Inversion method of complex thin interbed clamping VTI thin layer and related equipment

Abstract

The invention provides an inversion method for a complex thin interbed with a VTI-sandwiched single thin layer. The method comprises the steps that an initial model parameter matrix is constructed according to parameterization of an underground medium; and calculating a reflection coefficient matrix of the underground medium according to the initial model parameter matrix, and utilizing the reflection coefficient matrix to perform forward modeling simulation to synthesize a seismic record. Wherein the synthetic seismic record comprises a PP wave synthetic record and a PS wave synthetic record. And constructing an inversion objective function according to the actual seismic record and the synthetic record of the target underground medium, wherein the model parameter matrix and the synthetic seismic record are utilized when the objective function is constructed. Wherein the actual seismic record comprises a PP wave actual record and a PS wave actual record. And solving the inversion objective function, and carrying out updating iteration on the initial parameter model to obtain thin interbed parameter information. Therefore, joint inversion of the PP wave and the PS wave of the complex thin interbed clamping the VTI thin layer is realized, and the inversion precision of the complex thin interbed clamping the VTI thin layer is improved.

Description

Technical Field

[0001] The present application relates to the field of seismic exploration technology, and in particular to a thin interbed inversion method. Background Art

[0002] In recent years, with the continuous deepening of oil and gas exploration, the wave field propagation laws and reservoir physical property inversion in complex structures have been studied more extensively and in-depth. In this research context, the detailed exploration and efficient development of thin interbedded reservoirs have become one of the important goals of oil and gas exploration and development, and the accuracy requirements for the characterization of their physical parameters have also increased accordingly. Traditional seismic inversion technology faces severe challenges when dealing with thin interbedded reservoirs: on the one hand, the thickness of a single layer in the thin interbed is generally lower than the conventional seismic resolution limit (usually less than 1 / 4 wavelength); on the other hand, the complex layered sedimentary structure causes transmission loss, destructive interference and dispersion attenuation of seismic wave energy, which in turn leads to problems such as insufficient vertical resolution of the inversion results and reduced inversion accuracy of physical property parameters.

[0003] Traditional AVO inversion uses the Zoeppritz equation and its approximate equations to calculate various parameters of the subsurface medium. This method is widely used. However, the Zoeppritz equation assumes a single interface. When inverting thin interbeds, it cannot directly calculate the reflection coefficient of each interface within the interbed. This makes it difficult to accurately depict the complex structure of the interbed and its wavefield propagation patterns. This can lead to calculation errors, especially in areas with complex interbed structures.

[0004] Other studies have used recursive matrix methods to invert complex media and thin interbeds. Compared to inversion methods based on the Zoeppritz equation, these methods can more accurately calculate complex wavefield patterns such as transmission loss, interlayer multiples, and wave mode conversion, making them more suitable for inverting thin interbeds. Numerous studies have examined the recursive matrix-based AVO method, with the Kennett recursive matrix reflectivity forward modeling (KRM) method proposed by Kennett (1983) being the most widely used. Most existing studies consider thin interbeds as multilayered isotropic media. However, in some complex thin interbeds, individual thin layers exhibit short-term cyclical characteristics, and the grain size within the thin layers exhibits rhythmic and periodic patterns. Some thin layers, composed of multiple extremely thin layers, exhibit regularly varying lithologies. These thin layers inherently exhibit VTI characteristics, and treating them as isotropic layers fails to accurately characterize the interbed physical properties. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a thin interlayer inversion method, device, electronic device and storage medium.

[0006] Based on the above objectives, this application provides a thin interbed inversion method, including:

[0007] An initial model parameter matrix is ​​constructed based on the parameterization of the underground medium. The reflection coefficient matrix of the underground medium is calculated based on the initial model parameter matrix, and the reflection coefficient matrix is ​​used to forward simulate synthetic seismic records. The synthetic seismic records include PP wave synthetic records and PS wave synthetic records. According to the actual seismic records of the target underground medium and the synthetic records, the corresponding forward modeling operator and algorithm (the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm) are selected. The actual seismic records include actual PP wave records and actual PS wave records. The inversion objective function is solved, the model parameters are iteratively updated, and the updated parameter model is used as the new initial model parameters. The above steps are repeated to finally obtain the thin interlayer parameter information. In this way, the joint inversion of PP waves and PS waves of complex thin interlayers with VTI thin layers is realized, and the inversion accuracy of complex thin interlayers with VTI thin layers is improved.

[0008] In some embodiments, the reflection coefficient matrix of the underground medium is calculated according to the initial model parameters, and the reflection coefficient matrix is ​​used to simulate the synthetic seismic record, specifically including: parameterizing the underground medium to obtain the initial model parameter matrix: m = [V P0 V S0 ρδε] T , where V P0 、V S0 , ρ, δ, and ε represent the P-wave velocity and S-wave velocity density parameter vectors and two Thomson parameter vectors, respectively. Calculation is performed based on the model parameters to obtain a reflection coefficient matrix; the synthetic seismic record is calculated based on the reflection coefficient matrix and a preset wavelet matrix; the synthetic seismic record is calculated using the following formula: d(m,θ,t)=W(t)R(m,θ,t); where d(m,θ,t) represents the synthetic seismic record, W(t) represents the wavelet matrix, R(m,θ,t) represents the reflection coefficient matrix, m represents the model parameter matrix, θ represents the reflection angle of the seismic wave, and t represents the time required for the seismic wave to be transmitted and received.

[0009] In some embodiments, calculating the reflection coefficient matrix specifically includes: calculating the PP wave reflection coefficient and the PS wave reflection coefficient corresponding to the model parameters using the Kennett second-order approximation formula according to the initial model parameter matrix to obtain the reflection coefficient matrix; the slowness-frequency domain second-order approximation reflection coefficient is calculated using the following formula: Where ω represents the angular frequency, p represents the horizontal slowness, represents the VTI medium single interface reflection coefficient matrix of the downlink wave at interface n-1 in the VTI medium, represents the VTI medium single interface reflection coefficient matrix of the downlink wave at interface n in the VTI medium, represents the single interface transmission coefficient matrix of the VTI medium for the downlink wave at interface n, represents the single-interface reflection coefficient matrix of the VTI medium for the upgoing wave at interface n, represents the single-interface transmission coefficient matrix of the VTI medium for the upgoing wave at interface n, is the phase shift factor when the wave propagates from interface n-1 to interface n. When calculating synthetic seismic records, the second-order approximate reflection coefficient in the angle-time domain is required, which is converted by the following formula: m represents the model parameter matrix, θ represents the reflection angle of the seismic wave, and t represents the time required for the seismic wave to be transmitted and received.

[0010] In some embodiments, constructing an inversion objective function based on the synthetic seismic record specifically includes: calculating the difference between the synthetic seismic record and the measured data to obtain a deviation seismic record; calculating the difference between the model parameter matrix and the measured data to obtain a deviation model parameter; constructing an inversion objective function based on the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm, and utilizing the model parameter matrix and synthetic seismic record when constructing the objective function; the inversion objective function is expressed by the following formula: J(m) = || (H + λ1I)Δm-J T d ref || 2 +λ2||Δm+m ref ||,; where λ1 represents the damping coefficient, λ2 represents the sparse constraint coefficient, J represents the Jacobian matrix, and H represents the Hessian matrix H=J T J, I represent the identity matrix, d ref represents the deviation seismic record, Δm represents the update amount of the model parameter matrix, m ref represents the deviation model parameter. The J expansion form under multi-wave joint inversion is:

[0011] In some embodiments, solving the inversion objective function and updating the model parameter matrix to obtain parameter information of a complex thin interbedded layer sandwiched between VTI thin layers specifically includes: setting an update amount of the model parameters, iterating the inversion objective function according to the update amount of the model parameters; in response to the inversion objective function approaching 0, using the current model parameters as the parameter information of the thin interbedded layer; the update amount of the model parameters is expressed by the following formula: Among them, d PP represents the PP wave synthesis record, d PS Represents the PS wave synthesis record, s PPrepresents the measured data of PP wave, s PS Represents the PS wave measured data.

[0012] A thin interbed inversion device comprises: a parameter construction module for constructing an initial model parameter matrix according to preset seismic parameters; a seismic calculation module for calculating a reflection coefficient matrix according to the initial model parameter matrix, and then calculating a synthetic seismic record; wherein the synthetic seismic record includes a PP wave synthetic record and a PS wave synthetic record; an inversion module for constructing an inversion objective function according to a second-order approximation of the Kennett reflection coefficient formula and a Levenberg-Marquardt (LM) algorithm, wherein the model parameter matrix and the synthetic seismic record are utilized in constructing the objective function; and a solution module for solving the inversion objective function and updating the model parameter matrix to obtain parameter information of a complex thin interbed with a VTI thin layer.

[0013] In some embodiments, the seismic calculation module specifically includes: a forward modeling module, which calculates the PP wave reflection coefficient and the PS wave reflection coefficient matrix corresponding to the model parameters according to the Kennett second-order approximation formula; uses the reflection coefficient matrix and the preset wavelet matrix to perform calculations to obtain the PP wave synthetic record and the PS wave synthetic record; the synthetic seismic record is calculated by the following formula: d(m,θ,t)=W(t)R(m,θ,t); wherein, d(m,θ,t) represents the synthetic seismic record, W(t) represents the wavelet matrix, R(m,θ,t) represents the reflection coefficient matrix, m represents the model parameter matrix, θ represents the reflection angle of the seismic wave, and t represents the time required for the seismic wave to be transmitted and received.

[0014] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, any one of the methods described above is implemented.

[0015] A non-transitory computer-readable storage medium stores computer instructions, wherein the computer instructions are used to enable a computer to execute any of the above methods.

[0016] As can be seen from the above description, the inversion method for complex thin interlayers with VTI thin layers provided by the present application constructs an initial model parameter matrix, and calculates the corresponding PP wave reflection coefficient and PS wave reflection coefficient matrix based on the initial model parameter matrix; uses the reflection coefficient matrix and the preset wavelet matrix to perform calculations to obtain the PP wave synthetic record and the PS wave synthetic record, and constructs an inversion objective function based on the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm. The model parameter matrix and the synthetic seismic record are used when constructing the objective function to solve the objective function and perform model parameter iteration, thereby realizing the joint inversion of PP waves and PS waves and improving the inversion accuracy of complex thin interlayers with VTI thin layers. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in this application or related technologies, the following briefly introduces the drawings required for use in the embodiments or related technical descriptions. Obviously, the drawings described below are merely embodiments of this application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0018] Figure 1 A schematic flow chart of the thin interbed inversion method provided in an embodiment of the present application;

[0019] Figure 2 A schematic diagram of an AVA gather used to simulate calculation results in an embodiment of the present application;

[0020] Figure 3 is an inversion result diagram obtained by inversion according to the method of this application;

[0021] Figure 4 The inversion result diagram is obtained based on the exact Zoeppritz equation inversion;

[0022] Figure 5 A schematic diagram of an AVA gather containing noise used for simulating calculation results in an embodiment of the present application;

[0023] Figure 6 The inversion result diagram is obtained by inverting the AVA gather containing noise according to the method of the present application;

[0024] Figure 7 A schematic structural diagram of a thin interbed inversion device provided in an embodiment of the present application;

[0025] Figure 8 This is a more specific schematic diagram of the hardware structure of an electronic device provided in this application. DETAILED DESCRIPTION

[0026] In order to make the objectives, technical solutions and advantages of this application more clear, this application is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

[0027] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application should have the usual meanings understood by people with ordinary skills in the field to which this application belongs. The "first", "second" and similar words used in the embodiments of the present application do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0028] It is understandable that before using the technical solutions of each embodiment of the present disclosure, the type, scope of use, usage scenarios, etc. of the personal information involved will be informed to the user in an appropriate manner, and the user's authorization will be obtained.

[0029] For example, in response to a user's active request, a prompt message is sent to the user to clearly inform the user that the requested operation will require the acquisition and use of the user's personal information. This allows the user to independently choose whether to provide personal information to the electronic device, application, server, storage medium, or other software or hardware that performs the operation of the disclosed technical solution based on the prompt message.

[0030] As an optional but non-limiting implementation, in response to a user's active request, the prompt information may be sent to the user in the form of a pop-up window, in which the prompt information may be presented in text form. Furthermore, the pop-up window may also contain a selection control for the user to select "agree" or "disagree" to provide personal information to the electronic device.

[0031] It is understandable that the above notification and user authorization process are merely illustrative and do not constitute a limitation on the implementation of the present disclosure. Other methods that comply with relevant laws and regulations may also be applied to the implementation of the present disclosure.

[0032] Thomsen parameters are a set of parameters used in seismic geophysics to describe the elastic properties of rocks. These parameters describe the relationship between elastic wave velocity and density in isotropic rocks. Thomsen parameters include ε (epsilon), δ (delta), and γ (gamma), which describe the elastic anisotropy, inelastic effects, and isotropy of rocks, respectively. In this application, only ε and δ are used.

[0033] PP waves: These are P waves (compression waves) emitted from an earthquake source that return to the surface after reflecting off a subsurface interface. When a P wave encounters a subsurface interface, some of its energy is reflected back to the surface, forming PP waves. PP waves are primarily used to detect the density and elastic properties of underground rock formations and are one of the most common waveforms used in seismic exploration.

[0034] PS waves: These are P waves that, after reflecting off a subsurface interface, are converted into S waves (shear waves) before returning to the surface. S waves propagate through solids but not fluids, making them more sensitive to the internal structure of rock formations. PS waves, after reflecting off a subsurface interface and returning to the surface, provide crucial information about rock physical properties. Compared to PP waves, PS waves offer higher resolution and accuracy in imaging fluid-saturated rocks.

[0035] Ricker wavelet matrix: It is a signal with a certain starting time, limited energy and a certain duration. It is the basic unit in seismic records.

[0036] like Figure 1 As shown, the present application provides a thin interbed inversion method, comprising:

[0037] Step S1: construct an initial model parameter matrix according to preset earthquake parameters.

[0038] In this embodiment, the model parameter matrix includes the longitudinal wave velocity, the shear wave velocity, the density parameter vector, and the Thomson parameter vector. In a thin layer with anisotropy, the model parameter matrix is ​​represented by the following format:

[0039] m=[V P0 V S0 ρδε]T;

[0040] Among them, V P0 represents the longitudinal wave velocity, V S0 represents the shear wave velocity, ρ represents the density parameter vector, δ represents the elastic anisotropy in the Thomsen parameter, and ε represents the inelastic effect in the Thomsen parameter.

[0041] Step S2, calculating a reflection coefficient matrix based on the initial model parameter matrix; and calculating a synthetic seismic record based on the wave reflection coefficient matrix and a preset wavelet matrix, wherein the synthetic seismic record includes a PP wave synthetic record and a PS wave synthetic record.

[0042] Step S3, based on the actual seismic records of the target underground medium and the synthetic records, select the corresponding forward operator and algorithm (the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm) to construct the inversion objective function, and the model parameter matrix and synthetic seismic records are used when constructing the objective function.

[0043] Step S4: solving the inversion objective function to obtain thin interbed parameter information.

[0044] Among them, the inversion objective function is the optimization target for inverting seismic waves. The parameters in the inversion process are adjusted according to the inversion objective function, so that the parameter information of the thin interbed obtained by inversion gradually approaches the actual geological conditions.

[0045] In some embodiments, step S2 specifically includes:

[0046] Step S21 : calculating the PP wave reflection coefficient and the PS wave reflection coefficient matrix corresponding to the model parameters using the Kennett second-order approximation formula according to the initial model parameter matrix.

[0047] Step S22: obtaining a synthetic seismic record by calculation based on the reflection coefficient matrix and the preset wavelet matrix.

[0048] In this embodiment, the wavelet matrix is ​​a Ricker wavelet matrix.

[0049] The synthetic seismic record is calculated by the following formula:

[0050] d(m,θ,t)=W(t)R(m,θ,t).

[0051] Where d(m,θ,t) represents the synthetic seismic record, W(t) represents the wavelet matrix, R(m,θ,t) represents the reflection coefficient matrix, m represents the model parameter matrix, θ represents the reflection angle of the seismic wave, and t represents the time required for the seismic wave to be transmitted and received.

[0052] In some embodiments, step S21 specifically includes:

[0053] Step S211 : Calculate the PP wave reflection coefficient and the PS wave reflection coefficient corresponding to the model parameters according to Kennett's second-order approximation formula.

[0054] In this example, the inversion process uses the second-order approximation of the Kennett reflection coefficient equation proposed by Huang and Lu (2022) for calculating the reflection coefficient of thin VTI layers. By transforming the isotropic single-interface reflection coefficient term in the second-order approximation of the Kennett equation into a single-interface reflection coefficient term under the VTI medium assumption, a second-order approximation of the Kennett equation for VTI media is obtained. This method is suitable for calculating the reflection coefficient matrix of thin VTI layers for PP and PS waves. Then, using the recursive method proposed by Kennett (1983), the second-order approximate reflection coefficient for a thin interlayer system with a VTI layer in the slowness-frequency domain is derived, where the incident wave is a P-wave or S-wave at any interface n.

[0055] Step S212: Calculate a synthetic seismic record based on the wave reflection coefficient and a preset wavelet matrix.

[0056] In this embodiment, the reflection coefficient matrix is ​​expressed by the following formula:

[0057]

[0058] Where m represents the model parameter matrix, ω represents the angular frequency, and p represents the horizontal slowness. represents the PP wave reflection coefficient, represents the PS wave reflection coefficient, represents the SP wave reflection coefficient, Represents the SS wave reflection coefficient.

[0059] Preferably, in the inversion process, since only the PP wave reflection coefficient and the PS wave reflection coefficient need to be calculated, in practical applications, the above formula can be simplified to obtain:

[0060]

[0061] In some embodiments, step S211 specifically includes:

[0062] Step S201: Construct a second-order approximate reflection coefficient matrix according to Kennett's second-order approximate formula. The second-order approximate reflection coefficient is calculated by the following formula:

[0063]

[0064] Where ω represents the angular frequency, p represents the horizontal slowness, represents the VTI medium single interface reflection coefficient matrix of the downlink wave at interface n-1 in the VTI medium, represents the VTI medium single interface reflection coefficient matrix of the downlink wave at interface n in the VTI medium, represents the single interface transmission coefficient matrix of the VTI medium for the downlink wave at interface n, represents the single-interface reflection coefficient matrix of the VTI medium for the upgoing wave at interface n, represents the single-interface transmission coefficient matrix of the VTI medium for the upgoing wave at interface n, is the phase shift factor when the wave propagates from interface n-1 to interface n.

[0065] in, It is used to express the primary reflection coefficient of interface n, It includes the first-order reflection coefficient of interface n-1 and the first-order and second-order multiple reflection coefficients of n-1 layer.

[0066] Under the isotropic assumption, the single interface coefficients in Kennett's second-order approximation formula are displacement reflection and transmission coefficients. Huang and Lu (2020) replaced the single interface reflection and transmission coefficients under isotropic conditions with the VTI medium single interface reflection and transmission coefficients calculated based on the Graebner formula (1992) under the VTI medium assumption. It should be noted that the single interface coefficients in the Graebner formula are displacement reflection and transmission coefficients, which are different from the displacement reflection and transmission coefficients in the Kennett formula. In order to achieve the correct replacement between the two types of coefficients, the reflection and transmission coefficients calculated by Graebner must be multiplied by the ratio of the corresponding wave velocities on both sides of the interface, so as to convert them into a displacement reflection and transmission coefficient matrix that conforms to the VTI medium assumption. and

[0067]

[0068] Among them, the element r in the matrix ** , t ** Respectively represent the single interface reflection and transmission coefficients of different modes calculated by Graebner formula, V P 、V S Represents the longitudinal and shear wave velocities, and the superscripts n and n-1 of the elements represent the nth and n-1th layers of media.

[0069] In this embodiment, the phase shift factor is used to ensure the phase continuity of the wave when passing through the interface in the propagation matrix method. The phase shift factor matrix in the VTI medium is expanded as follows:

[0070]

[0071] q P (θ P ) and q S (θ S ) is the vertical slowness of P wave and S wave, h(n-1) is the thickness of n-1 layer. P (θ P ) and qS (θ S ), both have:

[0072]

[0073] in:

[0074]

[0075] c 11 , c 33 , c 55 , c 13 are independent stiffness coefficients (Thomsen, 1986):

[0076]

[0077] c 11 =2c 33 ε+c 33 ;

[0078]

[0079] For weakly anisotropic media, according to the Christoffel equation, the ray parameters of the P wave are

[0080]

[0081] The ray parameters of the S wave are:

[0082]

[0083] Since the reflection coefficient matrix calculated according to the second-order approximate reflection coefficient calculation formula is in the slowness-frequency domain, and in this application, the reflection coefficient used for inversion should be in the angle-time domain, it is necessary to convert the second-order approximate reflection coefficient calculation formula. According to the inverse Fourier transform and Snell's law, the total reflection coefficient formula in the angle-time domain can be obtained:

[0084]

[0085] Step S203: Express the preset PS wave AVA gather in the PP wave time domain to obtain a converted PS wave AVA gather.

[0086] Preferably, the PS AVA gathers can be compressed to the PP time domain by a conversion factor. The corresponding conversion factor for each sampling point is:

[0087] Where i represents different incident angles, and j represents different time sampling. P,ij represents the P-wave velocity at incident angle i and time sampling j; VS,ij represents the S-wave velocity at incident angle i and time sampling j.

[0088] In some embodiments, step S3 specifically includes:

[0089] Step S31, calculating the difference between the synthetic seismic record and the measured data to obtain the deviation seismic record.

[0090] In this embodiment, the deviation of the seismic record is calculated according to the following formula:

[0091]

[0092] Among them, d PP represents the PP wave synthesis record, d PS represents PS wave synthesis record, s PP represents the actual seismic data of PP wave, s PS Represents the actual seismic data of PS wave.

[0093] Step S32: Calculate the difference between the model parameter matrix and the measured data to obtain the deviation model parameters.

[0094] The deviation model parameters are calculated according to the following formula:

[0095] m ref =m0-m true ;

[0096] Among them, m0 represents the model parameter matrix currently involved in the calculation; m true Represents the model parameter matrix obtained by actual measurement, usually using well logging data.

[0097] Step S33: constructing an inversion objective function based on the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm, wherein the model parameter matrix and the synthetic seismic records are used when constructing the objective function.

[0098] The inversion objective function is expressed as follows:

[0099] J(m)=||(H+λ1I)Δm-J T d ref || 2 +λ2||Δm+m ref ||.

[0100] Where λ1 represents the damping coefficient, λ2 represents the sparse constraint coefficient, J represents the Jacobian matrix, and H represents the Hessian matrix H=J T J, I represent the identity matrix, d ref represents the deviation seismic record, Δm represents the update amount of the model parameter matrix, mref represents the bias model parameter.

[0101] Among them, the inversion objective function is constructed according to the LM algorithm under the ideal state that the forward seismic record is noise-free.

[0102] Preferably, the J expansion form under multi-wave joint inversion is:

[0103]

[0104] In some embodiments, step S4 specifically includes:

[0105] Step S41: setting the model parameter update amount, and iterating the inversion objective function according to the model parameter update amount.

[0106] Step S42: In response to the inversion objective function approaching 0, the current model parameters are used as thin interbed parameter information.

[0107] In this embodiment, when the inversion objective function approaches 0, the model parameter matrix m0 currently involved in the calculation is equal to the measured model parameter matrix m true Very close, that is, at this time:

[0108]

[0109] As an optional implementation, an inversion threshold may be set for the inversion objective function. When the value of the inversion objective function is lower than the inversion threshold, the inversion is stopped, thereby improving the inversion efficiency.

[0110] The model parameter update amount is expressed by the following formula:

[0111]

[0112] Among them, d PP represents the PP wave synthesis record, d PS represents PS wave synthesis record, s PP represents the measured data of PP wave, s PS Represents the PS wave measured data.

[0113] It can be seen from the above embodiments of the present application that the thin interlayer inversion method provided by the present application constructs an initial model parameter matrix, and then calculates the synthetic seismic records including the PP wave synthetic records and the PS wave synthetic records according to the initial model parameter matrix, and constructs the inversion objective function according to the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm. The model parameter matrix and the synthetic seismic records are used when constructing the objective function, and the objective function is solved and the model parameter matrix is ​​updated, thereby realizing the joint inversion of PP waves and PS waves, and improving the inversion accuracy of complex thin interlayers sandwiched between VTI thin layers.

[0114] As an exemplary embodiment, this application designs a thin interbedded model with a single VTI layer to verify the inversion method. The parameters are shown in the following table:

[0115]

[0116] The model is forward simulated with a frequency calculation range of 0 to 105 Hz and a 30 Hz Ricker wavelet as the source wavelet. The PP and PS wave AVA gathers of the model are obtained, as shown in the following figure: Figure 2 As shown, considering that the incident angle range of the angle gather data of actual data is usually narrow, the angle range of the thin interbed model angle gather is 5° to 30°, with an interval of 5°.

[0117] Smooth the true model to obtain the inversion initial model. Figure 3 The multi-wave AVA gathers shown are the target data for inversion. During the inversion, the reflection coefficients were calculated using the Kennett second-order approximation formula for VTI media and the exact Zoeppritz equation for comparison.

[0118] in, Figure 3 represents the inversion result obtained by the inversion method of this application, Figure 3 (a) represents the longitudinal wave velocity, Figure 3 (b) represents the shear wave velocity, Figure 3 (c) is the density, Figure 3 (d) is the δ value, Figure 3 (e) is the ε value. The black line is the initial model, the red line is the true model, and the blue line is the inversion result. It can be seen that the inversion result obtained by the application method is highly consistent with the true value.

[0119] in, Figure 4 The inversion result based on the exact Zoeppritz equation is: Figure 4 (a) represents the longitudinal wave velocity, Figure 4 (b) represents the shear wave velocity Figure 4(c) is the density. The black line represents the initial model, the red line represents the true model, and the blue line represents the inversion result. It can be seen that the inversion results based on the Zoeppritz equation fluctuate somewhat. This is likely due to the complex structure within the thin interbeds and the influence of VTI characteristics on the wave field. The Zoeppritz equation does not consider these effects when calculating the reflection coefficient, resulting in reduced accuracy.

[0120] As an exemplary embodiment, in order to test the anti-noise ability of the inversion method, the present application also designs a synthetic record of a thin interbed model with a random noise signal added. The synthetic record containing noise is as follows: Figure 5 shown.

[0121] The smoothing model is used as the initial model and inversion is performed based on the method provided in this application.

[0122] Figure 6 As shown in the inversion results, it can be seen that due to the influence of random noise, the inversion results will have certain fluctuations, but at the target layer position, the inversion results can still better reflect the true parameters of the formation, which shows that the inversion method has good noise resistance.

[0123] in, Figure 6 Indicates the inversion result obtained by inverting noisy data using the method provided in this application: Figure 6 (a) represents the longitudinal wave velocity, Figure 6 (b) represents the shear wave velocity, Figure 6 (c) is the density, Figure 6 (d) is the δ value, Figure 6 (e) is the ε value. The black line represents the initial model, the red line represents the true model, and the blue line represents the inversion result. This result demonstrates that the proposed method is more suitable for inverting complex internal wave fields in complex structures with thin interbeds, and can invert more accurate physical parameter models.

[0124] It should be noted that the method of the embodiment of the present application can be performed by a single device, such as a computer or server. The method of this embodiment can also be applied in a distributed scenario and performed by multiple devices working together. In such a distributed scenario, one of the multiple devices may only perform one or more steps of the method of the embodiment of the present application, and the multiple devices will interact with each other to complete the method.

[0125] It should be noted that the above description is limited to some embodiments of the present application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in an order different from that described in the above embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0126] Based on the same inventive concept, corresponding to any of the above-mentioned embodiment methods, the present application also provides a thin interlayer inversion device.

[0127] refer to Figure 7 , thin interbed inversion device, including:

[0128] The parameter construction module 100 is used to construct a model parameter matrix according to preset earthquake parameters.

[0129] The seismic calculation module 200 calculates the reflection coefficient matrix of the underground medium according to the initial model parameter matrix, and uses the reflection coefficient matrix to forward simulate synthetic seismic records; wherein the synthetic seismic records include PP wave synthetic records and PS wave synthetic records.

[0130] The inversion module 300 constructs an inversion objective function based on the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm, and the model parameter matrix and the synthetic seismic records are used when constructing the objective function.

[0131] The solution module 400 is used to solve the inversion objective function to obtain the thin interbed parameter information.

[0132] In some embodiments, the earthquake calculation module 200 specifically includes:

[0133] The forward modeling module 210 calculates the PP wave reflection coefficient and the PS wave reflection coefficient matrix corresponding to the model parameters according to the Kennett second-order approximation formula;

[0134] The reflection coefficient matrix and the preset wavelet matrix are used to perform calculations to obtain the PP wave synthesis record and the PS wave synthesis record.

[0135] The synthetic seismic record is calculated by the following formula:

[0136] d(m,θ,t)=W(t)R(m,θ,t).

[0137] Where d(m,θ,t) represents the synthetic seismic record, W(t) represents the wavelet matrix, R(m,θ,t) represents the reflection coefficient matrix, m represents the model parameter matrix, θ represents the reflection angle of the seismic wave, and t represents the time required for the seismic wave to be transmitted and received.

[0138] For the convenience of description, the above devices are described as being divided into various modules according to their functions. Of course, when implementing this application, the functions of each module can be implemented in the same or multiple software and / or hardware.

[0139] The device of the above embodiment is used to implement the corresponding thin interbed inversion method in any of the above embodiments, and has the beneficial effects of the corresponding method embodiment, which will not be described in detail here.

[0140] Based on the same inventive concept, corresponding to any of the above-mentioned embodiments and methods, the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and runnable on the processor, wherein when the processor executes the program, the thin interlayer inversion method described in any of the above embodiments is implemented.

[0141] Figure 8 10 is a schematic diagram showing a more specific hardware structure of an electronic device provided in this embodiment. The device may include: a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040 are communicatively connected to each other within the device via the bus 1050.

[0142] The processor 1010 can be implemented using a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0143] The memory 1020 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage devices, dynamic storage devices, etc. The memory 1020 can store an operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 1020 and is called and executed by the processor 1010.

[0144] The input / output interface 1030 is used to connect input / output modules to implement information input and output. The input / output modules can be configured as components within the device (not shown in the figure) or can be externally connected to the device to provide corresponding functions. Input devices may include a keyboard, mouse, touch screen, microphone, various sensors, etc., and output devices may include a display, speaker, vibrator, indicator light, etc.

[0145] The communication interface 1040 is used to connect to a communication module (not shown) to enable communication between the device and other devices. The communication module can communicate via a wired method (such as USB, network cable, etc.) or a wireless method (such as mobile network, WiFi, Bluetooth, etc.).

[0146] The bus 1050 comprises a pathway for transmitting information between the various components of the device (eg, the processor 1010 , the memory 1020 , the input / output interface 1030 , and the communication interface 1040 ).

[0147] It should be noted that although the above device only shows the processor 1010, the memory 1020, the input / output interface 1030, the communication interface 1040, and the bus 1050, in a specific implementation, the device may also include other components necessary for normal operation. In addition, it will be understood by those skilled in the art that the above device may only include the components necessary to implement the embodiments of this specification, and does not necessarily include all the components shown in the figure.

[0148] The electronic device of the above embodiment is used to implement the corresponding thin interlayer inversion method in any of the above embodiments, and has the beneficial effects of the corresponding method embodiment, which will not be described in detail here.

[0149] Based on the same inventive concept, corresponding to any of the above-mentioned embodiment methods, the present application also provides a non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the thin interlayer inversion method described in any of the above embodiments.

[0150] The computer-readable media of this embodiment include permanent and non-permanent, removable and non-removable media that can be used to store information by any method or technology. The information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device.

[0151] The computer instructions stored in the storage medium of the above embodiment are used to enable the computer to execute the thin interbed inversion method described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0152] It should be noted that the embodiments of the present application can be further described in the following manner:

[0153] A thin interbed inversion method, comprising:

[0154] Construct the model parameter matrix according to the preset earthquake parameters.

[0155] The reflection coefficient matrix is ​​calculated based on the model parameter matrix, and then the synthetic seismic record is calculated based on the reflection coefficient matrix and the preset wavelet matrix. The synthetic seismic record includes the PP wave synthetic record and the PS wave synthetic record.

[0156] An inversion objective function is constructed based on the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm, and the model parameter matrix and the synthetic seismic records are used when constructing the objective function.

[0157] The inversion objective function is solved and the model parameter matrix is ​​updated to obtain the thin interbed parameter information.

[0158] In some embodiments, calculating a synthetic seismic record based on the model parameter matrix specifically includes:

[0159] The reflection coefficient matrix is ​​calculated based on the model parameters.

[0160] The synthetic seismic record is calculated based on the reflection coefficient matrix and the preset wavelet matrix.

[0161] The synthetic seismic record is calculated by the following formula:

[0162] d(m,θ,t)=W(t)R(m,θ,t).

[0163] Where d(m,θ,t) represents the synthetic seismic record, W(t) represents the wavelet matrix, R(m,θ,t) represents the reflection coefficient matrix, m represents the model parameter matrix, θ represents the reflection angle of the seismic wave, and t represents the time required for the seismic wave to be transmitted and received.

[0164] In some embodiments, forward modeling of the PP wave composite record and the PS wave composite record specifically includes:

[0165] The PP wave reflection coefficient and PS wave reflection coefficient corresponding to the model parameters are calculated according to Kennett's second-order approximation formula.

[0166] Synthetic seismic records are calculated based on the wave reflection coefficients and the preset wavelet matrix.

[0167] In some embodiments, the PP wave reflection coefficient and the PS wave reflection coefficient corresponding to the model parameters are calculated according to the Kennett second-order approximation formula, specifically including:

[0168] The second-order approximate reflection coefficient matrix is ​​constructed according to Kennett's second-order approximation formula.

[0169] The second-order approximate reflection coefficient is calculated by the following formula:

[0170]

[0171] Where ω represents the angular frequency, p represents the horizontal slowness, represents the VTI medium single interface reflection coefficient matrix of the downlink wave at interface n-1 in the VTI medium, represents the VTI medium single interface reflection coefficient matrix of the downlink wave at interface n in the VTI medium, represents the single interface transmission coefficient matrix of the VTI medium for the downlink wave at interface n, represents the single-interface reflection coefficient matrix of the VTI medium for the upgoing wave at interface n, represents the single-interface transmission coefficient matrix of the VTI medium for the upgoing wave at interface n, is the phase shift factor when the wave propagates from interface n-1 to interface n.

[0172] In some embodiments, an inversion objective function is constructed based on the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm. The objective function is constructed using the model parameter matrix and the synthetic seismic records, specifically including:

[0173] The difference between the synthetic seismic record and the measured data is calculated to obtain the deviation seismic record.

[0174] The difference between the model parameter matrix and the measured data is calculated to obtain the deviation model parameters.

[0175] The inversion objective function is constructed based on the deviation seismic records and deviation model parameters.

[0176] The inversion objective function is expressed as follows:

[0177] J(m)=||(H+λ1I)Δm-J T d ref || 2 +λ2||Δm+m ref ||.

[0178] Where λ1 represents the damping coefficient, λ2 represents the sparse constraint coefficient, J represents the Jacobian matrix, and H represents the Hessian matrix H=J T J, I represent the identity matrix, d ref represents the deviation seismic record, Δm represents the update amount of the model parameter matrix, m ref represents the bias model parameter.

[0179] In some embodiments, solving the inversion objective function and updating the model parameter matrix to obtain thin interbed parameter information specifically includes:

[0180] Set the update amount of the model parameters and iterate the inversion objective function according to the update amount of the model parameters.

[0181] In response to the inversion objective function approaching 0, the current model parameters are used as thin interlayer parameter information.

[0182] The update amount of the model parameters is expressed by the following formula:

[0183]

[0184] Among them, d PP represents the PP wave synthesis record, d PS represents PS wave synthesis record, s PP represents the measured data of PP wave, s PS Represents the PS wave measured data.

[0185] The present application also provides a thin interbed inversion device, comprising:

[0186] The parameter construction module is used to construct the initial model parameter matrix according to the preset earthquake parameters.

[0187] The seismic calculation module calculates the reflection coefficient matrix of the underground medium according to the initial model parameter matrix, and uses the reflection coefficient matrix to simulate the synthetic seismic record.

[0188] In the inversion module, the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt (LM) algorithm are used to construct the inversion objective function, and the model parameter matrix and the synthetic seismic records are used when constructing the objective function.

[0189] The solution module is used to solve the inversion objective function and update the model parameter matrix to obtain the thin interlayer parameter information.

[0190] In some embodiments, the earthquake calculation module specifically includes:

[0191] The forward modeling module calculates the PP wave reflection coefficient and PS wave reflection coefficient matrix corresponding to the model parameters according to the Kennett second-order approximation formula;

[0192] The reflection coefficient matrix and the preset wavelet matrix are used to perform calculations to obtain the PP wave synthesis record and the PS wave synthesis record.

[0193] The synthetic seismic record is calculated by the following formula:

[0194] d(m,θ,t)=W(t)R(m,θ,t).

[0195] Where d(m,θ,t) represents the synthetic seismic record, W(t) represents the wavelet matrix, R(m,θ,t) represents the reflection coefficient matrix, m represents the model parameter matrix, θ represents the reflection angle of the seismic wave, and t represents the time required for the seismic wave to be transmitted and received.

[0196] The present application also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements any one of the above methods when executing the program.

[0197] The present application also provides a non-transitory computer-readable storage medium, which stores computer instructions, and the computer instructions are used to enable a computer to execute any of the above methods.

[0198] Those skilled in the art should understand that the discussion of any of the above embodiments is merely illustrative and is not intended to imply that the scope of the present application (including the claims) is limited to these examples. Within the scope of the present application, the technical features in the above embodiments or different embodiments may be combined, the steps may be implemented in any order, and there are many other variations of the different aspects of the embodiments of the present application as described above, which are not provided in detail for the sake of simplicity.

[0199] In addition, for simplicity of description and discussion, and in order not to make the embodiment of the application difficult to understand, the known power supply / ground connection with integrated circuit (IC) chip and other components may or may not be shown in the accompanying drawings provided. In addition, the device can be shown in the form of a block diagram to avoid making the embodiment of the application difficult to understand, and this also takes into account the following fact, that is, the details of the embodiment of these block diagram devices are highly dependent on the platform to be implemented in the embodiment of the application (that is, these details should be fully within the scope of understanding of those skilled in the art). When specific details (for example, circuit) are set forth to describe exemplary embodiments of the application, it will be apparent to those skilled in the art that the embodiment of the application can be implemented without these specific details or when these specific details are changed. Therefore, these descriptions should be considered to be illustrative rather than restrictive.

[0200] Although the present invention has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of these embodiments will be apparent to those skilled in the art based on the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may utilize the embodiments discussed.

[0201] The embodiments of the present application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present application should be included in the scope of protection of this application.

Claims

1. A thin interbed inversion method, comprising: Constructing the initial model parameter matrix based on the parameterization of underground media; Calculating a reflection coefficient matrix of the underground medium according to the initial model parameter matrix, and performing forward simulation using the reflection coefficient matrix to obtain a synthetic seismic record; wherein the synthetic seismic record includes a PP wave synthetic seismic record and a PS wave synthetic seismic record; Constructing an inversion objective function based on actual seismic records of the target underground medium and the synthetic seismic records; wherein the actual seismic records include actual PP wave records and actual PS wave records; The inversion objective function is solved, and the initial parameter model is updated and iterated to obtain thin interbed parameter information.

2. The thin interbed inversion method according to claim 1, wherein: Calculating a reflection coefficient matrix of the underground medium according to the initial model parameter matrix and forward modeling synthetic seismic records using the reflection coefficient matrix specifically includes: Calculate the reflection coefficient matrix using the second-order approximation of the Kennett reflection coefficient formula according to the initial model parameter matrix; The PP wave synthetic seismic record and the PS wave synthetic seismic record are obtained by forward simulation according to the reflection coefficient matrix and the preset wavelet matrix; The synthetic seismic record is calculated by the following formula: d(m,θ,t)=W(t)R(m,θ,t); Wherein, d(m,θ,t) represents the synthetic seismic record, W(t) represents the wavelet matrix, R(m,θ,t) represents the reflection coefficient matrix, m represents the model parameter matrix, θ represents the reflection angle of the seismic wave, and t represents the time required for the seismic wave to be transmitted and received.

3. The thin interbed inversion method according to claim 2, wherein: The PP wave synthetic seismic record and the PS wave synthetic seismic record are obtained by forward simulation according to the reflection coefficient matrix and the preset wavelet matrix, specifically including: Calculate the PP wave reflection coefficient and the PS wave reflection coefficient corresponding to the model parameters according to the Kennett second-order approximation formula; The PP wave synthetic seismic record and the PS wave synthetic seismic record are obtained by forward modeling based on the wave reflection coefficient and the preset wavelet matrix.

4. The thin interbed inversion method according to claim 3, wherein: Calculating the PP wave reflection coefficient and the PS wave reflection coefficient corresponding to the model parameters according to the Kennett second-order approximation formula specifically includes: Constructing a second-order approximate reflection coefficient matrix in the slowness-frequency domain according to the Kennett second-order approximate formula and the initial model parameter matrix; The second-order approximate reflection coefficient matrix is ​​calculated by the following formula: Where ω represents the angular frequency, p represents the horizontal slowness, represents the VTI medium single interface reflection coefficient matrix of the downlink wave at interface n-1 in the VTI medium, represents the VTI medium single interface reflection coefficient matrix of the downlink wave at interface n in the VTI medium, represents the single interface transmission coefficient matrix of the VTI medium for the downlink wave at interface n, represents the single-interface reflection coefficient matrix of the VTI medium for the upgoing wave at interface n, represents the single-interface transmission coefficient matrix of the VTI medium for the upgoing wave at interface n, is the phase shift factor when the wave propagates from interface n-1 to interface n; Since the required reflection coefficient matrix needs to be in the angle-time domain, according to the inverse Fourier transform and Snell's law, the total reflection coefficient matrix in the angle-time domain is calculated as follows:

5. The thin interbed inversion method according to claim 1, wherein: The constructing of the inversion objective function according to the model parameter matrix and the synthetic seismic record specifically includes: Calculating the difference between the synthetic seismic record and the measured data to obtain a deviation seismic record; Calculating the difference between the model parameter matrix and the measured data to obtain the deviation model parameters; constructing an inversion objective function based on the second-order approximation of the Kennett reflection coefficient formula and the Levenberg-Marquardt algorithm, wherein the model parameter matrix and the synthetic seismic records are utilized in constructing the objective function; According to the Levenberg-Marquardt algorithm and adding sparse constraints, the inversion objective function is expressed by the following formula: J(m)=||(H+λ1I)Δm-J T d ref || 2 +λ2‖Δm+m ref ‖; Where λ1 represents the damping coefficient, λ2 represents the sparse constraint coefficient, J represents the Jacobian matrix, and H represents the Hessian matrix H=J T J, I represent the identity matrix, d ref represents the deviation seismic record, Δm represents the update amount of the model parameter matrix, m ref represents the deviation model parameter; the J expansion form under multi-wave joint inversion is:

6. The thin interbed inversion method according to claim 5, wherein: Solving the inversion objective function and iterating the initial parameter model to obtain thin interbed parameter information specifically includes: Solve the objective function for a sufficiently small solution, obtain the update amount of the model parameters, and iterate the initial model parameters; In response to the inversion objective function approaching 0, using current model parameters as the thin interbed parameter information; The update amount of the model parameters is expressed by the following formula: Among them, d PP represents the PP wave synthesis record, d PS Represents the PS wave synthesis record, s PP represents the measured data of PP wave, s PS Represents the PS wave measured data.

7. A thin interbed inversion device comprising: A parameter construction module is used to construct an initial model parameter matrix based on the parameterization of the underground medium; a seismic calculation module, configured to calculate a reflection coefficient matrix of the underground medium based on the initial model parameter matrix, and perform forward modeling using the reflection coefficient matrix to obtain a synthetic seismic record; wherein the synthetic seismic record includes a PP wave synthetic record and a PS wave synthetic record; An inversion module, configured to construct an inversion objective function based on the model parameter matrix and the synthetic seismic record; wherein the actual seismic record includes an actual PP wave record and an actual PS wave record; The solution module is used to solve the inversion objective function, update and iterate the initial parameter model, and obtain thin interbed parameter information.

8. The thin interbed inversion device according to claim 7, wherein: The earthquake calculation module specifically includes: A forward modeling module is used to calculate the reflection coefficient matrix using the second-order approximation of the Kennett reflection coefficient formula according to the initial model parameter matrix; The PP wave synthetic seismic record and the PS wave synthetic seismic record are obtained by forward simulation according to the reflection coefficient matrix and the preset wavelet matrix; The synthetic seismic record is calculated by the following formula: d(m,θ,t)=W(t)R(m,θ,t); Wherein, d(m,θ,t) represents the synthetic seismic record, W(t) represents the wavelet matrix, R(m,θ,t) represents the reflection coefficient matrix, m represents the model parameter matrix, θ represents the reflection angle of the seismic wave, and t represents the time required for the seismic wave to be transmitted and received.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 6 when executing the program. 10 . A non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are configured to cause a computer to execute the method according to claim 1 .

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