A seismic frequency band-dependent impedance inversion method and apparatus

CN117991362BActive Publication Date: 2026-09-08PETROCHINA CO LTD
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Patent Information

Application Number
CN202211375726.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-11-04
Publication Date
2026-09-08
Estimated Expiration
2042-11-04

AI Technical Summary

Technical Problem

因此,在进行地震反演或储层预测时,如果不考虑频散效应,直接把测井弹性参数资料用于反演过程中的模型约束或解释工作中的横向地震预测,不可避免地给反演结果或储层定量预测带来误差

Benefits of technology

[0062] The acquired seismic data is inverted to generate AVF frequency gathers reflecting the variation of seismic amplitude with frequency. Based on the acquired core and well logging data, rock physical modulus inversion is performed to determine the basic data for the rock physical model of the study area, thus constructing a frequency-dependent P-wave impedance frequency gather profile within the seismic band. Using the P-wave impedance frequency gather profile as the initial wave impedance model, wave impedance inversion based on model constraints is performed channel-by-channel on the AVF frequency gathers to obtain the inverted wave impedance frequency gathers or velocity frequency gathers for the study area. Channel-by-channel inversion within the frequency band can solve... Conventional frequency-varying time-frequency analysis for fluid identification suffers from low resolution and difficulty in quantitative analysis. This paper achieves a leap from the post-stack domain, pre-stack angle gather domain, and frequency gather domain in wave impedance seismic inversion analysis. It can analyze the variation of wave impedance with frequency, perform wave impedance inversion within the frequency band, and more accurately analyze reservoir characteristics for reservoir prediction. It can study wave impedance and velocity characteristics by frequency division, thereby enabling quantitative prediction of reservoir parameters and fluid flow based on porosity elasticity theory. Its application range is wide, and it can also quantitatively evaluate the hydrocarbon content and attenuation characteristics of complex reservoirs.

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Abstract

The application discloses a kind of seismic frequency band in frequency variable impedance inversion method and device.It includes: based on the seismic data inversion of study area, the AVF frequency gather reflecting the variation law of seismic amplitude with frequency is generated;Rock physics modulus inversion is carried out according to core data and logging data, and the rock physics model basic data of study area is determined;Based on logging data and rock physics model basic data, the longitudinal wave impedance frequency gather profile related to frequency in seismic frequency band is constructed from multiple pore equivalent medium theory model and pore medium elastic wave velocity dispersion-damping mesoscopic model;Based on longitudinal wave impedance frequency gather profile, AVF frequency gather is carried out wave impedance inversion based on model constraint per channel, and the wave impedance frequency gather or velocity frequency gather of study area is obtained.In frequency band, wave impedance inversion is carried out, the change of wave impedance with frequency is analyzed, reservoir characteristics are accurately analyzed, reservoir prediction can be carried out, and the oil and gas content and attenuation characteristics of complex reservoir can be quantitatively evaluated.
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Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology, and in particular to a method and apparatus for frequency-varying impedance inversion within a seismic frequency band. Background Technology

[0002] Deep unconventional oil and gas reservoirs are an important area for exploration and development. However, their deep burial, strong concealment, and characteristics of low porosity, low permeability, and thin thickness lead to low reserve accuracy and increased exploration costs. Seismic prediction of deep unconventional reservoirs currently faces numerous challenges, including strong heterogeneity, diverse pore structures, complex gas-water relationships, and complex porosity-permeability relationships. On the one hand, deep seismic waves have long vertical propagation distances, and compared to shallow and medium-depth reservoirs, the effective signal incident angle range is narrow, often lacking large-angle seismic signals, severely restricting the application of conventional reservoir prediction techniques. On the other hand, the pore structure and gas-water relationships in deep unconventional reservoirs are highly complex, and seismic inversion theories based on steady-state assumptions often have low accuracy when applied to predicting these reservoirs, making it difficult to accurately predict high-yield enrichment zones and resulting in high drilling costs. Therefore, developing a non-steady-state signal seismic inversion method suitable for predicting heterogeneous reservoirs is of great significance for meeting the exploration, development, and production needs of deep and complex oil and gas reservoirs, and has broad application prospects.

[0003] Seismic impedance inversion is a key technology in seismic interpretation. It utilizes geophysical inversion methods based on convolution models or wave equations to convert interface-type reflection seismic records into stratigraphic profiles comparable to well logging data. Common seismic impedance inversion methods can be divided into post-stack inversion and pre-stack inversion. Post-stack inversion retrieves P-wave impedance from self-excited and self-received zero-offset seismic traces, while pre-stack inversion retrieves elastic data such as P-wave and S-wave velocities and densities from pre-stack amplitude variation with offset (AVO) traces (Russell, 1988). These two techniques have played a positive role in seismic reservoir prediction serving oil and gas exploration and development. However, both post-stack and pre-stack inversion are based on the theory of homogeneous elastic media, assuming that P-wave impedance or P-wave and S-wave velocities are independent of frequency and that the reflected seismic signals from the subsurface are steady-state. When the actual subsurface medium deviates significantly from these assumptions, the obtained impedance or elastic parameters will differ greatly from the actual rock, thus introducing significant errors into seismic reservoir prediction. On the other hand, since it is based on a homogeneous elastic medium and does not consider the influence of fluid flow on the elastic parameters, when inverting reservoir parameters from these parameters, only parameters such as porosity, saturation and clay content can often be obtained (Avseth et al., 2005; Mavko et al., 2009), thus limiting the development of seismic reservoir prediction.

[0004] Traditional wave impedance inversion based on homogeneous elastic medium theory has limitations. In recent years, the porosity elastic mesoscale theory has emerged. This theory reveals that if a seismic wave propagating underground encounters a non-homogeneous body smaller than the seismic wave wavelength but larger than the pore size, strong velocity dispersion and attenuation will occur within the seismic band. This results in a significant difference between the P-wave velocity measured in the well logging band and the seismic wave propagation velocity within the seismic band. The degree of velocity dispersion and attenuation is related to the fluid saturation, permeability, viscosity, and pore geometry parameters (White, 1975; Dutta et al., 1979; Chapman et al., 2002; Pride et al., 2004). Therefore, if the dispersion effect is not considered when performing seismic inversion or reservoir prediction, and well logging elastic parameter data is directly used for model constraints or lateral seismic prediction in the inversion process, errors will inevitably be introduced into the inversion results or quantitative reservoir prediction. Existing dispersion analysis techniques combine the classical AVO approximation formula with the velocity dispersion formula, and use time-frequency analysis methods to extract the gradient of P-wave reflectivity relative to frequency or fluid mobility properties indicating fluid from low-frequency seismic information (Wilson et al., 2009; Silin and Goloshubin, 2010). These methods only characterize the attenuation characteristics of reflected seismic wave amplitude and are qualitative analysis methods that cannot truly quantitatively assess velocity dispersion and attenuation within the seismic scale. Summary of the Invention

[0005] The inventors of this application have discovered that classical wave impedance or elastic parameter inversion techniques are based on the theory of elastic media, which assumes that reflected seismic signals from underground are steady-state, meaning that their signal energy does not attenuate or absorb during propagation. Therefore, in the inversion process, the reflected seismic signal is considered as a whole for use as input to the inversion algorithm. The resulting wave impedance reflects comprehensive information across the entire frequency band, failing to characterize velocity variations or attenuation within the seismic frequency band.

[0006] Frequency-varying impedance inversion techniques based on the porosity elastic mesoscale theory are still in the exploratory research stage. On the one hand, the porosity elastic theory itself is not mature enough, and on the other hand, there is a lack of inversion theory support. Therefore, it is not possible to make quantitative predictions about reservoirs based on the porosity elastic mesoscale theory. Although the classic frequency-varying AVO analysis technique introduces the mesoscale theory, it simply uses the time-spectrum decomposition method to qualitatively characterize the attenuation characteristics of seismic waveforms at the reflection interface. It cannot truly quantitatively assess the dispersion and attenuation of formation velocities within the seismic scale. Moreover, its results are strongly affected by the resolution of the spectral decomposition algorithm and "wavelet overprinting," and it cannot quantitatively predict reservoir parameters and fluid flow. Therefore, current seismic-scale dispersion and attenuation analysis techniques lack quantitative evaluation methods.

[0007] In view of the above problems, the present invention is proposed to provide a method and apparatus for seismic frequency-varying impedance inversion within a seismic frequency band, which overcomes or at least partially solves the above problems.

[0008] This invention provides a method for inverting frequency-varying impedance within a seismic frequency band, comprising:

[0009] Obtain core data, well logging data and seismic data for the study area;

[0010] Based on the aforementioned seismic data, AVF frequency gathers reflecting the variation of seismic amplitude with frequency are generated through inversion.

[0011] Based on the core data and well logging data, the rock physical modulus inversion was performed to determine the basic data of the rock physical model for the study area. Based on the well logging data and the basic data of the rock physical model, a frequency-dependent P-wave impedance frequency gather profile within the seismic band was constructed using the multi-pore equivalent medium theoretical model and the porous medium elastic wave velocity dispersion-attenuation mesoscopic model.

[0012] Using the longitudinal wave impedance frequency gather profile as the initial wave impedance model, wave impedance inversion based on model constraints is performed on the AVF frequency gather channel by channel to obtain the inverted wave impedance frequency gather or velocity frequency gather of the study area.

[0013] In some optional embodiments, acquiring core data, well logging data, and seismic data of the study area includes:

[0014] Acquire experimentally measured core velocity dispersion data, well logging data of high-frequency P-wave velocity and density, porosity, permeability and saturation, and seismic data within the study area.

[0015] In some optional embodiments, the step of performing rock physical modulus inversion based on the core data and well logging data to determine the basic data of the rock physical model for the study area includes:

[0016] Based on core velocity dispersion data and well logging data, nonlinear rock physics inversion was carried out using a multi-pore equivalent medium theoretical model and a porous medium elastic wave velocity dispersion-attenuation mesoscopic model to determine the rock matrix elastic modulus, the equivalent pore aspect ratio, and the dry rock skeleton model of the study area.

[0017] In some optional embodiments, based on the well logging data and rock physics model fundamental data, a frequency-dependent P-wave impedance frequency gather profile within the seismic band is constructed using a multi-porosity equivalent medium theoretical model and a porous medium elastic wave velocity dispersion-attenuation mesoscopic model, including:

[0018] Based on high-frequency logging data from well logging data and basic data from the obtained rock physics model, the equivalent porosity of the rock is obtained from the inversion based on the multi-pore equivalent medium theoretical model and the porosity medium elastic wave velocity dispersion-attenuation mesoscopic model, and the bulk modulus of the rock is determined.

[0019] Based on the equivalent porosity and bulk modulus of the rock, as well as the constant wave shear modulus and density in the well logging data, frequency-dependent P-wave impedance frequency gather profiles are constructed within the seismic band.

[0020] In some optional embodiments, the objective function of the nonlinear rock physics inversion is:

[0021]

[0022] In the formula: F1(K m G m ξ) is the objective function for rock physics inversion;

[0023] V p V s ρ and ρ represent the longitudinal wave velocity, transverse wave velocity, and density of the partially saturated rock as measured in the actual experiment.

[0024] For partially saturated porous rocks, the complex bulk modulus is denoted as .

[0025] Re denotes taking the real part of a complex number;

[0026] K m and G m These are the bulk modulus and shear modulus of the rock matrix to be determined, respectively.

[0027] ξ is the equivalent porosity aspect ratio;

[0028] in:

[0029] The theoretical model of the multi-porous equivalent medium adopted is as follows:

[0030]

[0031] and

[0032]

[0033] Where: K m and G m These are the bulk modulus and shear modulus of the rock matrix, respectively.

[0034] K dry and G dry These are the bulk modulus and shear modulus of the dry rock skeleton, respectively.

[0035] ξ is the equivalent porosity of the rock;

[0036] Φ represents the porosity of the rock;

[0037] a and b satisfy: P *i -Q *i =a+bK * (y) / G * (y), P *i and Q *i It is the polarization factor of the dry rock framework, K * (y) and G * (y) represents the equivalent bulk modulus and shear modulus of the rock;

[0038] in:

[0039] The porous medium elastic wave velocity dispersion-attenuation mesoscopic model used is as follows:

[0040]

[0041] In the formula: For partially saturated porous rocks, the complex bulk modulus is denoted as .

[0042] K ∞ The bulk modulus of saturated rock at the high-frequency limit;

[0043] R1, R2, Q1, and Q2 are constants related to parameters such as the elastic modulus of saturated rock and the skeleton modulus of dry rock; Z1 and Z2 are impedances, and r is the outer radius of the porphyritic saturated sphere. g ω is the inner radius of the gas contained in the center of the saturated sphere, i is the angular frequency, and i is the imaginary unit.

[0044] In some optional embodiments, when performing model-constrained impedance inversion channel-by-channel on the AVF frequency gather, the objective function for model-constrained impedance inversion is as follows:

[0045]

[0046] Where F2(m) is the objective function for wave impedance inversion, S is the actual seismic record, W is the wavelet matrix, D is the difference operator matrix, m is the inverted wave impedance, m0 is the initial wave impedance model, and λ is the damping factor.

[0047] In some optional embodiments, the above method further includes: generating a cross plot of the study area based on the inverted wave impedance frequency gather or velocity frequency gather, the cross plot reflecting the variation of wave impedance or velocity with frequency in the study area.

[0048] In some optional embodiments, the above method further includes:

[0049] Analyze the frequency variation characteristics of the seismic impedance of the target section in the reservoir based on the cross-plot; or

[0050] The zero-frequency impedance and gradient of the target segment in the reservoir are extracted from the inverted wave impedance frequency gather or velocity frequency gather, and the hydrocarbon-bearing properties and attenuation characteristics of the target segment in the reservoir are evaluated based on the zero-frequency impedance and gradient.

[0051] This invention provides a seismic frequency-varying impedance inversion device, comprising:

[0052] The acquisition module is used to acquire core data, well logging data, and seismic data of the study area;

[0053] The first inversion module is used to generate AVF frequency gathers that reflect the variation of earthquake amplitude with frequency based on the seismic data.

[0054] The profile construction module is used to perform rock physical modulus inversion based on the core data and well logging data, and determine the basic data of the rock physical model of the study area; based on the well logging data and the basic data of the rock physical model, the frequency-related P-wave impedance frequency gather profile in the seismic band is constructed using the multi-pore equivalent medium theoretical model and the porous medium elastic wave velocity dispersion-attenuation mesoscopic model.

[0055] The second inversion module is used to perform wave impedance inversion based on model constraints on the AVF frequency gather channel by channel using the longitudinal wave impedance frequency gather profile as the initial wave impedance model, so as to obtain the inverted wave impedance frequency gather or velocity frequency gather of the study area.

[0056] In some optional embodiments, the above-described apparatus further includes at least one of the following modules:

[0057] The plot generation module is used to generate a cross plot of the study area based on the inverted wave impedance frequency gather or velocity frequency gather. The cross plot reflects the change of wave impedance or velocity with frequency in the study area.

[0058] The evaluation and analysis module is used to analyze the frequency variation characteristics of the seismic impedance of the target segment in the reservoir based on the cross plot; or to extract the zero-frequency impedance and gradient of the target segment in the reservoir based on the inverted impedance frequency gather or velocity frequency gather, and to evaluate the hydrocarbon content and attenuation characteristics of the target segment in the reservoir based on the zero-frequency impedance and gradient.

[0059] This invention provides a computer storage medium, characterized in that the computer storage medium stores computer-executable instructions, which, when executed by a processor, implement the above-described seismic frequency band frequency-varying impedance inversion method.

[0060] This invention provides a computer device, characterized in that it includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described seismic frequency band frequency-varying impedance inversion method.

[0061] The beneficial effects of the above-described technical solutions provided in the embodiments of the present invention include at least the following:

[0062] The acquired seismic data is inverted to generate AVF frequency gathers reflecting the variation of seismic amplitude with frequency. Based on the acquired core and well logging data, rock physical modulus inversion is performed to determine the basic data for the rock physical model of the study area, thus constructing a frequency-dependent P-wave impedance frequency gather profile within the seismic band. Using the P-wave impedance frequency gather profile as the initial wave impedance model, wave impedance inversion based on model constraints is performed channel-by-channel on the AVF frequency gathers to obtain the inverted wave impedance frequency gathers or velocity frequency gathers for the study area. Channel-by-channel inversion within the frequency band can solve... Conventional frequency-varying time-frequency analysis for fluid identification suffers from low resolution and difficulty in quantitative analysis. This paper achieves a leap from the post-stack domain, pre-stack angle gather domain, and frequency gather domain in wave impedance seismic inversion analysis. It can analyze the variation of wave impedance with frequency, perform wave impedance inversion within the frequency band, and more accurately analyze reservoir characteristics for reservoir prediction. It can study wave impedance and velocity characteristics by frequency division, thereby enabling quantitative prediction of reservoir parameters and fluid flow based on porosity elasticity theory. Its application range is wide, and it can also quantitatively evaluate the hydrocarbon content and attenuation characteristics of complex reservoirs.

[0063] The method provided in this invention is based on the multi-pore equivalent medium theory and the elastic wave velocity dispersion-attenuation mesoscopic model of porous media. It inverts the equivalent porosity aspect ratio of rocks from well logging data and constructs a frequency-dependent P-wave impedance gather profile within the seismic frequency band. Based on the model inversion method, it establishes wave impedance seismic traces for each frequency component inverted from the AVF seismic frequency gather, forming a "frequency-varying impedance gather" profile where velocity varies with frequency, which can obtain more accurate analysis results.

[0064] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings.

[0065] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0066] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0067] Figure 1 This is a flowchart of the frequency-varying impedance inversion method within the seismic frequency band in Embodiment 1 of the present invention;

[0068] Figure 2 This is a flowchart of the frequency-varying impedance inversion method within the seismic frequency band in Embodiment 2 of the present invention;

[0069] Figure 3 This is a schematic diagram illustrating the principle of the frequency-varying impedance inversion method within the seismic frequency band in Embodiment 2 of the present invention;

[0070] Figure 4 This is a schematic diagram of the logging results of well LT1 in Embodiment 2 of the present invention;

[0071] Figure 5 This is a schematic diagram of the reservoir velocity dispersion curve of well LT1 in Embodiment 2 of the present invention;

[0072] Figure 6 This is a schematic diagram of the equivalent porosity aspect ratio obtained by inversion in Embodiment 2 of the present invention;

[0073] Figure 7 This is a schematic diagram of the frequency gather of the initial velocity model established in Embodiment 2 of the present invention;

[0074] Figure 8 This is a schematic diagram of the AVF gather and ImpVF gather inverted from the post-stack seismic profile in Embodiment 2 of the present invention;

[0075] Figure 9 This is a schematic diagram of ImpVF cross-section analysis at the oil and gas layer and non-oil and gas layer in the well bypass in Embodiment 2 of the present invention;

[0076] Figure 10 This is a schematic diagram of the seismic frequency band frequency-varying impedance inversion device in an embodiment of the present invention. Detailed Implementation

[0077] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0078] Because seismic waves propagating in unconventional reservoirs exhibit extremely strong non-steady-state characteristics, i.e., the reflected signal varies significantly with frequency within the seismic frequency band, in order to accurately predict reservoir parameters and fluid flow properties, this invention provides a frequency-varying impedance inversion method within the seismic frequency band. This method is a frequency-varying seismic wave impedance inversion method that can evaluate velocity dispersion and attenuation within the seismic scale range, laying a reliable data foundation for quantitative prediction of reservoir parameters and fluid flow based on the porosity elastic mesoscale theory.

[0079] Example 1

[0080] Embodiment 1 of the present invention provides a method for inverting frequency-varying impedance within a seismic frequency band, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0081] Step S101: Obtain core data, well logging data and seismic data for the study area.

[0082] It can acquire experimentally measured core velocity dispersion data, well logging data of high-frequency P-wave velocity and density, porosity, permeability and saturation, as well as seismic data within the study area. The core velocity dispersion data can be obtained from broadband rock physics experiments, and the seismic data can be low-frequency seismic pure wave data, etc.

[0083] Step S102: Based on seismic data, generate AVF frequency gathers that reflect the variation of seismic amplitude with frequency.

[0084] The seismic data collected in step S101 are processed channel by channel for frequency-division seismic reflectivity inversion to generate AVF frequency gathers showing the amplitude variation of reflected seismic waves with frequency. Here, AVF stands for Amplitude Variation with Frequency.

[0085] Step S103: Perform rock physical modulus inversion based on core data and well logging data to determine the basic data of the rock physical model for the study area.

[0086] Based on core velocity dispersion data and well logging data, nonlinear rock physics inversion was performed using a multi-pore equivalent medium theoretical model and a porous medium elastic wave velocity dispersion-attenuation mesoscopic model to determine the rock matrix elastic modulus, the equivalent porosity, and the dry rock skeleton model of the study area. This study uses the rock matrix elastic modulus, equivalent porosity, and dry rock skeleton model as basic rock physics model data as an example; however, other basic rock physics model data can be calculated according to actual needs.

[0087] Among them, the White-Dutta-Ode mesoscopic model can be selected for the elastic wave velocity dispersion-attenuation mesoscopic model in porous media.

[0088] Step S104: Based on well logging data and rock physics model data, construct frequency-dependent P-wave impedance frequency gather profiles within the seismic band using the multi-pore equivalent medium theoretical model and the porous medium elastic wave velocity dispersion-attenuation mesoscopic model.

[0089] Based on high-frequency logging data and fundamental data from the obtained rock physics model, and using a multi-pore equivalent medium theoretical model and a porous medium elastic wave velocity dispersion-attenuation mesoscopic model, the equivalent porosity of the rock and its bulk modulus are obtained through inversion. Based on the rock's equivalent porosity, bulk modulus, and the constant wave shear modulus and density from the logging data, a frequency-dependent P-wave impedance frequency gather profile is constructed within the seismic band. This P-wave impedance frequency gather profile can characterize the wave impedance corresponding to different frequencies generated from the logging data.

[0090] Step S105: Using the longitudinal wave impedance frequency gather profile as the initial wave impedance model, perform wave impedance inversion based on model constraints on each channel of the AVF frequency gather to obtain the inverted wave impedance frequency gather or velocity frequency gather of the study area.

[0091] In this step, based on the previously established longitudinal wave impedance frequency gather profile, wave impedance inversion is performed channel by channel within the frequency band to reflect the wave impedance characteristics of different channels, resulting in a "frequency-varying impedance gather" profile that reflects the change in velocity with frequency. Since wave impedance equals velocity multiplied by density, in practical applications, the obtained "frequency-varying impedance gather" profile can be either a wave impedance frequency gather or a velocity frequency gather. The previously established longitudinal wave impedance frequency gather profile can be used as the initial model during the inversion.

[0092] In the above method of this embodiment, on the one hand, based on the multi-pore equivalent medium theory and the porosity elastic wave velocity dispersion-attenuation mesoscopic model, the equivalent porosity aspect ratio of the rock is inverted from the well logging data and a frequency-related P-wave impedance gather profile is constructed within the seismic frequency band; on the other hand, based on the model inversion method, wave impedance seismic traces of each frequency component are inverted from the AVF seismic frequency gather, forming a "frequency-varying impedance gather" profile where the velocity changes with frequency, thereby enabling quantitative prediction of reservoir parameters and fluid flow based on porosity elasticity theory.

[0093] Example 2

[0094] Embodiment 2 of the present invention provides another implementation process for the frequency-varying impedance inversion method within the seismic frequency band, the process of which is as follows: Figure 2 As shown, the principle block diagram is as follows: Figure 3 As shown, the method includes the following steps:

[0095] Step S201: Obtain core data, well logging data and seismic data for the study area.

[0096] like Figure 3 The data acquired, as shown, includes core velocity dispersion data, well logging data, and post-stack seismic data. Post-stack seismic data can be low-frequency pure wave seismic data. After collecting post-stack seismic data, well logging data, and core velocity dispersion data within the work area, and performing seismic and well logging horizon calibration, the inverted seismic wavelet is determined.

[0097] like Figures 4-7 The image shows a schematic diagram of mesoscopic rock physics modeling of well LT1 in a study area, such as the Tarim Basin. Figure 4 This is the logging data for well LT1, including curves of P-wave velocity, density, S-wave velocity, and interpreted data such as clay content, porosity, saturation, and permeability. The target reservoir of this well is a tight dolomite reservoir with a porosity of less than 5% and a permeability of less than 0.5 mD.

[0098] Step S202: Based on seismic data, generate AVF frequency gathers that reflect the variation of seismic amplitude with frequency.

[0099] like Figure 3 As shown, frequency-division seismic reflectivity inversion is performed on each channel of the collected post-stack seismic data to generate AVF frequency gathers showing the variation of reflected seismic amplitude with frequency. Figure 8 and Figure 9 This is a schematic diagram illustrating the analysis of the frequency-varying impedance inversion effect from the LT1 well bypass seismic data. For example, Figure 8 As shown in the left figure, an example of seismic data, such as the post-stack seismic traces of well LT1, yields the AVF frequency gather as follows: Figure 8 As shown in the middle diagram, this is the AVF gather next to the well in the diagram.

[0100] Step S203: Perform rock physical modulus inversion based on core data and well logging data to determine the basic data of the rock physical model for the study area.

[0101] See Figure 3 The steps for mesoscopic rock physics modeling shown above involve using the collected core velocity dispersion data and well logging data to perform nonlinear rock physics inversion based on the multi-pore equivalent medium theory model and the White-Dutta-Ode mesoscopic model. The inversion calculation can be performed using the following formula (1) to determine the basic data for the rock physics model, such as the rock matrix elastic modulus, the equivalent porosity of the rock, and the dry rock skeleton model, applicable to the study area. For example, as... Figure 5The image shows the velocity dispersion curve of the LT1 well reservoir. It is a velocity dispersion curve of the reservoir segment generated based on the multi-pore equivalent medium theory and the White-Dutta-Ode mesoscopic model. It can be seen that there is obvious dispersion of velocity in the seismic band, although their absolute values ​​are relatively small. Figure 6 The image shows an example of the equivalent porosity ratio inverted from the LT1 well, which displays the inverted equivalent porosity ratio curve. The pore shape of the reservoir rock varies greatly.

[0102] The objective function for nonlinear rock physics inversion is:

[0103]

[0104] In the formula: F1(K m G m ξ) is the objective function for rock physics inversion;

[0105] V p V s ρ and ρ represent the longitudinal wave velocity, transverse wave velocity, and density of the partially saturated rock as measured in the actual experiment.

[0106] For partially saturated porous rocks, the complex bulk modulus is... It can be calculated using the following formula (4);

[0107] Re denotes taking the real part of a complex number;

[0108] K m and G m Let α be the bulk modulus and shear modulus of the rock matrix to be determined, respectively, and α be the equivalent porosity. These can be calculated using the following formulas (2) and (3).

[0109] in:

[0110] The theoretical model of the multi-porous equivalent medium adopted is as follows:

[0111]

[0112] and

[0113]

[0114] Where: K m and G m These are the bulk modulus and shear modulus of the rock matrix, respectively.

[0115] K dry and G dry These are the bulk modulus and shear modulus of the dry rock skeleton, respectively.

[0116] ξ is the equivalent porosity of the rock;

[0117] Φ represents the porosity of the rock;

[0118] a and b satisfy: P *i -Q *i =a+bK * (y) / G * (y), P *i and Q *i It is the polarization factor of the dry rock framework, K * (y) and G * (y) represents the equivalent bulk modulus and shear modulus of the rock;

[0119] in:

[0120] The White-Dutta-Ode mesoscopic model for elastic wave velocity dispersion-attenuation in porous media is as follows:

[0121]

[0122] In the formula: For partially saturated porous rocks, the complex bulk modulus is denoted as .

[0123] K ∞ The bulk modulus of saturated rock at the high-frequency limit;

[0124] R1, R2, Q1, and Q2 are constants, which are related to parameters such as the elastic modulus of saturated rock and the skeleton modulus of dry rock; Z1 and Z2 are impedances, and r is the outer radius of the porphyritic saturated sphere. g ω is the inner radius of the gas contained in the center of the saturated sphere, i is the angular frequency, and i is the imaginary unit.

[0125] Step S204: Based on well logging data and rock physics model data, construct frequency gather profiles of P-wave impedance related to frequency within the seismic band using the multi-pore equivalent medium theoretical model and the porous medium elastic wave velocity dispersion-attenuation mesoscopic model.

[0126] Based on the high-frequency logging data collected in step S201 and the basic data of the rock physics model provided in step S203, the equivalent porosity of the rock is inverted from the logging data according to the multi-pore equivalent medium theory and the White-Dutta-Ode mesoscopic model. The bulk modulus of the saturated rock is calculated using the above formulas (2), (3), and (4). Then, together with the shear modulus and density of the logging data, a frequency-dependent P-wave impedance frequency gather profile in the seismic band is constructed as the initial model of frequency-varying impedance.

[0127] Steps S203 and S204 enable mesoscale rock physics modeling of well logging and core dispersion data, generating an initial frequency-varying impedance model. Figure 7 An example of the initial velocity model frequency gather established for LT1 well can be the velocity frequency gather within the seismic band of 5-60Hz established from high-frequency logging curves. Since wave impedance equals velocity multiplied by density, the velocity frequency gather can be obtained after obtaining the wave impedance frequency gather.

[0128] Step S205: Using the longitudinal wave impedance frequency gather profile as the initial wave impedance model, perform wave impedance inversion based on model constraints on each channel of the AVF frequency gather to obtain the inverted wave impedance frequency gather or velocity frequency gather of the study area.

[0129] like Figure 3 As shown, based on the AVF frequency gather obtained above, the determined seismic wavelet, and the obtained frequency-varying impedance initial model, a frequency-by-frequency trace-based wave impedance inversion is performed to obtain the wave impedance frequency gather. Of course, the velocity frequency gather can also be obtained. Since density is independent of frequency, the characteristics of the impedance frequency gather and the velocity frequency gather are the same; they differ only by a density constant. Figure 8 The diagram shows AVF gathers and ImpVF gathers inverted from post-stack seismic profiles. Based on Figure 8 The inverted AVF frequency gather shown in the middle figure is used to perform wave impedance inversion based on model constraints on a frequency-by-frequency basis. The initial model used is the initial model obtained in step S204, and the wave impedance at the corresponding frequency is generated from the well logging data, i.e. Figure 8 The right figure shows the wave impedance frequency gather, i.e., the well-side ImpVF gather. It can be seen that on the AVF gather profile, below the target layer Wusonggeer, the reflection amplitude increases significantly with increasing frequency, with the starting point appearing at 27Hz, as indicated by the arrow in the figure. On the corresponding ImpVF gather profile, a similar rapid increase in velocity with frequency is observed. This indicates that after hydrocarbons are present in the reservoir, a significant velocity dispersion effect will be observed within the seismic frequency band, and this phenomenon can be used to identify fluids.

[0130] When performing channel-by-channel wave impedance inversion based on model constraints on the AVF frequency gather, the objective function for model-constrained wave impedance inversion is as follows:

[0131]

[0132] Where F2(m) is the objective function for wave impedance inversion, S is the actual seismic record, W is the wavelet matrix, D is the difference operator matrix, m is the inverted wave impedance, m0 is the initial wave impedance model, and λ is the damping factor.

[0133] Step S206: Create a cross plot of the study area based on the inverted wave impedance frequency gather or velocity frequency gather.

[0134] A cross-plot is created using the wave impedance frequency gather data obtained in step S205, such as... Figure 9 The diagram shown is a schematic diagram of ImpVF cross-plot analysis between oil and gas layers and non-oil and gas layers in the wellbore. The cross-plot reflects the changes in wave impedance or velocity with frequency in the study area.

[0135] Step S207: Analyze the characteristics of seismic impedance variation with frequency in the target section of the reservoir based on the cross plot.

[0136] Cross plots can be used to analyze the characteristics of wave impedance as a function of frequency.

[0137] Step S208: Extract the zero-frequency impedance and gradient of the target segment in the reservoir from the inverted wave impedance frequency gather or velocity frequency gather, and evaluate the hydrocarbon-bearing properties and attenuation characteristics of the target segment in the reservoir based on the zero-frequency impedance and gradient.

[0138] Steps S207 and S208 can be executed simultaneously or one of them can be executed to analyze the seismic impedance variation characteristics of the target layer with frequency, or use the following formula (6) to extract the zero-frequency impedance (A when f=0) and gradient attributes from the wave impedance frequency gather data determined in step S205 based on the least squares inversion algorithm, and analyze and evaluate the hydrocarbon content and attenuation characteristics of the reservoir.

[0139] Imp(f) = A + Gln(f) (6)

[0140] In the formula, Imp(f) is the wave impedance obtained by inversion in step S205, f is the frequency, and A and G are the intercept and gradient to be determined.

[0141] Figure 9 This is an ImpVF cross plot analysis of the oil and gas layer and the non-oil and gas layer near the wellbore. The black square scatter points in the figure represent the points from... Figure 9 The velocity values ​​at various frequencies at t=4968ms in the reservoir were picked up. The black diamond scatter points represent the velocity values ​​from the reservoir at various frequencies. Figure 9 The velocity values ​​at various frequencies above the reservoir, at t=4936ms, are picked up. It can be seen that the increase in ImpVF after the reservoir contains oil and gas is much greater than that in the non-oil and gas layer, indicating that ImpVF can effectively identify oil and gas reservoirs.

[0142] The frequency-varying impedance seismic inversion method described in this invention, by performing channel-by-channel wave impedance inversion on AVF frequency gathers extracted from seismic traces, forms a "dispersion impedance" profile in which P-wave impedance varies with frequency. This breaks through the research scope of existing seismic impedance inversion methods and realizes a leap in seismic inversion from the post-stack domain, pre-stack angular gather domain, to the frequency gather domain. Conventional seismic inversion methods, including recursive inversion, model inversion, and elastic impedance inversion, are for time-domain and angular-domain seismic data; currently, there is no known seismic impedance inversion technique for the frequency domain.

[0143] The key technologies of the aforementioned frequency-varying impedance seismic inversion method are based on a mesoscopic rock physics model, inverting the equivalent porosity aspect ratio of rocks from well logging data, constructing an initial frequency impedance model gather within the seismic band, and implementing a frequency-varying impedance inversion algorithm. This method solves the problems of low resolution and low quantification of "interface type" attributes in conventional frequency-varying AVO (Amplitude Variation with Offset) methods, which rely on time-frequency analysis to identify fluid presence through amplitude spectrum changes with frequency. Furthermore, this method can be applied to both post-stack and pre-stack seismic data, thus expanding the application scope of post-stack seismic data and maximizing the extraction of hydrocarbon information contained in seismic waveforms. It provides a new tool for the quantitative evaluation of hydrocarbon-bearing properties and attenuation characteristics of complex reservoirs, especially for deep seismic exploration.

[0144] Based on the same inventive concept, embodiments of the present invention also provide a seismic frequency band frequency-varying impedance inversion device. This device can be installed in a device with computational processing capabilities, and its structure is as follows. Figure 10 As shown, it includes:

[0145] Module 11 is used to acquire core data, well logging data and seismic data of the study area;

[0146] The first inversion module 12 is used to generate AVF frequency gathers that reflect the variation of earthquake amplitude with frequency based on seismic data.

[0147] The profile construction module 13 is used to perform rock physical modulus inversion based on core data and well logging data, and determine the basic data of the rock physical model in the study area; based on well logging data and basic data of the rock physical model, the frequency-related P-wave impedance frequency gather profile in the seismic band is constructed using the multi-pore equivalent medium theoretical model and the porous medium elastic wave velocity dispersion-attenuation mesoscopic model.

[0148] The second inversion module 14 is used to perform wave impedance inversion based on model constraints on the AVF frequency gather channel by channel using the longitudinal wave impedance frequency gather profile as the initial wave impedance model, so as to obtain the inverted wave impedance frequency gather or velocity frequency gather of the study area.

[0149] In some optional embodiments, the above-described apparatus further includes at least one of the following modules:

[0150] The plot generation module 15 is used to generate a cross plot of the study area based on the inverted wave impedance frequency gather or velocity frequency gather. The cross plot reflects the change of wave impedance or velocity with frequency in the study area.

[0151] Evaluation and analysis module 16 is used to analyze the characteristics of seismic impedance variation with frequency in the target segment of the reservoir based on the cross plot; or to extract the zero-frequency impedance and gradient of the target segment in the reservoir based on the inverted impedance frequency gather or velocity frequency gather, and evaluate the hydrocarbon content and attenuation characteristics of the target segment in the reservoir based on the zero-frequency impedance and gradient.

[0152] This invention also provides a computer storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described seismic frequency band frequency-varying impedance inversion method.

[0153] This invention also provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described method for frequency-varying impedance inversion within the seismic frequency band.

[0154] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0155] Unless otherwise specifically stated, terms such as processing, calculation, operation, determination, display, etc., may refer to the actions and / or processes of one or more processing or computing systems or similar devices that represent the manipulation and conversion of data representing physical (e.g., electronic) quantities within the registers or memory of the processing system into other data similarly representing physical quantities within the memory, registers, or other such information storage, transmission, or display devices of the processing system. Information and signals can be represented using any of a variety of different techniques and methods. For example, data, instructions, commands, information, signals, bits, symbols, and chips mentioned throughout the above description can be represented by voltage, current, electromagnetic waves, magnetic fields or particles, light fields or particles, or any combination thereof.

[0156] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process may be rearranged without departing from the scope of this disclosure. The appended method claims provide elements of various steps in an exemplary order and are not intended to limit the scope to the specific order or hierarchy described.

[0157] In the detailed description above, various features are combined together in a single embodiment to simplify this disclosure. This approach to disclosure should not be construed as reflecting an intention that embodiments of the claimed subject matter require more features than are explicitly stated in each claim. Rather, as reflected in the appended claims, the invention is presented with fewer features than all of the features in a single disclosed embodiment. Therefore, the appended claims are hereby explicitly incorporated into the detailed description, with each claim representing a separate preferred embodiment of the invention.

[0158] Those skilled in the art will also understand that the various illustrative logic blocks, modules, circuits, and algorithm steps described in conjunction with the embodiments herein can be implemented as electronic hardware, computer software, or a combination thereof. To clearly illustrate the interchangeability between hardware and software, the various illustrative components, blocks, modules, circuits, and steps described above are generally described in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system. Those skilled in the art can implement the described functionality in alternative ways for each specific application; however, such implementation decisions should not be construed as departing from the scope of this disclosure.

[0159] The steps of the methods or algorithms described in conjunction with the embodiments herein can be directly embodied in hardware, software modules executed by a processor, or a combination thereof. The software modules can reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disks, removable disks, CD-ROMs, or any other form of storage medium well known in the art. An exemplary storage medium is connected to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and storage medium can reside in an ASIC. The ASIC can reside in a user terminal. Alternatively, the processor and storage medium can exist as discrete components in the user terminal.

[0160] For software implementation, the techniques described in this application can be implemented using modules (e.g., procedures, functions, etc.) that perform the functions described in this application. This software code can be stored in memory units and executed by a processor. The memory units can be implemented within the processor or outside the processor; in the latter case, they are communicatively coupled to the processor via various means, as is well known in the art.

[0161] The foregoing description includes examples of one or more embodiments. It is certainly impossible to describe all possible combinations of components or methods in order to describe the above embodiments, but those skilled in the art will recognize that further combinations and arrangements of the various embodiments are possible. Therefore, the embodiments described herein are intended to cover all such changes, modifications, and variations that fall within the scope of the appended claims. Furthermore, the term "comprising" as used in the specification or claims is interpreted in a manner similar to the term "including," as interpreted when used as a conjunction in the claims. Additionally, the use of any term "or" in the specification of the claims is intended to mean "non-exclusive or."

Claims

1. A method for inverting frequency-varying impedance within a seismic frequency band, characterized in that, include: Obtain core data, well logging data and seismic data for the study area; Based on the aforementioned seismic data, AVF frequency gathers reflecting the variation of seismic amplitude with frequency are generated through inversion. Based on the core data and well logging data, the rock physical modulus inversion was performed to determine the basic data of the rock physical model for the study area. Based on the well logging data and the basic data of the rock physical model, a frequency-dependent P-wave impedance frequency gather profile within the seismic band was constructed using the multi-pore equivalent medium theoretical model and the porous medium elastic wave velocity dispersion-attenuation mesoscopic model. Using the longitudinal wave impedance frequency gather profile as the initial wave impedance model, wave impedance inversion based on model constraints is carried out channel by channel on the AVF frequency gather to obtain the inverted wave impedance frequency gather or velocity frequency gather of the study area. The theoretical model of the multi-porous equivalent medium is as follows: ; and ; In the formula: and These are the bulk modulus and shear modulus of the rock matrix, respectively. and These are the bulk modulus and shear modulus of the dry rock skeleton, respectively. The equivalent porosity of the rock; Φ represents the porosity of the rock; a and b satisfy: , and It is the polarization factor of the dry rock framework. and For the equivalent bulk modulus and shear modulus of the rock; The porous medium elastic wave velocity dispersion-attenuation mesoscopic model is as follows: ; In the formula: For partially saturated porous rocks, the complex bulk modulus is denoted as . The bulk modulus of saturated rock at the high-frequency limit; X , , , , It is a constant and is related to the elastic modulus of saturated rock and the skeleton modulus of dry rock. , Let r be the impedance, and r be the outer radius of the mottled saturated sphere. The inner radius of the gas contained in the center of the mottled saturated sphere. ω is the angular frequency, and i is the imaginary unit; When performing channel-by-channel wave impedance inversion on the AVF frequency gather, the objective function for model-constrained wave impedance inversion is as follows: ; In the formula, Let be the objective function for wave impedance inversion. This is an actual earthquake record. For wavelet matrix, For difference operator matrices, For the inverted wave impedance, For the initial model of wave impedance, is the damping factor.

2. The method as described in claim 1, characterized in that, The acquisition of core data, well logging data, and seismic data for the study area includes: Acquire experimentally measured core velocity dispersion data, well logging data of high-frequency P-wave velocity and density, porosity, permeability and saturation, and seismic data within the study area.

3. The method as described in claim 2, characterized in that, The process of inverting the rock physical modulus based on the core data and well logging data to determine the basic data for the rock physical model of the study area includes: Based on core velocity dispersion data and well logging data, nonlinear rock physics inversion was carried out using a multi-pore equivalent medium theoretical model and a porous medium elastic wave velocity dispersion-attenuation mesoscopic model to determine the rock matrix elastic modulus, the equivalent pore aspect ratio, and the dry rock skeleton model of the study area.

4. The method as described in claim 3, characterized in that, Based on the well logging data and rock physics model data, a frequency-dependent P-wave impedance frequency gather profile within the seismic band is constructed using a multi-porosity equivalent medium theoretical model and a porous medium elastic wave velocity dispersion-attenuation mesoscopic model, including: Based on high-frequency logging data from well logging data and basic data from the obtained rock physics model, the equivalent porosity of the rock is obtained from the inversion based on the multi-pore equivalent medium theoretical model and the porosity medium elastic wave velocity dispersion-attenuation mesoscopic model, and the bulk modulus of the rock is determined. Based on the equivalent porosity and bulk modulus of the rock, as well as the constant wave shear modulus and density in the well logging data, frequency-dependent P-wave impedance frequency gather profiles are constructed within the seismic band.

5. The method as described in claim 4, characterized in that, The objective function for the nonlinear rock physics inversion is: ; In the formula: The objective function for rock physics inversion; , , These represent the longitudinal wave velocity, transverse wave velocity, and density of partially saturated rock as measured in practice. For partially saturated porous rocks, the complex bulk modulus is denoted as . Re denotes taking the real part of a complex number; and These are the bulk modulus and shear modulus of the rock matrix to be determined, respectively. The aspect ratio is the equivalent porosity.

6. The method according to any one of claims 1-5, characterized in that, Also includes: Based on the inverted wave impedance frequency gather or velocity frequency gather, a cross plot of the study area is prepared. The cross plot reflects the variation of wave impedance or velocity with frequency in the study area.

7. The method as described in claim 6, characterized in that, Also includes: Based on the cross-plot analysis, the characteristics of seismic impedance variation with frequency in the target layer of the reservoir are analyzed. or The zero-frequency impedance and gradient of the target segment in the reservoir are extracted from the inverted wave impedance frequency gather or velocity frequency gather, and the hydrocarbon-bearing properties and attenuation characteristics of the target segment in the reservoir are evaluated based on the zero-frequency impedance and gradient.

8. A frequency-varying impedance inversion device within a seismic frequency band, characterized in that, include: The acquisition module is used to acquire core data, well logging data, and seismic data of the study area; The first inversion module is used to generate AVF frequency gathers that reflect the variation of earthquake amplitude with frequency based on the seismic data. The profile construction module is used to perform rock physical modulus inversion based on the core data and well logging data, and determine the basic data of the rock physical model of the study area; based on the well logging data and the basic data of the rock physical model, the frequency-related P-wave impedance frequency gather profile in the seismic band is constructed using the multi-pore equivalent medium theoretical model and the porous medium elastic wave velocity dispersion-attenuation mesoscopic model. The theoretical model of the multi-porous equivalent medium is as follows: ; and ; In the formula: and These are the bulk modulus and shear modulus of the rock matrix, respectively. and These are the bulk modulus and shear modulus of the dry rock skeleton, respectively. The equivalent porosity of the rock; Φ represents the porosity of the rock; a and b satisfy: , and It is the polarization factor of the dry rock framework. and For the equivalent bulk modulus and shear modulus of the rock; The porous medium elastic wave velocity dispersion-attenuation mesoscopic model is as follows: ; In the formula: For partially saturated porous rocks, the complex bulk modulus is denoted as . The bulk modulus of saturated rock at the high-frequency limit; X , , , , It is a constant and is related to the elastic modulus of saturated rock and the skeleton modulus of dry rock. , Let r be the impedance, and r be the outer radius of the mottled saturated sphere. The inner radius of the gas contained in the center of the mottled saturated sphere. ω is the angular frequency, and i is the imaginary unit; The second inversion module is used to perform wave impedance inversion based on model constraints on the AVF frequency gather channel by channel using the longitudinal wave impedance frequency gather profile as the initial wave impedance model, so as to obtain the inverted wave impedance frequency gather or velocity frequency gather of the study area. When performing channel-by-channel wave impedance inversion on the AVF frequency gather, the objective function for model-constrained wave impedance inversion is as follows: ; In the formula, Let be the objective function for wave impedance inversion. This is an actual earthquake record. For wavelet matrix, For difference operator matrices, For the inverted wave impedance, For the initial model of wave impedance, is the damping factor.

9. The apparatus as claimed in claim 8, characterized in that, It also includes at least one of the following modules: The plot generation module is used to generate a cross plot of the study area based on the inverted wave impedance frequency gather or velocity frequency gather. The cross plot reflects the change of wave impedance or velocity with frequency in the study area. The evaluation and analysis module is used to analyze the frequency variation characteristics of seismic wave impedance in the target layer of the reservoir based on the cross plot. Alternatively, the zero-frequency impedance and gradient of the target segment in the reservoir can be extracted from the inverted wave impedance frequency gather or velocity frequency gather, and the hydrocarbon-bearing properties and attenuation characteristics of the target segment in the reservoir can be evaluated based on the zero-frequency impedance and gradient.

10. A computer storage medium, characterized in that, The computer storage medium stores computer-executable instructions, which, when executed by a processor, implement the seismic frequency-varying impedance inversion method according to any one of claims 1-7.

11. A computer device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the seismic frequency-varying impedance inversion method according to any one of claims 1-7.

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