CN106066490B - Prestack inversion of Density method and device based on spherical wave - Google Patents
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Abstract
The prestack inversion of Density method and device based on spherical wave that an embodiment of the present invention provides a kind of, wherein this method includes：The seismic data that incidence angle is single angle is obtained, seismic data includes observation seismic data and theoretical seismic data, and seismic data includes the frequency point of low-frequency range；The spherical wave reflectance factor of the spherical wave reflectance factor of the spherical wave reflectance factor of calculating observation seismic data and theoretical seismic data, the frequency point of low-frequency range changes with angular frequency and is changed；Using very fast simulated annealing algorithm, the prestack inversion of Density of frequency domain is carried out to the spherical wave reflectance factor of the spherical wave reflectance factor and theoretical seismic data of observing seismic data.The program becomes the disadvantage that information compensates for traditional prestack inversion of Density information content deficiency using low frequency frequency, and using the frequency change effect of spherical wave reflectance factor it is elastic parameter the fact that objectively respond so that becoming the prestack inversion of Density of information based on low frequency frequency, only to need incidence angle be that the seismic data of list angle can be realized.
Description
Technical Field
The invention relates to the technical field of geophysical exploration of oil and natural gas energy sources, in particular to a spherical wave-based prestack density inversion method and a spherical wave-based prestack density inversion device.
Background
In the field of seismic exploration, density is an important basis for distinguishing underground rock physical properties, and physical property parameters such as Poisson's ratio and fluid factors derived through density and speed are also important indicating tools for underground reservoir lithology, porosity and fluid components, and are very important for links such as reservoir characterization, reservoir development and detection. However, in the existing AVO (AVA) inversion method based on the plane wave theory, because the amount of information that can be utilized is limited, it is generally difficult to obtain independent density estimation, and two-parameter coupling inversion strategies such as inversion intercept gradient and longitudinal and transverse wave impedance are mostly adopted, and various regularization methods are adopted to enhance the stability and reliability of inversion. In addition, inversion density information is a bottleneck of an inversion method based on a plane wave AVO (AVA) theory, seismic data of multiple angles are necessarily applied to the inversion method based on the AVO (AVA) theory, and large-angle seismic data are also used, however, the acquisition and processing of the large-angle seismic data need extra care, and the quality of the seismic data can affect the inversion effect due to carelessness.
Disclosure of Invention
The embodiment of the invention provides a prestack density inversion method based on spherical waves, which aims to solve the technical problems that in the prior art, an AVO density parameter inversion method based on a plane wave theory must use seismic data of multiple angles and also use large-angle seismic data. The method comprises the following steps: acquiring seismic data with a single-angle incidence angle, wherein the seismic data comprise observed seismic data acquired through direct observation and theoretical seismic data acquired through calculation, and the seismic data comprise frequency points of a low frequency band; calculating the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data, wherein the spherical wave reflection coefficient of the frequency point of the low frequency band changes along with the change of angular frequency; and performing frequency domain pre-stack density inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data by adopting a very fast simulated annealing algorithm.
In one embodiment, the seismic data is seismic data with an angle of incidence less than 30 degrees and the seismic data is seismic data with an interface depth less than 500 meters.
In one embodiment, the spherical wave reflection coefficient of each frequency point in the theoretical seismic data is calculated by the following formula:
wherein,is the spherical wave reflection coefficient of each frequency point in the theoretical seismic data,
is the plane wave reflection coefficient, the angle of incidence for the plane wave is θ, x is cos (θ), ω is the angular frequency, J0Is a zero order Bessel function, r is the offset, h is the distance from the excitation source to the reflection plane, zris the distance from the receiving point to the interface, α1is the longitudinal wave velocity of the upper layer, α2Is the longitudinal wave velocity of the lower layer, ρ1Is the density of the upper layer, p2Is the density of the lower layer, and i is the imaginary unit.
In one embodiment, performing a pre-stack density inversion in the frequency domain for the spherical wave reflection coefficients of the observed seismic data and the spherical wave reflection coefficients of the theoretical seismic data using a very fast simulated annealing algorithm comprises: and performing density ratio and velocity ratio inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data simultaneously by adopting a very fast simulated annealing algorithm.
In one embodiment, before performing the pre-stack density inversion of the frequency domain on the spherical wave reflection coefficient by using the very fast simulated annealing optimization method, the method further comprises:
the elastic parameters that are inverted simultaneously with the density are determined by the following objective function formula:
f (m) represents the matching degree of the observed seismic data and the theoretical seismic data, N represents the number of the selected frequency points participating in calculation, m represents a set of elastic parameters which are inverted simultaneously, and AVAOBS(ωn) Is the spherical wave reflection coefficient record, AVA, of each frequency point in the observed seismic data obtained by Fourier transformTHEO(ωn) З the З method З comprises З the З steps З of З calculating З spherical З wave З reflection З coefficient З records З of З all З frequency З points З in З theoretical З seismic З data З, З wherein З n З is З the З number З of З the З selected З frequency З point З, З the З size З of З the З change З range З of З the З elastic З parameters З of З which З the З numerical З values З of З F З (З m З) З are З smaller З than З a З preset З minimum З value З is З in З direct З proportion З to З the З uncertainty З of З an З inversion З result З, З and З when З the З F З (З m З) З is З smaller З than З the З preset З minimum З value З, З the З elastic З parameters З with З the З minimum З change З range З in З all З the З elastic З parameters З and З the З density З are З determined З to З be З inverted З simultaneously З. З
The embodiment of the invention also provides a pre-stack density inversion device based on spherical waves, which is used for solving the technical problems that seismic data of multiple angles are required to be applied and large-angle seismic data are required to be applied in the inversion method based on the plane wave theory in the prior art. The device includes: the acquisition module is used for acquiring seismic data with a single-angle incidence angle, wherein the seismic data comprise observed seismic data acquired through direct observation and theoretical seismic data acquired through calculation, and the seismic data comprise frequency points of a low frequency band; the calculation module is used for calculating the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data, wherein the spherical wave reflection coefficient of the frequency point of the low frequency band changes along with the change of angular frequency; and the inversion module is used for performing frequency domain pre-stack density inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data by adopting a very fast simulated annealing algorithm.
In one embodiment, the seismic data is seismic data with an angle of incidence less than 30 degrees and the seismic data is seismic data with an interface depth less than 500 meters.
In one embodiment, the calculating module is specifically configured to calculate the spherical wave reflection coefficient of each frequency point in the theoretical seismic data according to the following formula:
wherein,is the spherical wave reflection coefficient of each frequency point in the theoretical seismic data,
is the plane wave reflection coefficient, the angle of incidence for the plane wave is θ, x is cos (θ), ω is the angular frequency, J0Is a zero order Bessel function, r is the offset, h is the distance from the excitation source to the reflection plane, zris the distance from the receiving point to the interface, α1is the longitudinal wave velocity of the upper layer, α2Is the longitudinal wave velocity of the lower layer, ρ1Is the density of the upper layer, p2Is the density of the lower layer, and i is the imaginary unit.
In one embodiment, the inversion module is specifically configured to perform density ratio and velocity ratio inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data simultaneously using a very fast simulated annealing algorithm.
In one embodiment, further comprising: an inversion determination module, configured to determine, by using a very fast simulated annealing algorithm, an elastic parameter for performing inversion simultaneously with density through the following objective function formula before performing pre-stack density inversion of a frequency domain on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data:
f (m) represents the matching degree of the observed seismic data and the theoretical seismic data, N represents the number of the selected frequency points participating in calculation, m represents a set of elastic parameters which are inverted simultaneously, and AVAOBS(ωn) Is the spherical wave reflection coefficient record, AVA, of each frequency point in the observed seismic data obtained by Fourier transformTHEO(ωn) З the З method З comprises З the З steps З of З calculating З spherical З wave З reflection З coefficient З records З of З all З frequency З points З in З theoretical З seismic З data З, З wherein З n З is З the З number З of З the З selected З frequency З point З, З the З size З of З the З change З range З of З the З elastic З parameters З of З which З the З numerical З values З of З F З (З m З) З are З smaller З than З a З preset З minimum З value З is З in З direct З proportion З to З the З uncertainty З of З an З inversion З result З, З and З when З the З F З (З m З) З is З smaller З than З the З preset З minimum З value З, З the З elastic З parameters З with З the З minimum З change З range З in З all З the З elastic З parameters З and З the З density З are З determined З to З be З inverted З simultaneously З. З
In the embodiment of the invention, the pre-stack density inversion of the frequency domain is carried out on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data obtained by calculation by obtaining the seismic data with the single-angle incidence angle, wherein the seismic data comprises the frequency points of the low frequency band, and then the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data are calculated, so that the pre-stack density inversion of the spherical wave reflection coefficient based on the frequency points of the low frequency band is realized. The spherical wave theory can more accurately reflect the propagation rule of the underground seismic wave, the spherical wave reflection coefficient of the frequency point of the low frequency band changes along with the change of the angular frequency, namely, low-frequency variation information is introduced, the information amount which can be adopted in the inversion process can be enriched, the defect that the traditional pre-stack density inversion information amount is insufficient is overcome by using the low-frequency variation information, and the fact that the frequency variation effect (namely, the change along with the change of the angular frequency) of the spherical wave reflection coefficient is the objective reflection of the elastic parameter is utilized, so that the pre-stack density inversion based on the low-frequency variation information can be realized only by using seismic data with a single-angle (small-angle) incidence angle, and no special requirement is provided for the angle size of. Meanwhile, a very fast simulated annealing optimization method is adopted for inversion so as to obtain an accurate inversion result and reduce the uncertainty of the inversion result.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flow chart of a spherical wave-based prestack density inversion method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a two-layer media model provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of a plane wave reflection coefficient curve according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a spherical wave reflection coefficient curve according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a result of multiple inversions of inversion parameters according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a convergence curve of an objective function of multiple inversion of inversion parameters according to an embodiment of the present invention;
fig. 7 is a block diagram of a structure of a spherical wave-based prestack density inversion apparatus according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
Under the condition that the oil and gas exploration degree is increasingly improved, the maximum utilization of developed or to be developed oil and gas resources by utilizing the existing data is a key problem to be solved by a geophysical method, the underground characteristics need to be more accurately simulated when the problem is solved, and the method is selected more pertinently and more resources provided by underground seismic waves are utilized. In the prior art, an AVO (Amplitude Variation With Offset) inversion method based on plane wave theory (non-vertical incidence Amplitude relationship, abbreviated as AVA) applies seismic data of multiple angles and also applies large-angle seismic data. However, the inventors have found that spherical wave theory has two major advantages over planar wave theory in the area of AVO (AVA) analysis and inversion, one: the spherical wave reflection coefficient can accurately describe the amplitude and phase information of the reflected wave at a near or supercritical angle (large angle); II, secondly: the reflection coefficient of the spherical wave is obviously characterized by changing with frequency in a low frequency band. Considering that the change of the reflection coefficient of the spherical wave along with the frequency is an objective reflection of the elastic parameter, and the angle of the used data is not strictly limited, and large-angle data which is easily affected by dynamic correction stretching and tuning effects is avoided, the inventor proposes that the frequency-dependent characteristic of the reflection coefficient of the spherical wave is utilized to perform inversion of the elastic parameter of the frequency domain of the small-angle data, namely the specific method is the inversion method of the prestack density based on the spherical wave.
In an embodiment of the present invention, a method for prestack density inversion based on spherical waves is provided, as shown in fig. 1, the method includes:
step 101: acquiring seismic data with a single-angle incidence angle, wherein the seismic data comprise observed seismic data acquired through direct observation and theoretical seismic data acquired through calculation, and the seismic data comprise frequency points of a low frequency band;
step 102: calculating the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data, wherein the spherical wave reflection coefficient of the frequency point of the low frequency band changes along with the change of angular frequency;
step 103: and performing frequency domain pre-stack density inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data by adopting a very fast simulated annealing algorithm.
As can be seen from the process shown in fig. 1, in the embodiment of the present invention, by obtaining seismic data with a single angle of incidence, where the seismic data includes frequency points in a low frequency band, and further calculating a spherical wave reflection coefficient of observed seismic data and a spherical wave reflection coefficient of theoretical seismic data, a spherical wave reflection coefficient including frequency points in the low frequency band is obtained, and finally, performing frequency domain pre-stack density inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data obtained through calculation by using a very fast simulated annealing algorithm, a pre-stack density inversion of the spherical wave reflection coefficient based on the frequency points in the low frequency band is achieved. The spherical wave theory can more accurately reflect the propagation rule of the underground seismic wave, the spherical wave reflection coefficient of the frequency point of the low frequency band changes along with the change of the angular frequency, namely, low-frequency variation information is introduced, the information amount which can be adopted in the inversion process can be enriched, the defect that the traditional pre-stack density inversion information amount is insufficient is overcome by using the low-frequency variation information, and the fact that the frequency variation effect (namely, the change along with the change of the angular frequency) of the spherical wave reflection coefficient is the objective reflection of the elastic parameter is utilized, so that the pre-stack density inversion based on the low-frequency variation information can be realized only by using seismic data with a single-angle (small-angle) incidence angle, and no special requirement is provided for the angle size of. Meanwhile, a very fast simulated annealing optimization method is adopted for inversion so as to obtain an accurate inversion result and reduce the uncertainty of the inversion result.
In specific implementation, in order to calculate the spherical wave reflection coefficient of each frequency point in the theoretical seismic data, in this embodiment, the spherical wave reflection coefficient of each frequency point in the theoretical seismic data is calculated by the following formula:
wherein,is the spherical wave reflection coefficient of each frequency point in the theoretical seismic data,
is the plane wave reflection coefficient, the angle of incidence for the plane wave is θ, x is cos (θ), ω is the angular frequency, J0Is a zero order Bessel function, r is the offset, h is the distance from the excitation source to the reflection plane, zris the distance from the receiving point to the interface, α1is the longitudinal wave velocity of the upper layer, α2Is the longitudinal wave velocity of the lower layer, ρ1Is the density of the upper layer, p2Is the density of the lower layer, and i is the imaginary unit. As shown in fig. 2, we assume that the interface depth is known and the positions of the excitation point and the receiving point are known, and for two homogeneous half-space acoustic medium models, the expression of the spherical wave reflection coefficient at the contact plane is shown in equation (1). For the convenience of subsequent analysis, we can write the spherical wave reflection coefficient as a function of the incident angle and angular frequency, as shown in equation (2):
the angle of the incidence angle of the seismic data is adopted, the calculation can be carried out through the interface depth, the positions of the receiving point and the excitation point, and omega is the angular frequency. ρ ═ ρ2/ρ1Is the density ratio, c is the integration path,
obviously, the spherical wave reflection coefficient is related to the density ratio and the velocity parameter of the upper and lower layers, and as can be seen from equation (2), the spherical wave reflection coefficient has a characteristic of varying with the angular frequency.
In specific implementation, after the spherical wave reflection coefficient of the theoretical seismic data is obtained through calculation by the formula (1) or (2), the elastic parameters of the upper medium and the lower medium can be inverted according to the frequency-dependent characteristics of the spherical wave reflection coefficient, and the information which can be utilized by people is greatly enriched. Fig. 3 illustrates this problem, and in fig. 3, there are shown information points utilized by the conventional AVO (AVA) analysis and inversion based on plane wave reflection coefficient, and it can be seen that the plane wave reflection coefficient curve varies with the incident angle, and the AVO (AVA) analysis and inversion technique developed by using the plane wave reflection coefficient has been greatly successful and widely applied in the industry. While fig. 4 is a schematic diagram showing the change of the reflection coefficient of the spherical wave with the angular frequency and the incident angle, it can be seen that, under the same condition, the conventional plane wave reflection coefficient-based AVO (AVA) method utilizes 3 points of information (as shown in fig. 3), and the inversion based on the reflection coefficient of the spherical wave can utilize 9 points of information (as shown in fig. 4), even though a certain incident angle is utilizedWe can still use the information of different angular frequenciesThe elastic parameter information of the upper side and the lower side of the interface is obtained, and an inversion method based on the spherical wave reflection coefficient development also becomes a powerful tool.
In specific implementation, inversion by using a spherical wave theory at the present stage is based on two elastic/acoustic media, some parameters of an upper layer or a lower layer are known, unknown parameters in three parameters (longitudinal and transverse wave speed and density) of the upper medium and the lower medium are inverted, low-frequency variation information is not utilized, and the parameter selection is random without theory and data support. In this embodiment of the present application, according to an expression of a frequency-dependent spherical wave reflection coefficient (that is, a spherical wave reflection coefficient changes with an angular frequency), an elastic parameter combination to be inverted is determined through feasibility analysis, and a selection strategy of inversion key parameters is given before inversion (for example, which parameters and densities are inverted simultaneously can reduce uncertainty of an inversion result), so that effective density inversion is finally achieved. For example, before performing pre-stack density inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data by using a very fast simulated annealing algorithm, the method further includes:
the elastic parameters that are inverted simultaneously with the density are determined by the following objective function formula:
f (m) represents the matching degree of the observed seismic data and the theoretical seismic data, N represents the number of the selected frequency points participating in calculation, m represents a set of elastic parameters which are inverted simultaneously, and AVAOBS(ωn) Is the spherical wave reflection coefficient record, AVA, of each frequency point in the observed seismic data obtained by Fourier transformTHEO(ωn) the spherical wave reflection coefficient record of each frequency point in the theoretical seismic data is obtained by calculation, n is the number of the selected frequency point, and the numerical value of F (m) is smaller than the elastic parameter of the preset small value of theand determining the elastic parameter with the minimum transformation range in all the elastic parameters and the density to perform inversion simultaneously when the F (m) is smaller than a preset minimum value of the fiveleaf.
Specifically, as shown in fig. 2, the adopted model matches the spherical wave reflection coefficient of the theoretical seismic data obtained by calculation using formula (1) with the spherical wave reflection coefficient of the observed seismic data obtained by forward modeling at different selected frequencies, and takes the 2 norm of the residual error between the spherical wave reflection coefficient result of the theoretical seismic data and the spherical wave reflection coefficient of the observed seismic data at each frequency point as an objective function, which is specifically shown in formula (3):
on the premise that wavelets are known, spherical wave reflection coefficient records AVA for observing each frequency point in seismic data can be obtained through Fourier transformOBS(ωn) The formula (1) can be used for calculating and obtaining the spherical wave reflection coefficient record AVA of each frequency point in the theoretical seismic dataTHEO(ωn)。
З the З inversion З is З performed З by З matching З observed З seismic З data З and З theoretically З calculated З seismic З data З to З obtain З m З ' З, З if З m З ' З enables З F З (З m З) З to З reach З a З minimum З value З, З m З ' З is З an З estimation З of З true З solution З m З, З namely З an З inversion З result З of З the З parameter З, З different З m З ' З can З generate З different З F З (З m З) З, З if З the З form З of З F З (З m З) З is З very З mild З, З the З acceptable З variation З range З of З m З ' З is З very З large З when З F З (З m З) З is З less З than З a З certain З small З value З, З and З the З inversion З method З is З difficult З to З obtain З a З good З estimation ЗThe morphology of F (m) for m' of different elastic parameter combinations is tested to determine the inversion elastic parameter combination. Disturbance within a certain range (m ═ m)true(1 +/-20%)) into the formula (1), and calculating forward spherical wave reflection coefficient record AVA of theoretical seismic dataTHEO(ωn) And then substituted into formula (3) to obtain the objective function value F (m).
For example, when we perturb the upper and lower layer velocities, the inverted objective function is characterized by a "canyon", and the contour lines of the objective function are distributed in a stripe shape, which indicates that the linear correlation degree of the parameter combinations constituting the objective function is relatively high, and no local minimum point appears within a certain perturbation range (e.g., 20%). And the target function does not converge to an ideal circle or an ellipse, which shows that the uncertainty of simultaneously inverting the upper and lower layer velocities is high, and the uncertainty is generated by simultaneously inverting the upper and lower layer velocities, so that the upper and lower layer velocity ratio rather than the upper and lower layer velocities is taken as a parameter representation. When the velocity ratio and the density ratio are selected to perform inversion simultaneously, the target function is good in form, and the target function is gradually converged into an ellipse. Performing pre-stack density inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data by adopting a very fast simulated annealing algorithm, wherein the pre-stack density inversion comprises the following steps: and performing density ratio and velocity ratio simultaneous inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data by adopting a very fast simulated annealing algorithm.
In specific implementation, the spherical wave-based prestack density inversion method is based on frequency domain matching, so that data of a certain frequency point needs to be selected for inversion, in principle, the elastic parameters are inverted by using low-frequency variation characteristics, enough low-frequency components need to be provided, and the point can be visually verified through the form of a target function (the target function shown in the formula (3)), if the frequency point of 15-40Hz is selected for drawing the target function, the poor form of the target function can be observed, and a minimum value point is not converged and is in a divergence shape; if a 40Hz single frequency is selected for drawing the target function, the target function value is observed to be almost unchanged, the parameter change cannot be effectively reflected, the parameter inversion cannot be carried out, and the importance of the low-frequency information on the frequency-dependent inversion is also proved. In addition, the important significance of low-frequency information at the present stage is widely recognized, and the information of low-frequency components in the data acquired by the earthquake is more and more, and the quality is better and better, so that the research of an inversion method utilizing the characteristics of the low-frequency information is facilitated.
However, the spherical wave reflection coefficient used in the spherical wave inversion is relatively complex to calculate and consumes much time, and how to correctly select the frequency point of the seismic data as the input data so that the inversion is more stable is also a topic worth studying. In view of the importance of low frequency and the need for a certain control of speed inversion at medium and high frequencies, in this embodiment, the seismic data includes frequency points at low frequency band, frequency points at medium frequency band, and frequency points at high frequency band, specifically, a strategy of sampling at 2Hz at low frequency band (typically, 2-12Hz at frequency point at low frequency band), sampling at 5Hz at medium frequency band (typically, 12-37Hz at frequency point at medium frequency band), and sampling at 10Hz at high frequency band (typically, 37-87Hz at frequency point at high frequency band) can be selected, so as to fully utilize low frequency information, and to appropriately thin out medium and high frequency information, that is, a frequency point combination of [ 24681012172227323747576787 ] Hz is used as the seismic data.
In specific implementation, after the frequency point combination of the seismic data is determined, inversion target functions of angles of different incident angles and interface depths can be analyzed. Specifically, the inversion objective function of equation (3) may be substituted with the same frequency points at different incident angles, for example, a set of frequency points with an interface depth of 150m, a set of frequency points with an interface depth of 500m, a set of frequency points with an incident angle of 10 degrees, a set of frequency points with an incident angle of 30 degrees, and a set of frequency points with an incident angle of 50 degrees may be selected. According to the objective function corresponding to each group of frequency points, the interface depth is shallower when the angle of incidence is larger, and the form of the objective function is better. When the interface depth is 150m and the incident angle is 50 degrees, the minimum value of the objective function is most converged, and when the visible interface depth is small, the inversion effect is better when the incident angle is large. Due to the frequency-varying characteristics of spherical waves, seismic data with small to medium angles can be selected for density inversion, the signal-to-noise ratio of the data is high, and inversion is facilitated, so that for the pre-stack density inversion method based on the spherical waves, the seismic data can be seismic data with an incidence angle smaller than 30 degrees, the seismic data with an incidence angle smaller than 30 degrees can be adopted compared with the inversion method based on a plane wave reflection coefficient, but the inversion method based on the plane wave reflection coefficient cannot be realized, and the seismic data can be seismic data with an interface depth smaller than 500 meters.
In addition, in order to compare the difference between the plane wave reflection coefficient and the spherical wave reflection coefficient, AVA is calculated using the plane wave reflection coefficient formula as a forward equation of the objective function (formula 3)THEO(ωn) The objective function morphology chart can be obtained when the interface depth h is 150m and the incident angle is 50 degrees. According to the objective function morphology graph, the difference exists between the minimum point of the objective function and the true value of the model, which indicates that the plane wave theory cannot describe the frequency variation phenomenon and cannot obtain a good inversion effect (namely, the minimum value of the objective function does not converge to the true value).
In specific implementation, the spherical wave-based prestack density inversion method adopts a nonlinear global optimization inversion algorithm, and the inventor performs a plurality of tests to verify the feasibility and accuracy of inversion. Specifically, the method for optimizing Very Fast Simulated Annealing (VFSA) is used in the present invention, in which the spherical wave frequency-dependent reflection coefficient AVA of observation at a selected frequency point (i.e. each frequency point of the seismic data) is first inputOBS(ωn) As observation data, and giving an initial value m of any one set of parameters0＝(α2/α1,ρ)0∈[mmin,mmax]M isTrue value of the parameter, mminAnd mmaxAre the upper and lower limits of the parameter. Setting a data matching error limit epsilon and a maximum iteration number itmaxCalculating the initial energy of the system, i.e. the objective functionFor the ith iteration, a random perturbation operator P is utilizediThe parameters may be updated as: m isi＝mi-1+ΔmiAnd m isi∈[mmin,mmax]，Δmi＝Pi×(mmax-mmin) let xi e (0,1) be a random number satisfying uniform distribution, then Pi＝Tisign(ξ-0.5)[(1+1/Ti)|2ξ-1|-1]Then synthesizing the frequency-dependent reflection coefficient theoretical calculation data AVA corresponding to the new parametersTHEO(ωn,m0) Updating system energy:
judging whether to accept the updated parameter value according to the probability acceptance criterion, if so, judging whether to accept the updated parameter value Ei＜{Ek}minAnd k is 0,1,2,3, …, i-1, the updated value of the currently accepted parameter is stored into the optimal solution moptIn the recorder. If E isiMore than epsilon and i < itmaxIf so, reducing the system temperature and continuing iteration; otherwise outputting the optimal solution m in the recorderoptI.e. an estimate of the parameter. By simulating the process of annealing and crystallization of the metal in the nature (namely the very fast simulated annealing optimization method), the adopted search method is more consistent with the natural phenomenon, the global optimal solution can be obtained, and the inversion stability of the density and speed information is ensured. And a plurality of inversion results can be obtained by inputting different initial models to carry out inversion result uncertainty analysis, and the accuracy and the feasibility of the provided inversion method based on spherical wave low-frequency variation information are verified.
Specifically, taking the seismic data with an incident angle of 20 degrees as an example, the inversion result (as shown in fig. 5) of multiple inversions of the very fast simulated annealing algorithm based on the spherical wave reflection coefficient and the convergence condition (as shown in fig. 6) of the objective function can be obtained. Multiple realizations are achieved by randomly altering the initial values initially given by the very fast simulated annealing algorithm. As shown in fig. 5, it can be seen that the projection points of the multiple inversion results are concentrated around the projection point of the true value, and the error (err) is less than 2%; as shown in fig. 6, it can be seen that the convergence curve of the objective function shows that the convergence condition can be reached in about 2500 times of fast convergence of the inversion, and the convergence curve is fast and correct, which explains the feasibility and accuracy of the inversion.
If we project the inversion result to the target function graph and enlarge and display the graph, it is known that the convergence of the target function is good, and the density and velocity estimates obtained by inversion are very stable. The simultaneous inversion of density and velocity can be obtained by single-angle seismic data inversion, which cannot be realized by the traditional AVO (AVA) inversion, and the fact that density inversion is feasible and effective by using the low-frequency-variation information ignored in the traditional technology is demonstrated.
Based on the same inventive concept, the embodiment of the present invention further provides a spherical wave-based prestack density inversion apparatus, as described in the following embodiments. The principle of solving the problems of the spherical wave-based prestack density inversion device is similar to that of the spherical wave-based prestack density inversion method, so that the implementation of the spherical wave-based prestack density inversion device can refer to the implementation of the spherical wave-based prestack density inversion method, and repeated parts are not described again. As used hereinafter, the term "unit" or "module" may be a combination of software and/or hardware that implements a predetermined function. Although the means described in the embodiments below are preferably implemented in software, an implementation in hardware, or a combination of software and hardware is also possible and contemplated.
Fig. 7 is a block diagram of a structure of a spherical wave-based prestack density inversion apparatus according to an embodiment of the present invention, as shown in fig. 5, including: an obtaining module 701, a calculating module 702, and an inverting module 703, which are described below.
An obtaining module 701, configured to obtain seismic data with a single angle of incidence, where the seismic data include observed seismic data obtained through direct observation and theoretical seismic data obtained through calculation, and the seismic data include frequency points of a low frequency band;
a calculating module 702, configured to calculate a spherical wave reflection coefficient of the observed seismic data and a spherical wave reflection coefficient of the theoretical seismic data, where the spherical wave reflection coefficient of the frequency point of the low frequency band changes with angular frequency;
the inversion module 703 is configured to perform frequency domain pre-stack density inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data by using a very fast simulated annealing algorithm.
In one embodiment, the seismic data is seismic data with an angle of incidence less than 30 degrees and the seismic data is seismic data with an interface depth less than 500 meters.
In one embodiment, the calculating module is specifically configured to calculate the spherical wave reflection coefficient of each frequency point in the theoretical seismic data according to the following formula:
wherein,is the spherical wave reflection coefficient of each frequency point in the theoretical seismic data,
is the plane wave reflection coefficient, the angle of incidence for the plane wave is θ, x is cos (θ), ω is the angular frequency, J0Is a zero order Bessel function, r is the offset, h is the distance from the excitation source to the reflection plane, zris the distance from the receiving point to the interface, α1Is an upper layerlongitudinal wave velocity, α2Is the longitudinal wave velocity of the lower layer, ρ1Is the density of the upper layer, p2Is the density of the lower layer, and i is the imaginary unit.
In one embodiment, the inversion module is specifically configured to perform density ratio and velocity ratio inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data simultaneously using a very fast simulated annealing algorithm.
In one embodiment, further comprising: an inversion determination module, configured to determine, by using a very fast simulated annealing algorithm, an elastic parameter for performing inversion simultaneously with density through the following objective function formula before performing pre-stack density inversion of a frequency domain on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data:
wherein, F (m) represents the matching degree of the observed seismic data and the theoretical seismic data, N represents the number of the selected frequency points participating in calculation, m represents the set of elastic parameters which are inverted simultaneously, and AVAOBS(ωn) Is the spherical wave reflection coefficient record, AVA, of each frequency point in the observed seismic data obtained by Fourier transformTHEO(ωn) З the З method З comprises З the З steps З of З calculating З spherical З wave З reflection З coefficient З records З of З all З frequency З points З in З theoretical З seismic З data З, З wherein З n З is З the З number З of З the З selected З frequency З point З, З the З size З of З the З change З range З of З the З elastic З parameters З of З which З the З numerical З values З of З F З (З m З) З are З smaller З than З a З preset З minimum З value З is З in З direct З proportion З to З the З uncertainty З of З an З inversion З result З, З and З when З the З F З (З m З) З is З smaller З than З the З preset З minimum З value З, З the З elastic З parameters З with З the З minimum З change З range З in З all З the З elastic З parameters З and З the З density З are З determined З to З be З inverted З simultaneously З. З
In the embodiment of the invention, the pre-stack density inversion of the frequency domain is carried out on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data obtained by calculation by obtaining the seismic data with the single-angle incidence angle, wherein the seismic data comprises the frequency points of the low frequency band, and then the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data are calculated, so that the pre-stack density inversion of the spherical wave reflection coefficient based on the frequency points of the low frequency band is realized. The spherical wave theory can more accurately reflect the propagation rule of the underground seismic wave, the spherical wave reflection coefficient of the frequency point of the low frequency band changes along with the change of the angular frequency, namely, low-frequency variation information is introduced, the information amount which can be adopted in the inversion process can be enriched, the defect that the traditional pre-stack density inversion information amount is insufficient is overcome by using the low-frequency variation information, and the fact that the frequency variation effect (namely, the change along with the change of the angular frequency) of the spherical wave reflection coefficient is the objective reflection of the elastic parameter is utilized, so that the pre-stack density inversion based on the low-frequency variation information can be realized only by using seismic data with a single-angle (small-angle) incidence angle, and no special requirement is provided for the angle size of. Meanwhile, a very fast simulated annealing optimization method is adopted for inversion so as to obtain an accurate inversion result and reduce the uncertainty of the inversion result.
It will be apparent to those skilled in the art that the modules or steps of the embodiments of the invention described above may be implemented by a general purpose computing device, they may be centralized on a single computing device or distributed across a network of multiple computing devices, and alternatively, they may be implemented by program code executable by a computing device, such that they may be stored in a storage device and executed by a computing device, and in some cases, the steps shown or described may be performed in an order different than that described herein, or they may be separately fabricated into individual integrated circuit modules, or multiple ones of them may be fabricated into a single integrated circuit module. Thus, embodiments of the invention are not limited to any specific combination of hardware and software.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the embodiment of the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A prestack density inversion method based on spherical waves is characterized by comprising the following steps:
acquiring seismic data with a single-angle incidence angle, wherein the seismic data comprise observed seismic data acquired through direct observation and theoretical seismic data acquired through calculation, and the seismic data comprise frequency points of a low frequency band;
calculating the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data, wherein the spherical wave reflection coefficient of the frequency point of the low frequency band changes along with the change of angular frequency;
performing frequency domain pre-stack density inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data by adopting a very fast simulated annealing algorithm;
calculating the spherical wave reflection coefficient of each frequency point in the theoretical seismic data by the following formula:
wherein,is the spherical wave reflection coefficient of each frequency point in the theoretical seismic data,
is the plane wave reflection coefficient, the angle of incidence for the plane wave is θ, x is cos (θ), ω is the angular frequency, J0Is a zero order Bessel function, r is the offset, h is the distance from the excitation source to the reflection plane, zris the distance from the receiving point to the interface, α1is the longitudinal wave velocity of the upper layer, α2Is the longitudinal wave velocity of the lower layer, ρ1Is the density of the upper layer, p2Is the density of the lower layer, and i is the imaginary unit.
2. The spherical wave-based prestack density inversion method of claim 1, characterized in that the seismic data are seismic data with an incidence angle of less than 30 degrees and the seismic data are seismic data with an interface depth of less than 500 meters.
3. The spherical wave-based prestack density inversion method of claim 1 or 2, characterized in that the frequency domain prestack density inversion is performed on the spherical wave reflection coefficients of the observed seismic data and the spherical wave reflection coefficients of the theoretical seismic data by using a very fast simulated annealing algorithm, comprising:
and performing density ratio and velocity ratio inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data simultaneously by adopting a very fast simulated annealing algorithm.
4. The spherical wave-based prestack density inversion method of claim 1 or 2, characterized in that before performing the prestack density inversion of the frequency domain on the spherical wave reflection coefficients of the observed seismic data and the spherical wave reflection coefficients of the theoretical seismic data by using a very fast simulated annealing algorithm, the method further comprises:
the elastic parameters that are inverted simultaneously with the density are determined by the following objective function formula:
f (m) represents the matching degree of the observed seismic data and the theoretical seismic data, N represents the number of the selected frequency points participating in calculation, m represents a set of elastic parameters which are inverted simultaneously, and AVAOBS(ωn) Is the spherical wave reflection coefficient record, AVA, of each frequency point in the observed seismic data obtained by Fourier transformTHEO(ωn) З the З method З comprises З the З steps З of З calculating З spherical З wave З reflection З coefficient З records З of З all З frequency З points З in З theoretical З seismic З data З, З wherein З n З is З the З number З of З the З selected З frequency З point З, З the З size З of З the З change З range З of З the З elastic З parameters З of З which З the З numerical З values З of З F З (З m З) З are З smaller З than З a З preset З minimum З value З is З in З direct З proportion З to З the З uncertainty З of З an З inversion З result З, З and З when З the З F З (З m З) З is З smaller З than З the З preset З minimum З value З, З the З elastic З parameters З with З the З minimum З change З range З in З all З the З elastic З parameters З and З the З density З are З determined З to З be З inverted З simultaneously З. З
5. A pre-stack density inversion device based on spherical waves is characterized by comprising:
the acquisition module is used for acquiring seismic data with a single-angle incidence angle, wherein the seismic data comprise observed seismic data acquired through direct observation and theoretical seismic data acquired through calculation, and the seismic data comprise frequency points of a low frequency band;
the calculation module is used for calculating the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data, wherein the spherical wave reflection coefficient of the frequency point of the low frequency band changes along with the change of angular frequency;
the inversion module is used for performing frequency domain pre-stack density inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data by adopting a very fast simulated annealing algorithm;
the calculation module is specifically configured to calculate spherical wave reflection coefficients of the frequency points in the theoretical seismic data by using the following formula:
wherein,is the spherical wave reflection coefficient of each frequency point in the theoretical seismic data,
is the plane wave reflection coefficient, the angle of incidence for the plane wave is θ, x is cos (θ), ω is the angular frequency, J0Is a zero order Bessel function, r is the offset, h is the distance from the excitation source to the reflection plane, zris the distance from the receiving point to the interface, α1is the longitudinal wave velocity of the upper layer, α2Is the longitudinal wave velocity of the lower layer, ρ1Is the density of the upper layer, p2Is the density of the lower layer, and i is the imaginary unit.
6. The spherical wave-based prestack density inversion apparatus of claim 5, characterized in that the seismic data are seismic data with an incidence angle of less than 30 degrees and the seismic data are seismic data with an interface depth of less than 500 meters.
7. The spherical wave-based prestack density inversion apparatus of claim 5 or 6, wherein the inversion module is specifically configured to perform density ratio and velocity ratio inversion on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data simultaneously using a very fast simulated annealing algorithm.
8. The spherical wave-based prestack density inversion apparatus of claim 5 or 6, further comprising:
an inversion determination module, configured to determine, by using a very fast simulated annealing algorithm, an elastic parameter for performing inversion simultaneously with density through the following objective function formula before performing pre-stack density inversion of a frequency domain on the spherical wave reflection coefficient of the observed seismic data and the spherical wave reflection coefficient of the theoretical seismic data:
f (m) represents the matching degree of the observed seismic data and the theoretical seismic data, N represents the number of the selected frequency points participating in calculation, m represents a set of elastic parameters which are inverted simultaneously, and AVAOBS(ωn) Is the spherical wave reflection coefficient record, AVA, of each frequency point in the observed seismic data obtained by Fourier transformTHEO(ωn) З the З method З comprises З the З steps З of З calculating З spherical З wave З reflection З coefficient З records З of З all З frequency З points З in З theoretical З seismic З data З, З wherein З n З is З the З number З of З the З selected З frequency З point З, З the З size З of З the З change З range З of З the З elastic З parameters З of З which З the З numerical З values З of З F З (З m З) З are З smaller З than З a З preset З minimum З value З is З in З direct З proportion З to З the З uncertainty З of З an З inversion З result З, З and З when З the З F З (З m З) З is З smaller З than З the З preset З minimum З value З, З the З elastic З parameters З with З the З minimum З change З range З in З all З the З elastic З parameters З and З the З density З are З determined З to З be З inverted З simultaneously З. З
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