation, i.e. the projection relation of the original grid coordinates to the varying grid coordinates, the selection is usually made according to the medium velocity and the main frequency of the wave field,/v>Is the first derivative of the first projection relation, < +.>For the second derivative of the first projection relationship, u' (t, X) represents the wave field under a variable grid coordinate system, X represents the (X, y, z) spatial coordinates, v represents the velocity of the subsurface medium, t represents the time of propagation, and γ is the transverse dispersion suppression coefficient. And carrying out high-order finite difference solution on the wave field propagation equation to realize the propagation of the seismic wave field. Wave field propagation equation->Is achieved by the introduction of a variable lattice propagation in the depth z propagation direction, provided that the embodiment selects the appropriate +.>The form can realize a plurality of samples in each seismic wavelet wavelength, so that the numerical dispersion in the depth direction can be well suppressed>Realize multiple mediasThe variable grid subdivision of the mass and propagation space is denser, the low-speed subdivision is sparser, and the variable grid subdivision is adaptive to change according to the change of the seismic wavelength, so that a plurality of samples in each seismic wavelet wavelength range are realized, and the simulated numerical dispersion is reduced.
In some possible embodiments, the transverse dispersion pressing coefficient is determined according to a sampling interval in the horizontal direction, and the transverse dispersion pressing coefficient is in a proportional relationship with the sampling interval in the horizontal direction.
Specifically, a proper gamma is set according to the sampling interval in the horizontal direction, and if the sampling interval in the horizontal direction is larger, the gamma is correspondingly larger, so that the horizontal direction dispersion is better suppressed, and otherwise, the value is smaller. Because the rightmost term of the equation derives the time direction, the attenuation function is actually achieved. The transverse interval is large, the high frequency is easier to disperse, and gamma is properly increased at the moment, so that the effect of attenuating the high frequency energy in the horizontal direction can be achieved, and the effect of suppressing the dispersion in the horizontal direction can be achieved. The introduction of gamma realizes the high-frequency wave field suppression in the horizontal direction, thereby controlling the dispersion and achieving better wave field simulation.
In some possible embodiments, when γ=0, andwhen, i.e. when the direction of the variegated propagation is along the depth, the wave field propagation equation is:
where X represents the (X, y, z) spatial coordinates, v represents the velocity of the subsurface medium, t represents the time of propagation, and u is the wavefield propagating to the t and X points. The most commonly used solution of the wave field propagation equation is to solve the wave field propagation equation by using finite difference, which requires fine subdivision of space and time directions to ensure stability of the finite difference and obtain a seismic wave field with higher accuracy, which brings about high calculation amount. Embodiments to ensure computation stability, the sampling interval in the time direction must satisfy:
wherein ,vmax Representing the maximum speed. According to the condition limitation of the sampling interval, obviously, the smaller the space grid is, the smaller the corresponding time step is needed, and the larger the required calculation amount is, so the size of the space grid is increased as much as possible, and the purpose of reducing the calculation amount is achieved.
As shown in FIGS. 2-7, the three-layer horizontal model wave field propagation snapshot of the present application. Wherein the relevant forward grid parameters are listed in table 1.
TABLE 1
FIG. 2 is a snapshot of the wavefield propagated with the coarse grid of equation (2), showing significant numerical dispersion; FIG. 3 is a snapshot of the wavefield propagated by the fine grid of equation (2), with better suppression of numerical dispersion; figure 4 is a wave field snapshot of the coarse grid propagation of equation (3),the grid change is not realized, the numerical dispersion can be well suppressed, but the main frequency of the wave field is obviously reduced; fig. 5 is a snapshot of the wavefield of the coarse grid propagation of equation (1), γ=0, i.e., no horizontal direction numerical dispersion suppression is performed, and it can be seen that horizontal direction numerical dispersion is still more serious; fig. 6 and 7 are snapshots of the wavefield of the coarse grid propagation of equation (1), with γ being 0.1 and 0.3, respectively, and it can be seen that the horizontal numerical dispersion is well suppressed. 2-7 and Table 1, the method of the embodiment of the application can realize better seismic wave field propagation with better dispersion suppression under the condition of lower calculation cost.
In a second aspect, the present application provides an anti-dispersive seismic forward system for use in the method of the first aspect, comprising:
the parameter determining module is used for acquiring an underground medium speed field and a forward wavelet dominant frequency and setting a first projection relation according to the underground medium speed field and the forward wavelet dominant frequency;
the resampling module is used for resampling in the depth direction according to the first projection relation to generate a second speed field;
and the forward modeling module is used for performing seismic wave field forward modeling through a wave field propagation equation according to the second velocity field.
In a third aspect, the present application further provides an anti-dispersion seismic wave forward modeling apparatus, including at least one processor; at least one memory for storing at least one program; the at least one program, when executed by the at least one processor, causes the at least one processor to perform an anti-scatter seismic forward method as in the first aspect.
The embodiment of the application also provides a storage medium storing a program, and the program is executed by a processor to implement the method as in the first aspect.
From the above specific implementation process, it can be summarized that, compared with the prior art, the technical solution provided by the present application has the following advantages or advantages:
according to the technical scheme, a wave equation for transverse anti-dispersion is introduced, so that the numerical dispersion of the transverse wave field propagation is reduced; and then, a variable grid propagation technology related to the speed is introduced in the longitudinal direction, grid change is converted into equation coefficients, a new equation is derived, longitudinal dispersion suppression is realized, and the seismic wave forward modeling method with efficiency and data quality compromise is obtained. The new equation can be calculated on fewer grids, and the algorithm is simple and efficient and has strong practicability. According to the application, the calculation cost, the geologic structure characteristics and the data quality are balanced, so that better balance is achieved, and a basic engine is provided for the design of an earthquake observation system, algorithm inspection, offset imaging, speed inversion and the like, so that the time cost of related calculation can be reduced.
In some alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flowcharts of the present application are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed, and in which sub-operations described as part of a larger operation are performed independently.
Furthermore, while the application is described in the context of functional modules, it should be appreciated that, unless otherwise indicated, one or more of the functions and/or features may be integrated in a single physical device and/or software module or may be implemented in separate physical devices or software modules. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary to an understanding of the present application. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be apparent to those skilled in the art from consideration of their attributes, functions and internal relationships. Accordingly, one of ordinary skill in the art can implement the application as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative and are not intended to be limiting upon the scope of the application, which is to be defined in the appended claims and their full scope of equivalents.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the application, the scope of which is defined by the claims and their equivalents.
While the preferred embodiment of the present application has been described in detail, the present application is not limited to the above embodiments, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the present application, and these equivalent modifications and substitutions are intended to be included in the scope of the present application as defined in the appended claims.
Claims (7)
1. The forward modeling method of the anti-dispersion seismic wave is characterized by comprising the following steps of:
acquiring an underground medium velocity field and a forward wavelet dominant frequency, and setting a first projection relation according to the underground medium velocity field and the forward wavelet dominant frequency;
resampling in the depth direction according to the first projection relation to generate a second velocity field;
according to the second velocity field, forward modeling of the seismic wave field is performed through a wave field propagation equation;
the step of obtaining the underground medium velocity field and the forward wavelet dominant frequency and setting a first projection relation according to the underground medium velocity field and the forward wavelet dominant frequency comprises the following steps:
calculating to obtain the wave length of the seismic waves according to the forward wavelet dominant frequency and the medium speed in the underground medium speed field;
correlating the seismic wave wavelength with a longitudinal space grid, and determining a first projection relation according to the correlation relation;
the step of resampling in depth direction according to the first projection relation to generate a second velocity field comprises the following steps: sampling the seismic wave wavelength according to the first projection relation, and performing variable grid subdivision according to a sampling result to obtain a low-speed area grid and a high-speed area grid;
the step of forward modeling of the seismic wavefield by a wavefield propagation equation based on the second velocity field, comprising:
determining a first derivative of the first projection relationship and a second derivative of the first projection relationship;
the wave field propagation equation is:
wherein ,for the first projection relation +.>Is the first derivative of the first projection relation, < +.>For the second derivative of the first projection relationship, u' (t, X) represents the wave field under a variable grid coordinate system, X represents the (X, y, z) spatial coordinates, v represents the velocity of the subsurface medium, t represents the time of propagation, and γ is the transverse dispersion suppression coefficient.
2. The anti-dispersion seismic wave forward modeling method of claim 1, wherein the transverse dispersion suppression coefficient is determined according to a sampling interval in a horizontal direction, and the transverse dispersion suppression coefficient is in a proportional relationship with the sampling interval in the horizontal direction.
3. The anti-dispersion seismic wave forward modeling method of claim 1, wherein when the direction of the variable grid propagation is along the depth, the wave field propagation equation is:
where u (t, X) is the wavefield propagating to the t and X points.
4. A method of forward modeling anti-dispersive seismic waves according to any one of claims 1 to 3, further comprising the steps of:
an attenuation equation is introduced into the transverse space grid, and calculation and numerical dispersion suppression are balanced through the attenuation equation.
5. An anti-dispersion seismic wave forward modeling system, comprising:
the parameter determining module is used for acquiring an underground medium speed field and a forward wavelet dominant frequency and setting a first projection relation according to the underground medium speed field and the forward wavelet dominant frequency;
the resampling module is used for resampling in the depth direction according to the first projection relation to generate a second speed field;
the forward modeling module is used for performing seismic wave field forward modeling through a wave field propagation equation according to the second velocity field;
the step of obtaining the underground medium velocity field and the forward wavelet dominant frequency and setting a first projection relation according to the underground medium velocity field and the forward wavelet dominant frequency comprises the following steps:
calculating to obtain the wave length of the seismic waves according to the forward wavelet dominant frequency and the medium speed in the underground medium speed field;
correlating the seismic wave wavelength with a longitudinal space grid, and determining a first projection relation according to the correlation relation;
the step of resampling in depth direction according to the first projection relation to generate a second velocity field comprises the following steps:
sampling the seismic wave wavelength according to the first projection relation, and performing variable grid subdivision according to a sampling result to obtain a low-speed area grid and a high-speed area grid;
the step of forward modeling of the seismic wavefield by a wavefield propagation equation based on the second velocity field, comprising:
determining a first derivative of the first projection relationship and a second derivative of the first projection relationship;
the wave field propagation equation is:
wherein ,for the first projection relation +.>Is the first derivative of the first projection relation, < +.>For the second derivative of the first projection relationship, u' (t, X) represents the wave field under a variable grid coordinate system, X represents the (X, y, z) spatial coordinates, v represents the velocity of the subsurface medium, t represents the time of propagation, and γ is the transverse dispersion suppression coefficient.
6. An anti-dispersion seismic wave forward modeling device, comprising:
at least one processor;
at least one memory for storing at least one program;
the at least one program, when executed by the at least one processor, causes the at least one processor to perform an anti-scatter seismic forward method as claimed in any one of claims 1-4.
7. A storage medium having stored therein a processor executable program which when executed by a processor is adapted to run an anti-scatter seismic forward method as claimed in any one of claims 1-4.
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