Longitudinal wave impedance and porosity joint inversion method, system, device and storage medium

Abstract

This invention discloses a method, system, device, and storage medium for joint inversion of P-wave impedance and porosity. The method includes: constructing a hybrid network; establishing a forward modeling framework; establishing a composite loss function; introducing the forward modeling framework and the composite loss function into the training of the hybrid network, and training the inversion to obtain the final P-wave impedance and porosity. Introducing a seismic data error loss term into the objective function can enhance the consistency between the predicted results and the actual earthquake waveform; adding a physical constraint loss term for P-wave impedance-porosity can constrain the intrinsic correlation between the inversion results of P-wave impedance and porosity, thereby improving the accuracy of the joint inversion and enhancing the lateral resolution of the profile. Through comparison of different network modules, introducing a BiLSTM module into the ResUNet network module can improve the inter-layer transition stability and inversion accuracy; further adding inter-channel attention to the Transformer network effectively suppresses the "striped" phenomenon of the joint inversion results and enhances the lateral resolution.

Description

Technical Field

[0001] This invention belongs to the technical field of geophysical exploration and oil and gas reservoir characterization technology, and particularly relates to the method, system, equipment and storage medium for joint inversion of longitudinal wave impedance and porosity. Background Technology

[0002] Seismic inversion is used to infer reservoir information such as P-wave and S-wave velocities, density, and porosity from seismic data. Due to the bandwidth limitations of seismic data, inversion techniques often require auxiliary constraints from well logging and geological information. Porosity and other physical properties have traditionally relied on core and well logging data, but these methods are often expensive, time-consuming, and difficult to implement, making them unsuitable for predicting and describing oil and gas reservoirs.

[0003] In recent years, deep learning methods have been widely used in the field of geophysical inversion due to their powerful nonlinear mapping capabilities. Existing research on the inversion of elastic physical parameters based on deep learning has made considerable progress, but when facing the joint prediction of elastic and physical parameters, problems remain, such as the difficulty in maintaining consistency in the physical relationships between different parameters and the lack of effective physical constraints on the loss function. Summary of the Invention

[0004] The purpose of this invention is to provide a method, system, device, and storage medium for the joint inversion of longitudinal wave impedance and porosity, and to solve the technical problems of difficulty in maintaining consistent physical relationships between different parameters and lack of effective physical constraints on the loss function.

[0005] The embodiments of this application are implemented as follows: a method for joint inversion of longitudinal wave impedance and porosity is provided, including: S01, constructing a hybrid network; S02. Establish the forward modeling framework; S03. Establish the composite loss function; S04. Introduce a forward modeling framework and a composite loss function into the hybrid network training, and train the inversion to obtain the final longitudinal wave impedance and porosity.

[0006] Optionally, in some embodiments of this application, the hybrid network includes a residual U-Net network, a bidirectional long short-term memory network, and a Transformer model.

[0007] Optionally, in some embodiments of this application, the expression of the forward modeling framework is as follows: ; In the formula, Represents the seismic wavelet. Indicates time, Represents the convolution operator, Indicates effective porosity. This represents the longitudinal wave impedance.

[0008] Optionally, in some embodiments of this application, the forward modeling framework is obtained as follows: Post-stack seismic response under the assumption of horizontally layered medium Described as the longitudinal wave vertical reflection coefficient With seismic wavelets The formula for the convolution is as follows: ; In the formula, Indicates the post-stack seismic response. Represents the vertical reflection coefficient of longitudinal waves. Represents the seismic wavelet. Indicates time, Represents the convolution operator; No. j The reflectance of the layer It is described by the difference in longitudinal wave impedance between the upper and lower media at the horizontal interface, as shown in the following formula: ; In the formula, Indicates the first j The reflectivity of the layer, Indicates time, , Indicates the upper and lower media. Indicates longitudinal wave impedance, Indicates the longitudinal wave velocity. Indicates the density of the rock layer medium; Equivalent P-wave velocity of saturated rock The functional relationship with porosity is as follows: ; In the formula, Represents the equivalent P-wave velocity of saturated rock. Indicates effective porosity. Represents the longitudinal wave velocity of the rock matrix. Represents the longitudinal wave velocity of pore fluid; Similarly, the equivalent density of rocks with fluid pores It is also described as a function of porosity, as follows: ; In the formula, This represents the equivalent density of rocks containing fluid pores. For effective porosity, Indicates the density of the rock matrix. The sum and density represent the pore fluid; comprehensive and To obtain effective porosity to longitudinal wave impedance The mapping relationship is as follows: ; In the formula, Indicates longitudinal wave impedance, Represents the equivalent P-wave velocity of saturated rock. This represents the equivalent density of rocks containing fluid pores; Will and Substitute In the end, the relationship between effective porosity and P-wave impedance and seismic response was established, namely the forward modeling framework.

[0009] Optionally, in some embodiments of this application, the composite loss function is as follows: ; In the formula, , , These represent the seismic data error loss function, the well logging curve fitting loss function, and the P-wave impedance-porosity physical constraint loss function, respectively. , , Used to balance the contribution of each loss term to the total loss function.

[0010] Optionally, in some embodiments of this application, the seismic data error loss function As shown below: ; In the formula, Indicates a synthetic seismic record. Represents actual earthquake records, Total number of seismic traces Indicates a seismic trace index; and / or Well logging curve fitting loss function As shown below: ; In the formula, , These represent the measured porosity and P-wave impedance well curves, respectively. , These represent the porosity and mixed longitudinal wave impedance predicted by the network, respectively. This represents the weighting coefficient for the porosity error term. Total number of seismic traces Indicates a seismic trace index; and / or Longitudinal wave impedance-porosity physical constraint loss function As shown below: ; In the formula, This represents the longitudinal wave impedance calculated from the predicted porosity. This is the longitudinal wave impedance predicted by the hybrid network. Total number of seismic traces This indicates the seismic trace index.

[0011] Optionally, in some embodiments of this application, a hybrid network is constructed to minimize the composite loss function. Various loss functions in , and The predicted longitudinal wave impedance and porosity are obtained. ,like The training phase of the hybrid network minimizes... Obtain the optimal parameters ,Will Substitute The final longitudinal wave impedance and porosity are obtained. The inversion results.

[0012] Accordingly, embodiments of this application also provide a joint inversion system for longitudinal wave impedance and porosity, including: Hybrid network module, used to build hybrid networks; The forward modeling framework module is used to build the forward modeling framework; The composite loss function module is used to create composite loss functions; The longitudinal wave impedance and porosity module introduces a forward modeling framework and a composite loss function into the hybrid network training, and obtains the final longitudinal wave impedance and porosity through training inversion.

[0013] Accordingly, embodiments of this application also provide a computer device, including a storage device and a processor, wherein the storage device stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.

[0014] Accordingly, embodiments of this application also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method described above.

[0015] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: This application proposes a joint inversion method for P-wave impedance and porosity based on a ResUNet-BiLSTM-Transformer hybrid network model, utilizing post-stack seismic data, prior low-frequency trends, and rock physics consistency constraints. The effectiveness of this method is verified by Marmousii model testing and real-world data applications. Introducing a seismic data error loss term into the objective function enhances the waveform consistency between the predicted results and actual earthquakes. Adding a P-wave impedance-porosity physical constraint loss term constrains the intrinsic correlation between the P-wave impedance and porosity inversion results, thereby improving the accuracy of the joint inversion and enhancing the lateral resolution of the profile. Through comparison of different network modules, introducing a BiLSTM module into the ResUNet network improves inter-layer transition stability and inversion accuracy. Further addition of inter-channel attention in the Transformer network effectively suppresses the "striped" phenomenon in the joint inversion results and enhances the lateral resolution. This application primarily focuses on the joint inversion of P-wave impedance and porosity. Future research could explore extending this method to the joint inversion of more reservoir parameters (such as saturation and permeability) to achieve a more comprehensive reservoir evaluation. Attached Figure Description

[0016] Figure 1 This is a diagram of the ResUNet-BiLSTM-Transformer hybrid network structure of the present invention; Figure 2 The Marmousii model and synthetic seismic records of this invention; Figure 3 This invention provides a comparison of the joint inversion of longitudinal wave impedance and porosity based on different network structures. Figure 4 This is based on actual work area data and a low-frequency model; Figure 5 This invention provides a hybrid network model for the joint inversion of longitudinal wave impedance and porosity. Figure 6 This invention provides a comparison of single-channel wave impedance and porosity. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0018] While significant progress has been made in the research on the inversion of elastic property parameters based on deep learning, there are still some problems when it comes to the joint prediction of elasticity and physical property parameters. These problems include difficulty in maintaining consistency in the physical relationships between different parameters, weak generalization ability under conditions of few training samples, inability of network structure to effectively learn nonlinear relationships between data, and lack of effective physical constraints on loss function.

[0019] The technical solution of this application is as follows: Firstly, please refer to Figure 1 This application provides a method for joint inversion of longitudinal wave impedance and porosity, including: S01. Construct a hybrid network; S02. Establish the forward modeling framework; S03. Establish the composite loss function; S04. Introduce a forward modeling framework and a composite loss function into the hybrid network training, and train the inversion to obtain the final longitudinal wave impedance and porosity.

[0020] This application constructs a ResUNet-BiLSTM-Transformer network, using post-stack 2D seismic profiles and low-frequency trend models of P-wave impedance and porosity as input, and providing supervised constraints using P-wave impedance and porosity curves from a small number of wells. Simultaneously, this application employs the Wyllie empirical formula to establish the relationship between P-wave impedance and porosity, and embeds the seismic forward modeling process into the network training. The network parameters are optimized by constructing a composite loss function consisting of a seismic data fitting term, a well logging curve supervision term, and a P-wave impedance-porosity physical constraint term. Ultimately, high-precision joint inversion of P-wave impedance and porosity is achieved.

[0021] In S01: In some embodiments, the hybrid network includes a residual U-Net network, a bidirectional long short-term memory network, and a Transformer model.

[0022] Please see Figure 1 The hybrid network, comprising ResUNet, BiLSTM, and Transformer models, can fully learn the nonlinear mapping relationship between post-stack seismic records and wave impedance and porosity. The sensitivity of post-stack seismic records to medium parameters is mainly reflected in the waveform morphology of reflection events, which contains high-frequency reflection details corresponding to thin-layer interfaces and low-frequency trend information.

[0023] Figure 1 In this system, the network inputs include seismic records, low-frequency models, and well logging data, and the outputs are wave impedance and porosity. The ResUNet module extracts multi-scale local features, the BiLSTM module establishes a single-channel stratigraphic sequence along the time axis, and the Transformer module aggregates cross-channel features in the spatial dimension.

[0024] It is understandable that ResUNet represents U-Net network and BiLSTM represents bidirectional long short-term memory network.

[0025] It is understood that the hybrid network in this application is the ResUNet-BiLSTM-Transformer hybrid network.

[0026] First, the hybrid network uses ResUNet modules to characterize the multi-scale features of a single-channel waveform. During feature fusion, trend information from the low-frequency model is introduced to jointly constrain the inversion at both the low-frequency background and high-frequency detail scales. This ensures that the inversion results not only depict the local waveform differences between thin layers and interfaces but also maintain consistency with the trends provided by the low-frequency model. The feature extraction of the residual U-Net network in the time dimension is represented as follows: ; In the formula, Indicates the first Layer features; , Convolution kernel weights and biases It is a non-linear activation function.

[0027] Secondly, after representing the waveform's multi-scale information, the joint inversion also needs to mitigate the jagged edges or isolated outliers appearing in adjacent layers of the output results. To this end, a BiLSTM module is introduced into the time feature sequence output by the ResUNet module in the hybrid network. This module utilizes adjacent waveform information through bidirectional time series modeling to improve the stability of inter-layer transitions. Let the time series feature of a single channel provided by the ResUNet module be... Then the bidirectional time series recursion is as follows: ; In the formula, This is a hidden state representation for integrating temporal information before and after the process. index for time sampling points , for The feature vector input at time step 1, The feature dimension, and These represent the forward and backward hidden states, respectively.

[0028] Finally, post-stack data exhibits inter-trace correlation in addition to longitudinal information correlation. If inversion is performed independently for each trace, lateral discontinuities can easily occur due to noise and lateral non-stationarity. Therefore, explicitly incorporating inter-trace correlation into network modeling is an effective way to improve profile consistency. This application introduces an inter-trace self-attention mechanism from the Transformer module after the BiLSTM module, constructs spatial attention units using several adjacent traces, and performs linear mapping on them to construct query, key, and value matrices. To achieve horizontal information aggregation, ; In the formula, This indicates row-wise normalization. The channel dimension of the key vector is used to control the numerical scale; Depend on The obtained attention weight matrix characterizes the similarity between several adjacent traces, and based on this, inter-trace information is adaptively fused to enhance the characterization of seismic inter-trace correlation of reflection events. Subsequently, the hybrid network output layer maps the features aggregated from the spatial attention unit information, and the corresponding output is obtained. .

[0029] In S02: In some embodiments, the expression of the forward model is as follows: ; In the formula, Represents the seismic wavelet. Indicates time, Represents the convolution operator, Indicates effective porosity. This represents the longitudinal wave impedance.

[0030] Furthermore, the forward modeling framework is obtained as follows: Post-stack seismic response under the assumption of horizontally layered medium Described as the longitudinal wave vertical reflection coefficient With seismic wavelets The formula for the convolution is as follows: ; In the formula, Indicates the post-stack seismic response. Represents the vertical reflection coefficient of longitudinal waves. Represents the seismic wavelet. Indicates time, Represents the convolution operator; No. j The reflectance of the layer It is described by the difference in longitudinal wave impedance between the upper and lower media at the horizontal interface, as shown in the following formula: ; In the formula, Indicates the first j The reflectivity of the layer, Indicates time, , Indicates the upper and lower media. Indicates longitudinal wave impedance, Indicates the longitudinal wave velocity. Indicates the density of the rock layer medium; It is understandable that, for fluid-containing porous media, under the assumptions of a relatively stable rock matrix, homogeneous pore structure, and Newtonian pore fluid, the Wyllie time-averaged equation (Wyllie et al., 1956) establishes the equivalent P-wave velocity of saturated rocks. Functional relationship with porosity.

[0031] Equivalent P-wave velocity of saturated rock The functional relationship with porosity is as follows: ; In the formula, Represents the equivalent P-wave velocity of saturated rock. Indicates effective porosity. Represents the longitudinal wave velocity of the rock matrix. Represents the longitudinal wave velocity of pore fluid; Similarly, the equivalent density of rocks with fluid pores It is also described as a function of porosity, as follows: ; In the formula, This represents the equivalent density of rocks containing fluid pores. For effective porosity, Indicates the density of the rock matrix. The sum and density represent the pore fluid; comprehensive and To obtain effective porosity to longitudinal wave impedance The mapping relationship is as follows: ; In the formula, Indicates longitudinal wave impedance, Represents the equivalent P-wave velocity of saturated rock. This represents the equivalent density of rocks containing fluid pores; Will and Substitute In the end, the relationship between effective porosity and P-wave impedance and seismic response was established, namely the forward modeling framework.

[0032] It is understandable that the above forward modeling process establishes a nonlinear relationship between porosity, P-wave impedance, and post-stack seismic records.

[0033] Furthermore, using the least squares method, we obtain... Longitudinal wave velocity in rock matrix and pore fluid longitudinal wave velocity The specific solution process is as follows: Rewritten ; The elastic physical property parameters of n wells are constructed using the following equations: ;

[0034] In the formula, superscript n Indicates the first n The well curve of the well is obtained by solving the above equation using the least squares method. ; Similarly, establish a solution Rock matrix density and pore fluid density The equation: ; ; Solving the above equation using the least squares method yields the optimal solution. .

[0035] In S03: In some embodiments, the composite loss function is as follows: ; In the formula, , , These represent the seismic data error loss function, the well logging curve fitting loss function, and the P-wave impedance-porosity physical constraint loss function, respectively. , , Used to balance the contribution of each loss term to the total loss function.

[0036] Understandable. , , This can be determined through cross-validation.

[0037] It is understandable that the seismic data error loss function It is used to measure the difference between synthetic seismic records and actual seismic records, so that the far-well area is subject to the overall constraint of the seismic waveform, thereby reducing the ambiguity of the inversion to a certain extent.

[0038] Furthermore, the seismic data error loss function As shown below: ; In the formula, Indicates a synthetic seismic record. Represents actual earthquake records, Total number of seismic traces This indicates the seismic trace index.

[0039] Understandable. From the formula get.

[0040] It is understandable that the loss function for well logging curve fitting... The error relationship between the porosity (and P-wave impedance) output by the network and the measured porosity (and P-wave impedance) well curves is described to introduce high-resolution constraints on the well curves, thereby compensating for the low-frequency trend of the porosity and P-wave impedance inversion results.

[0041] Furthermore, the well logging curve fitting loss function As shown below: ; In the formula, , These represent the measured porosity and P-wave impedance well curves, respectively. , These represent the porosity and mixed longitudinal wave impedance predicted by the network, respectively. This represents the weighting coefficient for the porosity error term. Total number of seismic traces This indicates the seismic trace index.

[0042] Understandable. Used to balance the relative contributions of porosity and longitudinal wave impedance to the loss function.

[0043] It is understandable that the longitudinal wave impedance-porosity physical constraint loss function It is used to measure the deviation between the longitudinal wave impedance calculated from the predicted porosity and the longitudinal wave impedance output by the network. It can suppress solutions that do not conform to the laws of rock physics, thereby improving the consistency between parameters.

[0044] Furthermore, the longitudinal wave impedance-porosity physical constraint loss function As shown below: ; In the formula, This represents the longitudinal wave impedance calculated from the predicted porosity. This is the longitudinal wave impedance predicted by the hybrid network. Total number of seismic traces This indicates the seismic trace index.

[0045] In S04: In some embodiments, a hybrid network is constructed to minimize the composite loss function. Various loss functions in , and The predicted longitudinal wave impedance and porosity are obtained. ,like The training phase of the hybrid network minimizes... Obtain the optimal parameters ,Will Substitute The final longitudinal wave impedance and porosity are obtained. The inversion results.

[0046] It is understandable that the input data for the hybrid network is the actual earthquake record. Longitudinal wave impedance low-frequency model Low-frequency porosity model The mapping relationship is as follows: .

[0047] Secondly, embodiments of this application provide a joint inversion system for longitudinal wave impedance and porosity, including: Hybrid network module, used to build hybrid networks; The forward modeling framework module is used to build the forward modeling framework; The composite loss function module is used to create composite loss functions; The longitudinal wave impedance and porosity module introduces a forward modeling framework and a composite loss function into the hybrid network training, and obtains the final longitudinal wave impedance and porosity through training inversion.

[0048] In the hybrid network module: In some embodiments, the hybrid network includes a residual U-Net network, a bidirectional long short-term memory network, and a Transformer model.

[0049] Please see Figure 1 The hybrid network, comprising ResUNet, BiLSTM, and Transformer models, can fully learn the nonlinear mapping relationship between post-stack seismic records and wave impedance and porosity. The sensitivity of post-stack seismic records to medium parameters is mainly reflected in the waveform morphology of reflection events, which contains high-frequency reflection details corresponding to thin-layer interfaces and low-frequency trend information.

[0050] Figure 1 In this system, the network inputs include seismic records, low-frequency models, and well logging data, and the outputs are wave impedance and porosity. The ResUNet module extracts multi-scale local features, the BiLSTM module establishes a single-channel stratigraphic sequence along the time axis, and the Transformer module aggregates cross-channel features in the spatial dimension.

[0051] It is understandable that ResUNet represents U-Net network and BiLSTM represents bidirectional long short-term memory network.

[0052] It is understood that the hybrid network in this application is the ResUNet-BiLSTM-Transformer hybrid network.

[0053] First, the hybrid network uses ResUNet modules to characterize the multi-scale features of a single-channel waveform. During feature fusion, trend information from the low-frequency model is introduced to jointly constrain the inversion at both the low-frequency background and high-frequency detail scales. This ensures that the inversion results not only depict the local waveform differences between thin layers and interfaces but also maintain consistency with the trends provided by the low-frequency model. The feature extraction of the residual U-Net network in the time dimension is represented as follows: ; In the formula, Indicates the first Layer features; , Convolution kernel weights and biases It is a non-linear activation function.

[0054] Secondly, after representing the waveform's multi-scale information, the joint inversion also needs to mitigate the jagged edges or isolated outliers appearing in adjacent layers of the output results. To this end, a BiLSTM module is introduced into the time feature sequence output by the ResUNet module in the hybrid network. This module utilizes adjacent waveform information through bidirectional time series modeling to improve the stability of inter-layer transitions. Let the time series feature of a single channel provided by the ResUNet module be... Then the bidirectional time series recursion is as follows: ; In the formula, This is a hidden state representation for integrating temporal information before and after the process. index for time sampling points , for The feature vector input at time step 1, The feature dimension, and These represent the forward and backward hidden states, respectively.

[0055] Finally, post-stack data exhibits inter-trace correlation in addition to longitudinal information correlation. If inversion is performed independently for each trace, lateral discontinuities can easily occur due to noise and lateral non-stationarity. Therefore, explicitly incorporating inter-trace correlation into network modeling is an effective way to improve profile consistency. This application introduces an inter-trace self-attention mechanism from the Transformer module after the BiLSTM module, constructs spatial attention units using several adjacent traces, and performs linear mapping on them to construct query, key, and value matrices. To achieve horizontal information aggregation, ; In the formula, This indicates row-wise normalization. The channel dimension of the key vector is used to control the numerical scale; Depend on The obtained attention weight matrix characterizes the similarity between several adjacent traces, and based on this, inter-trace information is adaptively fused to enhance the characterization of seismic inter-trace correlation of reflection events. Subsequently, the hybrid network output layer maps the features aggregated from the spatial attention unit information, and the corresponding output is obtained. .

[0056] In the forward modeling framework module: In some embodiments, the expression of the forward model is as follows: ; In the formula, Represents the seismic wavelet. Indicates time, Represents the convolution operator, Indicates effective porosity. This represents the longitudinal wave impedance.

[0057] Furthermore, the forward modeling framework is obtained as follows: Post-stack seismic response under the assumption of horizontally layered medium Described as the longitudinal wave vertical reflection coefficient With seismic wavelets The formula for the convolution is as follows: ; In the formula, Indicates the post-stack seismic response. Represents the vertical reflection coefficient of longitudinal waves. Represents the seismic wavelet. Indicates time, Represents the convolution operator; No. j The reflectance of the layer It is described by the difference in longitudinal wave impedance between the upper and lower media at the horizontal interface, as shown in the following formula: ; In the formula, Indicates the first j The reflectivity of the layer, Indicates time, , Indicates the upper and lower media. Indicates longitudinal wave impedance, Indicates the longitudinal wave velocity. Indicates the density of the rock layer medium; It is understandable that, for fluid-containing porous media, under the assumptions of a relatively stable rock matrix, homogeneous pore structure, and Newtonian pore fluid, the Wyllie time-averaged equation (Wyllie et al., 1956) establishes the equivalent P-wave velocity of saturated rocks. Functional relationship with porosity.

[0058] Equivalent P-wave velocity of saturated rock The functional relationship with porosity is as follows: ; In the formula, Represents the equivalent P-wave velocity of saturated rock. Indicates effective porosity. Represents the longitudinal wave velocity of the rock matrix. Represents the longitudinal wave velocity of pore fluid; Similarly, the equivalent density of rocks with fluid pores It is also described as a function of porosity, as follows: ; In the formula, This represents the equivalent density of rocks containing fluid pores. For effective porosity, Indicates the density of the rock matrix. The sum and density represent the pore fluid; comprehensive and To obtain effective porosity to longitudinal wave impedance The mapping relationship is as follows: ; In the formula, Indicates longitudinal wave impedance, Represents the equivalent P-wave velocity of saturated rock. This represents the equivalent density of rocks containing fluid pores; Will and Substitute In the end, the relationship between effective porosity and P-wave impedance and seismic response was established, namely the forward modeling framework.

[0059] It is understandable that the above forward modeling process establishes a nonlinear relationship between porosity, P-wave impedance, and post-stack seismic records.

[0060] Furthermore, using the least squares method, we obtain... Longitudinal wave velocity in rock matrix and pore fluid longitudinal wave velocity The specific solution process is as follows: Rewritten ; The elastic physical property parameters of n wells are constructed using the following equations: ; ; In the formula, superscript n Indicates the first n The well curve of the well is obtained by solving the above equation using the least squares method. ; Similarly, establish a solution Rock matrix density and pore fluid density The equation: ; ; Solving the above equation using the least squares method yields the optimal solution. .

[0061] In the composite loss function module: In some embodiments, the composite loss function is as follows: ; In the formula, , , These represent the seismic data error loss function, the well logging curve fitting loss function, and the P-wave impedance-porosity physical constraint loss function, respectively. , , Used to balance the contribution of each loss term to the total loss function.

[0062] Understandable. , , This can be determined through cross-validation.

[0063] It is understandable that the seismic data error loss function It is used to measure the difference between synthetic seismic records and actual seismic records, so that the far-well area is subject to the overall constraint of the seismic waveform, thereby reducing the ambiguity of the inversion to a certain extent.

[0064] Furthermore, the seismic data error loss function As shown below: ; In the formula, Indicates a synthetic seismic record. Represents actual earthquake records, Total number of seismic traces This indicates the seismic trace index.

[0065] Understandable. From the formula get.

[0066] It is understandable that the loss function for well logging curve fitting... The error relationship between the porosity (and P-wave impedance) output by the network and the measured porosity (and P-wave impedance) well curves is described to introduce high-resolution constraints on the well curves, thereby compensating for the low-frequency trend of the porosity and P-wave impedance inversion results.

[0067] Furthermore, the well logging curve fitting loss function As shown below: ; In the formula, , These represent the measured porosity and P-wave impedance well curves, respectively. , These represent the porosity and mixed longitudinal wave impedance predicted by the network, respectively. This represents the weighting coefficient for the porosity error term. Total number of seismic traces This indicates the seismic trace index.

[0068] Understandable. Used to balance the relative contributions of porosity and longitudinal wave impedance to the loss function.

[0069] It is understandable that the longitudinal wave impedance-porosity physical constraint loss function It is used to measure the deviation between the longitudinal wave impedance calculated from the predicted porosity and the longitudinal wave impedance output by the network. It can suppress solutions that do not conform to the laws of rock physics, thereby improving the consistency between parameters.

[0070] Furthermore, the longitudinal wave impedance-porosity physical constraint loss function As shown below: ; In the formula, This represents the longitudinal wave impedance calculated from the predicted porosity. This is the longitudinal wave impedance predicted by the hybrid network. Total number of seismic traces This indicates the seismic trace index.

[0071] In the longitudinal wave impedance and porosity module: In some embodiments, a hybrid network is constructed to minimize the composite loss function. Various loss functions in , and The predicted longitudinal wave impedance and porosity are obtained. ,like The training phase of the hybrid network minimizes... Obtain the optimal parameters ,Will Substitute The final longitudinal wave impedance and porosity are obtained. The inversion results.

[0072] It is understandable that the input data for the hybrid network is the actual earthquake record. Longitudinal wave impedance low-frequency model Low-frequency porosity model The mapping relationship is as follows: .

[0073] Thirdly, this application provides a computer device including a storage device and a processor, wherein the storage device stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the above-described method for joint inversion of longitudinal wave impedance and porosity.

[0074] The computer device can be a desktop computer, laptop, handheld computer, or cloud server, etc. The computer device can interact with the user via a keyboard, mouse, remote control, touchpad, or voice control.

[0075] The memory includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or D-interface display memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, etc. In some embodiments, the memory may be an internal storage unit of the computer device, such as the hard disk or memory of the computer device. In other embodiments, the memory may also be an external storage device of the computer device, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the computer device. Of course, the memory may include both internal storage units and external storage devices of the computer device. In this embodiment, the memory is often used to store the operating system and various application software installed on the computer device, such as the program code of the longitudinal wave impedance and porosity joint inversion method. In addition, the memory can also be used to temporarily store various types of data that have been output or will be output.

[0076] In some embodiments, the processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip. The processor is typically used to control the overall operation of the computer device. In this embodiment, the processor is used to run program code stored in the memory or process data, such as running program code for a joint inversion method of longitudinal wave impedance and porosity.

[0077] Fourthly, this application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the above-described method for joint inversion of longitudinal wave impedance and porosity.

[0078] The computer-readable storage medium stores an interface display program that can be executed by at least one processor to cause the at least one processor to perform the steps of the joint inversion method of longitudinal wave impedance and porosity as described above.

[0079] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the longitudinal wave impedance and porosity joint inversion method described in the embodiments of this application.

[0080] Example Model testing analysis To verify the effectiveness and practicality of the method proposed in this application, this application uses the Marmousii model to conduct comparative experiments on the inversion of elastic physical property parameters by different network structure combinations. Figure 2 ). Figure 2 The image shows the Marmousii model and synthetic seismic record. Subfigures (a) and (b) show the P-wave impedance and corresponding low-frequency model, respectively. Figures (c) and (d) show the porosity (according to...). Figure (e) shows the synthetic seismic record, obtained by convolution of the P-wave reflection coefficient and the 20Hz Ricker wavelet. The label information required for network training was obtained by uniformly sampling 20 data points from the P-wave impedance and porosity model; the remaining seismic traces were treated as unlabeled samples. The labeled samples were then used for calculation. Calculate for unlabeled samples .

[0081] Figure 2 In this context, Impedance is the wave impedance; Porosity is the porosity; Amplitude is the amplitude; and Time is the time interval.

[0082] While maintaining consistent training data, network parameters, and loss term configurations, the BiLSTM and Transformer modules were gradually introduced, using the ResUNet module as a baseline. The effects of different network structure combinations on the inversion of strongly heterogeneous bodies, lateral continuity, and sequence stability were compared to verify the generalization ability of the constructed hybrid network under complex geological conditions and its accuracy in characterizing strongly heterogeneous bodies. Since other experimental conditions, except for the network structure, remained consistent, the differences in output from different network structure combinations can be mainly attributed to their feature extraction and seismic trace information fusion capabilities. The joint inversion results of P-wave impedance and porosity based on different network structures are shown below. Figure 3 As shown. Figure 3In the figure, subfigures (a) and (b) show the longitudinal wave impedance and porosity inversion results based on the ResUNet network structure, respectively; (c) and (d) show the longitudinal wave impedance and porosity inversion results based on the ResUNet and BiLSTM combined network structure (ResUNet-BiLSTM network), respectively; and (e) and (f) show the longitudinal wave impedance and porosity inversion results based on the ResUNet, BiLSTM and Transformer hybrid network structure proposed in this application, respectively.

[0083] Figure 3 In this context, Impedance is the wave impedance; Porosity is the porosity; and Time is the time interval.

[0084] To quantitatively evaluate the joint inversion results of different network structures, this application selects root mean square error (RMSE), mean absolute error (MAE), square of correlation coefficient (SCC), structural similarity (SSIM), and lateral gradient MAE (L-MAE) as evaluation indicators, as shown in Tables 1 and 2. Tables 1 and 2 respectively evaluate the inversion results of longitudinal wave impedance and porosity for different network structures.

[0085] Table 1 Evaluation of the longitudinal wave impedance inversion results for different network structures

[0086] Table 2 Evaluation of Porosity Inversion Results by Different Network Structures

[0087] analyze Figure 3 It can be seen that the ResUNet model provides inversion results for longitudinal wave impedance and porosity ( Figure 3 (a and 3b) The interlayer transition is unstable and the lateral continuity is poor; the introduction of BiLSTM network forms the inversion result of ResUNet–BiLSTM model ( Figure 3 Compared to the inversion results of the ResUNet model (c and 3d) Figure 3 At the points indicated by arrows a and 3b), the deep inversion performance of the ResUNet–BiLSTM model is significantly improved. Figure 3 (at the c and 3d arrows) and closer to the original model ( Figure 2(Arrows a and 2c). However, a "striped" phenomenon still exists in the horizontal direction, resulting in slightly poor lateral resolution. Further introduction of a Transformer network into this network yields the ResUNet–BiLSTM–Transformer model, which significantly reduces the "striped" phenomenon in the inversion results and significantly enhances the lateral resolution. Figure 3 (at the points marked e and 3f), and it matches the original model ( Figure 2 (Arrows a and 2c). Quantitative analysis of the inversion results of longitudinal wave impedance (Table 1) and porosity (Table 2) shows that the hybrid network model proposed in this application has lower RMSE, MAE, and SCC values ​​in the inversion results, indicating a lower numerical deviation from the original model; while the SSIM value is higher, indicating that the structural morphology of the inversion results is closer to the original model; the L-MAE value is also lower, indicating that the newly proposed model has stronger lateral continuity and higher lateral resolution in the inversion results compared with other models.

[0088] Application Example 2 To verify the application effect of the proposed hybrid network model in a real work area, this application selects post-stack seismic data and a low-frequency model of a certain work area to carry out joint inversion of P-wave impedance and porosity. Figure 4 The seismic profile passes through one blind well (Well A) and five training wells (Well B, etc.). Figure 4 In the diagram, subplot (a) shows seismic data with a time depth of 1200ms-1580ms and a sampling interval of 1ms. Subplots (b) and (c) show the low-frequency P-wave impedance model and the porosity model, respectively. The well logs from five training wells, as labeled data, are used to examine the fitting accuracy and stability of the inversion results under well data constraints compared to the measured data. Well A, as a validation well, has its logging curve not involved in any training or gradient updates; it is only used for comparison and evaluation during the testing phase to verify the model's generalization ability to non-training samples.

[0089] Figure 4 In this context, Impedance is the wave impedance; Porosity is the porosity; Amplitude is the amplitude; and Time is the time interval.

[0090] Seismic data and a low-frequency model are input into the hybrid network model proposed in this application. After multiple training iterations, the final output is the P-wave impedance. Figure 5 a) and the joint inversion results of porosity ( Figure 5 b). To balance the total loss function ( To determine the relative contribution of each loss term to network optimization, this application adjusts and filters the weights through multiple experiments and by considering the convergence characteristics (descent rate and stability) of the experimental loss curves. The final weights are then determined. , The values ​​are 1 and 0.3 respectively; considering that unlabeled constraints may lead to unstable optimization in the early stages of training, this application will Set as dynamic parameters: take the values ​​in the first 10% of training epochs. Within the 10%–80% round range It increases linearly to 0.6 and remains stable after reaching 80%. The weight decay coefficient is 0.6. To ensure stable convergence during training under the above weight configuration, this application uses the ADAM optimizer to update network parameters during training. The total number of training iterations is 120, the batch size (sample size per iteration) is 190, and the weight decay coefficient is [missing value]. To achieve stable convergence with an adaptive learning rate, a learning rate scheduling strategy based on the total loss value, ReduceLROnPlateau, is adopted: Let the initial learning rate be set to... When the total loss value does not exceed a certain threshold within four consecutive iterations When improving, the learning rate is decayed by 0.6 times, and the lower limit of the learning rate is set to... .

[0091] In the figure, the black curves are the longitudinal wave impedance curve (a) and the porosity curve (b) of the well bypass, respectively.

[0092] To more intuitively compare the joint inversion results, the inversion results of the verification wells and training wells were extracted and compared with the measured well curves, as shown below. Figure 6 As shown. Figure 6 In the figure, subfigures (a) and (b) show the comparison between the inversion results of the longitudinal wave impedance of the wellbore channel of wells A and B and the measured curves, respectively. Subfigures (c) and (d) show the comparison between the inversion results of the porosity of the wellbore channel of wells A and B and the measured curves, respectively.

[0093] In the figure, red, green, and blue represent the original model, low-frequency model, and inversion result of longitudinal wave impedance (or porosity), respectively.

[0094] To quantitatively evaluate the accuracy of the P-wave impedance and porosity inversion results, this application conducts an error statistical analysis on the P-wave impedance (Table 3) and porosity (Table 4) inversion results of the wellbore bypass channels of wells A and B. Tables 3 and 4 present the root mean square error (RMSE), mean absolute error (MAE), and squared correlation coefficient (SCC) of the measured and predicted results of the wellbore bypass channels as evaluation indicators.

[0095] Table 3. Quantitative Analysis of the Longitudinal Wave Impedance Inversion Results for Wells A and B Table 3. Quantitative Analysis of the Side-Channel Longitudinal Wave Impedance Inversion Results for Wells A and B

[0096] Table 4. Quantitative Analysis of Porosity Inversion Results for Well A and B (External Channels)

[0097] analyze Figure 4 and 5 It can be seen that the joint inversion results show a decrease in P-wave impedance in the target section of the gas-bearing sandstone reservoir (red arrow). Figure 5 a) Increased porosity ( Figure 5 (b) This is consistent with the well curve of verification well A, demonstrating the reliability of the inversion results of the hybrid network model proposed in this application. Single-channel analysis of the well bypass ( Figure 6 This indicates that the well bypass inversion results of training well B ( Figure 6 (b and 6d) are basically consistent with the corresponding well curves of well B, indicating that the model training samples can converge effectively; the inversion results of the well bypass of well A are verified. Figure 6 (a) and (6c) still largely match the curve of well A, indicating that the proposed inversion method has high lateral resolution, strong stability, and is reliable. Quantitative analysis of the well bypass inversion results (Tables 3 and 4) shows that the error between the inversion results and the measured curves is small and the correlation is strong. Furthermore, the inversion results of the unlabeled sample data (well bypass of well A) do not show a significant dependence on the training sample data (well bypass of well B).

[0098] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for joint inversion of longitudinal wave impedance and porosity, characterized in that, include: Constructing hybrid networks; Establish a forward modeling framework; Establish a composite loss function; In the training of the hybrid network, a forward modeling framework and a composite loss function are introduced, and the final longitudinal wave impedance and porosity are obtained through training inversion.

2. The method for joint inversion of longitudinal wave impedance and porosity according to claim 1, characterized in that, Hybrid networks include residual U-Net networks, bidirectional long short-term memory networks, and Transformer models.

3. The method for joint inversion of longitudinal wave impedance and porosity according to claim 1, characterized in that, The expression for the forward modeling framework is as follows: ； In the formula, Represents the seismic wavelet. Indicates time, Represents the convolution operator, Indicates effective porosity. This represents the longitudinal wave impedance.

4. The method for joint inversion of longitudinal wave impedance and porosity according to claim 3, characterized in that, The forward modeling framework is obtained as follows: Post-stack seismic response under the assumption of horizontally layered medium Described as the longitudinal wave vertical reflection coefficient With seismic wavelets The formula for the convolution is as follows: ； In the formula, Indicates the post-stack seismic response. Represents the vertical reflection coefficient of longitudinal waves. Represents the seismic wavelet. Indicates time, Represents the convolution operator; No. j The reflectance of the layer It is described by the difference in longitudinal wave impedance between the upper and lower media at the horizontal interface, as shown in the following formula: ； In the formula, Indicates the first j The reflectivity of the layer, Indicates time, , Indicates the upper and lower layers of medium. Indicates longitudinal wave impedance, Indicates the longitudinal wave velocity. Indicates the density of the rock layer medium; Equivalent P-wave velocity of saturated rock The functional relationship with porosity is as follows: ； In the formula, Represents the equivalent P-wave velocity of saturated rock. Indicates effective porosity. Represents the longitudinal wave velocity of the rock matrix. Represents the longitudinal wave velocity of pore fluid; Similarly, the equivalent density of fluid-porous rocks It is also described as a function of porosity, as follows: ； In the formula, This represents the equivalent density of rocks containing fluid pores. For effective porosity, Indicates the density of the rock matrix. The sum and density represent the pore fluid; comprehensive and To obtain effective porosity to longitudinal wave impedance The mapping relationship is as follows: ； In the formula, Indicates longitudinal wave impedance, Represents the equivalent P-wave velocity of saturated rock. This represents the equivalent density of rocks containing fluid pores; Will and Substitute In the end, the relationship between effective porosity and P-wave impedance and seismic response was established, namely the forward modeling framework.

5. The method for joint inversion of longitudinal wave impedance and porosity according to claim 1, characterized in that, The composite loss function is shown in the following equation: ； In the formula, , , These represent the seismic data error loss function, the well logging curve fitting loss function, and the P-wave impedance-porosity physical constraint loss function, respectively. , , Used to balance the contribution of each loss term to the total loss function.

6. The method for joint inversion of longitudinal wave impedance and porosity according to claim 5, characterized in that, Seismic data error loss function As shown below: ； In the formula, Indicates a synthetic seismic record. Represents actual earthquake records, Total number of seismic traces Indicates a seismic trace index; and / or Well logging curve fitting loss function As shown below: ； In the formula, , These represent the measured porosity and P-wave impedance well curves, respectively. , These represent the porosity and mixed longitudinal wave impedance predicted by the network, respectively. This represents the weighting coefficient for the porosity error term. Total number of seismic traces Indicates a seismic trace index; and / or Longitudinal wave impedance-porosity physical constraint loss function As shown below: ； In the formula, This represents the longitudinal wave impedance calculated from the predicted porosity. This is the longitudinal wave impedance predicted by the hybrid network. Total number of seismic traces This indicates the seismic trace index.

7. The method for joint inversion of longitudinal wave impedance and porosity according to claim 1, characterized in that, By constructing a hybrid network to minimize the composite loss function Various loss functions in , and The predicted longitudinal wave impedance and porosity were obtained. ,like ; The training phase of the hybrid network is achieved by minimizing Obtain the optimal parameters ,Will Substitute The final longitudinal wave impedance and porosity are obtained. The inversion results.

8. A joint inversion system for longitudinal wave impedance and porosity, characterized in that, include: Hybrid network module, used to build hybrid networks; The forward modeling framework module is used to build the forward modeling framework; The composite loss function module is used to create composite loss functions; The longitudinal wave impedance and porosity module introduces a forward modeling framework and a composite loss function into the hybrid network training, and obtains the final longitudinal wave impedance and porosity through training inversion.

9. A computer device, characterized in that, It includes a storage device and a processor, the storage device storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The device stores a computer program that, when executed by a processor, causes the processor to perform the steps of the method as described in any one of claims 1-7.

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