Low-frequency model building method based on spatial structure features and joint sparse representation

Abstract

The present invention utilizes regularization technology and joint sparse representation technology to propose a method for establishing a low-frequency model based on spatial structural features and joint sparse representation. First, dictionary learning and sparse representation technology are used to address the impact of vertical differences in logging data on the results when using interpolation methods. The existing logging data is transformed from a single weight value for a piece of logging data to multiple weight values ​​for multiple segments on a piece of logging data, which to a certain extent solves the bull's eye effect caused by vertical differential characteristics. Second, joint sparse representation technology and a large-scale overdetermined equation solution method based on optimization are used to introduce the spatial structural features of seismic data and the spatial information of logging data into the low-frequency model. A large-scale overdetermined equation system based on an inversion framework is constructed for optimization and solution. By continuously iteratively updating the low-frequency model, a low-frequency model with a smaller error than the true model is ultimately obtained.

Description

Technical Field

[0001] The present invention belongs to the field of geophysical science, and specifically relates to a method for establishing a low-frequency model based on spatial structure characteristics and joint sparse representation. Background Art

[0002] For unconventional oil and gas reservoirs, the economic efficiency and effectiveness of oil and gas development are crucial. High-precision reservoir prediction is an important means to achieve this. In the process of high-precision reservoir prediction, the establishment of a low-frequency model is a key step, which involves a preliminary description and representation of the overall changes in the underground structure of the entire work area. A low-frequency model typically contains a variety of parameters that describe underground geological characteristics, generally including compressional wave velocity, shear wave velocity, density, sequence structure, etc. At the same time, the low-frequency model provides a starting point for the inversion process and imposes certain constraints on the inversion process, allowing for more accurate prediction of the true underground structural characteristics. In short, the quality of the low-frequency model plays a vital role in obtaining a high-precision and reliable inversion result. A low-frequency model that can accurately reflect the underground structure can reduce the number of iterations in the inversion process, speed up the inversion process, and achieve high-precision inversion.

[0003] Low-frequency modeling methods can be broadly categorized into two types based on the data used: interpolation methods that infer unknown regions based on existing well logging data, and methods that build low-frequency models based on seismic data. When building low-frequency models based on seismic data, reservoir parameters for the entire work area are generally predicted using seismic attributes, resulting in a low-frequency model for the entire area. While seismic data can well reflect the lateral continuity of stratigraphic distribution, its frequency band, typically between 10 and 50 Hz, significantly lacks low-frequency information. While it is possible to compensate for the missing low-frequency components in seismic data, which can somewhat increase the low-frequency range, it is difficult to fully compensate for the missing low-frequency components. In practical applications, low-frequency models are often constructed using interpolation methods that employ reasonable interpolation and extrapolation within constraints using well logging data with full-band information. While well logging data provides full-band information, it is expensive to acquire, and the amount of well logging data available for a given work area is generally limited. Therefore, building a low-frequency model that aligns with the true subsurface structure from this limited data is challenging.

[0004] Interpolation methods assume that subsurface spatial variation is continuous and that attribute values ​​at adjacent locations are similar. They fail to consider lateral variations in the formation and rely excessively on a priori assumptions. During interpolation, multiple well-logging curves are used to calculate a weight based on spatial structural relationships. These multiple well-logging curves are then weighted according to this weight to produce the well-logging curve for the unknown well, resulting in a single weighted well-logging curve. Furthermore, interpolation methods fail to account for the vertical variability of well-logging data. If the assumed subsurface structure does not match the actual subsurface structure or the well-logging data is of poor quality, the low-frequency model can easily exhibit a bull's-eye effect, significantly deviating from the actual low-frequency model. Summary of the Invention

[0005] The purpose of the present invention is to propose a low-frequency model establishment method based on spatial structural features and joint sparse representation, so as to solve the technical problems proposed in the above background technology that the existing interpolation method has a single weight, over-reliance on prior assumptions, and cannot cope with the irregularity and diversity of data.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for establishing a low-frequency model based on spatial structural features and joint sparse representation, specifically comprising the following steps:

[0008] S01. Obtain seismic data S and existing well logging curves for the work area and perform block processing;

[0009] S02. After normalizing the block processing results, perform joint dictionary D training and divide the joint dictionary D into logging curve dictionary D w and earthquake data dictionary D sei ;

[0010] S03. Using the earthquake data dictionary D sei Perform joint sparse characterization to obtain the sparse coefficient α of the seismic data in the work area;

[0011] S04. Using the logging curve dictionary D w and the sparse coefficient α to perform reconstruction processing to obtain an initial low-frequency model;

[0012] S05. Construct an optimization solution process similar to the inversion process based on optimization theory and inversion theory;

[0013] S06. Add the interpolation function as a regularization constraint to the optimization process to further reduce the size of the solution space;

[0014] S07. Solve a large-scale overdetermined system of equations using a conjugate gradient descent algorithm, and perform sparse representation and sparse reconstruction on the solved low-frequency model; calculate the error σ between the reconstructed low-frequency model and the low-frequency model of the previous iteration; and calculate the error σ1 between the reconstructed seismic data and the actual seismic data;

[0015] S08. Repeat the process from step S05 to step S07 until the error σ and error σ1 remain stable, then the iterative process is completed, and the sparse coefficient is finally calculated. And reconstruct the low-frequency model

[0016] S09. Perform denormalization and other processing on the iterated low-frequency model data to restore the original low-frequency model format.

[0017] Furthermore, in step S02, all data for training the joint dictionary D are normalized to 0-1, and the joint dictionary D is trained by the K-SVD algorithm.

[0018] The training of the joint dictionary D is expressed as an energy minimization optimization problem, and the objective function is:

[0019]

[0020]

[0021] Where A is a sparse coefficient matrix, and D is a joint dictionary trained with the three elastic parameters of the well logging curve and seismic data. A single atom in this joint dictionary is trained with the four parameters at the same position in the same trace. It also contains the characteristics of the four parameters and the relationship between them, which can be expressed as follows:

[0022]

[0023] Among them, D P 、D S 、D R 、D Sei dictionaries representing compressional wave velocity, shear wave velocity, density, and seismic data, respectively;

[0024] Y is the sample data for training the joint dictionary. The sample data is formed by combining the sample data of the four parameters by taking small blocks and expressing it as follows:

[0025]

[0026] Among them, Y P 、Y S 、Y R 、Y SeiRepresents a collection of sample blocks of compressional wave velocity, shear wave velocity, density, and seismic data, respectively. The joint dictionary D is divided into a well logging dictionary Dw and a seismic data dictionary Dsei. The dictionary atoms of the joint dictionary are composed of well logging curves and seismic data. The dictionary atoms contain correlation information between well logging curves and seismic data. Therefore, seismic data and well logging curves can share a sparse coefficient.

[0027] Furthermore, in step S03, since the corresponding seismic data and well logging curves can be obtained by sparse reconstruction using the joint dictionary, the orthogonal matching pursuit OMP algorithm is used to utilize the existing seismic data S and the seismic data dictionary D. sei Sparse representation can be used to obtain the sparse coefficient α of seismic data, as shown in the following formula:

[0028] α=OMP(S,D sei ).

[0029] Furthermore, in step S05, an iterative method is used to solve a stable sparse coefficient using multiple iterations, and its objective function is expressed as follows:

[0030]

[0031] Where m represents the low-frequency model to be solved, s represents the seismic data, and α i represents the sparse representation obtained from seismic data, R i They represent the small block matrices of the samples of P-wave velocity, S-wave velocity, density and seismic data respectively, η represents the weight of the initial sparsely reconstructed low-frequency model in the iterative process, λ represents the weight of the seismic data introduced for correction in the iterative process, and m0 represents the initial low-frequency model reconstructed using sparse methods.

[0032] Furthermore, in step S06, the interpolation function is an interpolation low-frequency model. The interpolation low-frequency model with spatial characteristics is introduced into the iterative process of sparse representation as a constraint term, and the spatial structure information of the logging curve is introduced. The objective function is as follows:

[0033]

[0034] Among them, m I represents the low-frequency model obtained using the interpolation function, and γ represents the weight of the interpolated low-frequency model during the iteration process.

[0035] The interpolated low-frequency model is obtained by introducing prior knowledge interpolation based on the structure of considering spatial distance, which contains specific spatial structure information and prior information.

[0036] Another object of the present invention is to provide a low-frequency model based on spatial structural features and joint sparse representation established by the above method.

[0037] The present invention has the following beneficial effects:

[0038] The present invention analyzes practical problems and proposes a new method for establishing a low-frequency model using regularization technology and joint sparse representation technology. First, dictionary learning and sparse representation technology are used to solve the impact of vertical differences in logging data on the results when using interpolation methods. The existing logging data is transformed from a single weight value of a logging data to multiple weight values ​​of multiple segments on a logging data. To a certain extent, this solves the bull's eye effect caused by vertical differences. Second, joint sparse representation technology and a large-scale overdetermined equation solution method based on optimization are used to introduce the spatial structural characteristics of seismic data and the spatial information of logging data into the low-frequency model. A large-scale overdetermined equation system similar to an inversion framework is constructed for optimization and solution. By continuously iteratively updating the low-frequency model, a low-frequency model with a smaller error than the true model is ultimately obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0040] Figure 1 Normalized plots of elastic parameters and seismic data;

[0041] Figure 2 This is the cross-sectional view of the longitudinal wave model of the marmousi model;

[0042] Figure 3 Synthesize post-stack seismic data for the Marmousi model;

[0043] Figure 4 This is the cross-sectional diagram of the marmousi model longitudinal wave 20Hz low-frequency model;

[0044] Figure 5 (a) is a single well with low-frequency model established by interpolation method; Figure 5 (b) is a single well with a low-frequency model established by the method of the present invention;

[0045] Figure 6 (a) is the interpolation method to establish the low-frequency model of longitudinal waves; Figure 6 (b) is a joint sparse representation to establish a low-frequency model of longitudinal waves; Figure 6(c) is a method for establishing a low-frequency model based on spatial structure and joint sparse representation of the present invention;

[0046] Figure 7 (a) is the comparison between the real well and the established well using the interpolation method; Figure 7 (b) is a comparison between the actual well of the present invention and the established well;

[0047] Figure 8 (a) is the low-frequency model established by interpolation method; Figure 8 (b) is the low-frequency model established by the joint sparse representation method; Figure 8 (c) is a low-frequency model based on spatial structure and joint sparse representation method;

[0048] Figure 9 (a) is the low-frequency model established by interpolation method; Figure 9 (b) is the low-frequency model established by the joint sparse representation method; Figure 9 (c) is a low-frequency model based on spatial structure and joint sparse representation method;

[0049] Figure 10 (a) is the low-frequency model established by interpolation method; Figure 10 (b) is a low-frequency model established by the method of the present invention;

[0050] Figure 11 (a) is the inversion result of the low-frequency model established by the interpolation method; Figure 11 (b) is the inversion result of the low-frequency model established by the method of the present invention;

[0051] Figure 12 (a) is the blind well correlation diagram of the low-frequency model established using different numbers of wells by interpolation method; Figure 12 (b) is a blind well correlation diagram of a low-frequency model established using different numbers of wells based on the spatial structure and joint sparse representation method of the present invention;

[0052] Figure 13 Relative error diagram of inversion for the low-frequency models established by the three methods. DETAILED DESCRIPTION

[0053] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] See Figure 1-13 As shown in FIG, a method for establishing a low-frequency model based on spatial structure features and joint sparse representation includes the following steps:

[0055] S01. Obtain seismic data S and existing well logging curves for the work area and perform block processing;

[0056] Images of different resolutions known as training sample sets are taken as two different sample sets. Each training set with different resolutions has different characteristics. According to this characteristic, the images are divided into blocks according to the resolution. Small blocks of images with different resolutions are pieced together to form a new training set sample. In this way, the same block contains images with high and low resolutions. At the same time, in the process of sparse representation, the high-resolution and low-resolution image blocks of the same block have the same sparse coefficient.

[0057] S02. After normalizing the block processing results of step S01, perform joint dictionary training and divide the obtained joint dictionary into a well logging curve dictionary and a seismic data dictionary;

[0058] In the process of training the joint dictionary, the data must be normalized, and the parameters required for training the dictionary must be normalized to the same range. This ensures that the weight of each parameter feature is equal, and each feature can make the same contribution to the dictionary, thereby ensuring that the dictionary can better reflect the characteristics of the data. In actual logging data, the range of elastic parameters is very large, the range of longitudinal waves is about 4000-6000, the range of shear waves is about 2000-3500, and the range of density is about 1-3. In addition, the range of seismic data is also very different. Generally, the range of seismic data is about -10000 to 10000. In order to simplify the operation, the present invention normalizes all data for training the joint dictionary to 0-1. The normalization diagram of elastic parameters and seismic data is shown in Figure 2. Figure 1 shown.

[0059] The joint dictionary D of seismic data and well logging curves is obtained by training the K-SVD (K-Singular Value Decomposition) algorithm. The training of the joint dictionary D can be described as the objective function to be optimized as shown in Equations (1) to (4):

[0060]

[0061] The process of training an overcomplete dictionary, namely the joint dictionary D, that can represent the characteristics of the entire work area from the existing well logging curves and seismic data can be described as an optimization problem of energy minimization. The objective function is:

[0062]

[0063]

[0064] Where A is a sparse coefficient matrix, and D is a joint dictionary trained with the elastic three parameters of the well logging curve and seismic data. The single atom in the joint dictionary is trained with the four parameters at the same position in the same trace, and contains the characteristics of the four parameters and the relationship characteristics between the parameters, which can be expressed as formula (6):

[0065]

[0066] Among them, D P 、D S 、D R 、D Sei Dictionaries representing compressional wave velocity, shear wave velocity, density, and seismic data, respectively.

[0067] Y is the sample data for training the joint dictionary. The sample data is formed by combining the sample data of the four parameters by taking small blocks and expressing it as formula (7):

[0068]

[0069] Among them, Y P 、Y S 、Y R 、Y Sei A collection of sample patches representing compressional wave velocity, shear wave velocity, density, and seismic data, respectively.

[0070] Split the joint dictionary D into the well logging dictionary D w and earthquake data dictionary D sei The dictionary atoms of the joint dictionary are composed of well logging curves and seismic data. There is correlation information between well logging curves and seismic data between dictionary atoms. Therefore, seismic data and well logging curves can share a sparse coefficient.

[0071] S03. Using the earthquake data dictionary D obtained in step S02 sei Perform joint sparse characterization to obtain the sparse coefficients of seismic data in the work area;

[0072] Since the sparse reconstruction using the joint dictionary can obtain the corresponding seismic data and well logging curves, the Orthogonal Matching Pursuit (OMP) algorithm is used to use the existing seismic data S and the seismic data dictionary D obtained in step S02. sei The sparse coefficient α of seismic data can be obtained by sparse representation, as shown in formula (8):

[0073] α=OMP(S,D sei ) (8)

[0074] S04. Using the well logging curve dictionary D obtained in step S02 w Reconstruct the sparse coefficient α obtained in step S03 to obtain an initial low-frequency model;

[0075] Since the seismic data and the well logging curve share a sparse coefficient, and the sparse reconstruction using the joint dictionary can obtain the corresponding seismic data and well logging curve, the sparse coefficient α is used to reconstruct the well logging curve to obtain the well logging curve That is, the initial sparse reconstruction low-frequency model is as shown in formula (9):

[0076]

[0077] The stratigraphic changes in the entire work area are almost consistent, and the seismic data of the entire work area exist. The seismic data of the entire work area are used to obtain an approximate logging curve for the entire work area. This logging data not only selects the most obvious and most consistent features corresponding to the entire work area, but also considers the differences vertically, and also has the characteristics of lateral continuity of seismic data.

[0078] S05. Construct an optimization solution process similar to the inversion process based on optimization theory and inversion theory;

[0079] Sparse representation is based on data only, considering the data features and the relationship between data. Although it eliminates the bull's eye effect and has the lateral characteristics of seismic data, it will lead to the initial low-frequency model established. Excessive adherence to the characteristics of seismic data without considering the spatial structure between wells leads to the establishment of an initial low-frequency model. There is a certain gap with the real low-frequency model.

[0080] At the same time, the sparse representation algorithm is an unstable algorithm. The sparse coefficients solved each time are different. Using the iterative method, multiple iterations can solve a stable sparse coefficient. Its objective function is formula (10):

[0081]

[0082] Where m represents the low-frequency model to be solved, s represents the seismic data, and α i represents the sparse representation obtained from seismic data, R i They represent the small block matrices of the samples of P-wave velocity, S-wave velocity, density and seismic data respectively, η represents the weight of the initial sparsely reconstructed low-frequency model in the iterative process, λ represents the weight of the seismic data introduced for correction in the iterative process, and m0 represents the initial low-frequency model reconstructed using sparse methods.

[0083] This process reduces the uncertainty of sparse representation through continuous iteration and ultimately obtains a stable low-frequency model.

[0084] S06. Add the interpolation function as a regularization constraint to the optimization process to further reduce the size of the solution space;

[0085] The interpolated low-frequency model is obtained by interpolating prior knowledge from the structure considering spatial distance, which contains specific spatial structural information and prior information. The interpolated low-frequency model with spatial characteristics is introduced into the iterative process of sparse representation as a constraint term, introducing the spatial structural information of the logging curve. Its objective function is formula (11):

[0086]

[0087] Among them, m I represents the low-frequency model obtained using the interpolation function, and γ represents the weight of the interpolated low-frequency model during the iteration process.

[0088] S07. Use the conjugate gradient descent algorithm to solve the large-scale overdetermined system of equations, and perform sparse representation and sparse reconstruction on the solved low-frequency model; calculate the error σ between the reconstructed low-frequency model and the low-frequency model of the previous iteration, as shown in formula (12); and calculate the error σ1 between the reconstructed seismic data and the real seismic data, as shown in formula (13);

[0089]

[0090] S08. Repeat the process from step S05 to step S07 until the error σ and error σ1 remain stable, then the iterative process is completed, and the sparse coefficient is finally calculated. And reconstruct the low-frequency model

[0091] For the objective function (11), we first obtain an initial sparse coefficient through the known seismic data, and then solve it iteratively. During the solution process, we need to continuously calculate the corresponding error so that the obtained sparse coefficient meets the conditions of formula (14):

[0092]

[0093] Finally, the sparse coefficient is calculated Through the sparse coefficient Reconstructing the low-frequency model As shown in formula (15):

[0094]

[0095] S09. Perform denormalization and other processing on the iterated low-frequency model data to restore the original low-frequency model format.

[0096] In order to verify the effectiveness of the present invention, model experiments were carried out using the interpolation method, the joint sparse method, and the spatial structure and joint sparse representation method of the present invention.

[0097] Comparative experiments were conducted from three aspects, simulating the use of three methods to establish low-frequency models when there are few logging curves and the curves vary greatly, as well as the use of three methods to establish low-frequency models when there are many logging curves and non-uniform and uniform logging curves.

[0098] Firstly, according to the three elastic parameter data of the Marmousi model, a Marmousi model seismic data is synthesized using the forward modeling process and Ricker wavelet with a frequency of 18.263 Hz. Figure 2 This is the real marmousi model longitudinal wave profile.

[0099] Figure 3 The seismic data profile is synthesized using the forward modeling process and the Ricker wavelet with a frequency of 18.263Hz. The real marmousi longitudinal wave model data is then processed with a low-frequency filter of 20Hz to obtain low-frequency model data below 20Hz. Figure 4 This is the model image after applying a 20Hz low-frequency filter to the real P-wave model of Marmousi. From the Marmousi P-wave model image, we can see that the Marmousi model contains complex stratigraphic structures that simulate various conditions in the real geological environment, such as faults, folds, tilts, and non-uniform rock layers.

[0100] In extreme cases, when there are only a few well logging curves and the existing log variations vary significantly, interpolation can cause layer crossover and layer line mismatches, resulting in a significant discrepancy between the interpolated low-frequency model and the true low-frequency model, leading to poor inversion results. To simulate this extreme situation, two very different traces were extracted from the true low-frequency model for experimental verification. This experiment selected the 2nd and 998th model curves as simulated true well logging curves. The significant difference in the variation trends of these two model curves can be roughly interpreted as the case of layer crossover when constructing the initial model through interpolation in a true well logging situation. Figure 5 This is a comparison diagram of a single blind well between the low-frequency model established using the 2nd and 998th track model data by the present invention method and the interpolation method, respectively, and the real low-frequency model.

[0101] As can be seen from the blind wells, the model data calculated using interpolation differs significantly from the true model data for a single well, and the change trend does not correspond. However, the model data calculated by this method maintains the same change trend as the true model data and has a high degree of consistency and high correlation.

[0102] For reservoir inversion, the relative change trend of a profile is the most important. An ideal low-frequency model should be able to fully reflect the relative change trend. Figure 6 The P-wave low-frequency model profiles were constructed using three methods to select the real logging curves of the 2nd and 998th model data.

[0103] When the number of wells is small and the log curves used vary widely, the low-frequency model constructed using interpolation does not correspond to the true horizon. The overall low-frequency model exhibits a gradual shift from high to low values ​​at the same location on the log curve. While the model matches well in areas of horizontal variation near the selected trace, it differs significantly in areas with more dramatic variations, such as pinch-outs and spikes. This suggests that the interpolation model is more suitable for areas with less stratal variation and flat formations. The low-frequency model constructed using the joint sparse method performs better in this extreme case. By learning the characteristics of both the model data and the seismic data, the model demonstrates excellent vertical performance, matching the true model to a certain extent and avoiding layer crosstalk. However, due to the instability of the sparse representation, redundant feature blocks appear in some locations, which is inconsistent with the true model. Furthermore, although the joint sparse representation incorporates the lateral continuity of the seismic data, it still exhibits some lateral continuity deficiencies, resulting in suboptimal performance in the lateral direction. The low-frequency model based on spatial structure and joint sparse representation performs slightly better than the two aforementioned methods. Compared to interpolation, it maintains vertical features to a certain extent, avoiding layer-by-layer problems. Compared to joint sparse representation, the use of a quasi-inversion approach further incorporates the spatial structure of the model data, demonstrating stronger lateral continuity and eliminating the redundant feature blocks that arise in joint sparse representation. The resulting low-frequency model is closer to the true model.

[0104] In the case of a large number of well logging curves, verification was performed. To ensure the rationality of the experiment, 20 randomly selected and 50 regularly spaced model data were used as test data to simulate real well logging curves. To ensure the fairness of the experiment, the parameters used for training the dictionary and representation in the two cases were consistent.

[0105] For the random selection of 20 model data, first randomly extract 20 well data and corresponding seismic data from 1000 seismic data and model data as known well logging curves and seismic data to train the joint dictionary, and obtain the joint dictionary of seismic data and well logging curves. Figure 7The blind well effects of the interpolation method, the low-frequency model established based on spatial structure and the joint sparse representation method when a large number of wells are randomly selected for logging are given. The blind well here is the 350th model data. The low-frequency model is established using the interpolation method, the joint sparse representation method, the spatial structure and the joint sparse representation method. The established low-frequency model is shown in Figure 2. Figure 8 .Depend on Figure 8 It can be seen from the low-frequency model that the low-frequency model established by the interpolation method does not respond obviously to the layer, and cannot accurately reflect some vertical features. The horizontal continuity in the vertical direction is not strong, and the details are not significant. However, the features on the horizontal layer can be well reflected and processed, and the model of the horizontal layer is very consistent with the real model. In the joint sparse representation method, the vertical features in the model can be well reflected and are consistent with the real model. For the horizontal continuity features, it is generally consistent with the real model, but there is still a big gap. For the changes in the real model that are more intense and detailed, the joint sparse representation method can better handle them, and the low-frequency model established is more accurate. In the spatial structure-based and joint sparse representation methods, the vertical features and horizontal continuity features in the real model can be well processed, and the detail features can also be better processed. The low-frequency model established by this method is more consistent with the real low-frequency model.

[0106] For the rule of selecting 20 model data, first, from the 1000 model data, one model data is taken every 49 model data as the simulated logging curve, and the seismic data of the corresponding channel in the synthetic seismic data is extracted. Then, the 20 model data and the synthetic seismic data are used as known data to train the joint dictionary, and the trained joint dictionary is used to establish a low-frequency model using the joint sparse representation and the method based on spatial structure and joint sparse representation. In order to ensure the effectiveness of the comparison, it is also necessary to use the interpolation method to establish a low-frequency model using these 20 model data. The low-frequency models established by the three methods are as follows Figure 9 .Depend on Figure 9It can be seen from the low-frequency model established that when the model data selected by the rules are used as the simulation logging curve, the effect of the low-frequency model established by using interpolation is better than that of the randomly selected model data, especially the more obvious reaction to the vertical feature. However, compared with the method proposed by the present invention, the method of joint sparse characterization is that in terms of the features and continuity in the horizontal direction, although the joint sparse characterization introduces the lateral features of the seismic data, so that the low-frequency model established has a certain lateral continuity, the interpolation method is better than the joint sparse characterization, and for the vertical features and continuity, the joint sparse characterization is better than the interpolation method. The low-frequency model established based on the spatial structure and the joint sparse characterization method of the present invention is better in both the horizontal and vertical features. Although it still has a certain error with the real model, it cannot well reflect many regional features that are not detailed, but it can still clearly reflect the general trend of change and features that are consistent with the real model.

[0107] To more accurately compare the accuracy of the low-frequency models established by the three methods under different circumstances, the initial models were used in the actual inversion process to compare their impact on the inversion results. To ensure fairness, the parameters and iterations of the inversion process were kept consistent, using sparse inversion, 10 iterations, and a sparsity of 1.

[0108] For the case where only the layers and features with large differences are selected, the low-frequency model established using the three methods is added to the inversion process, and the inversion profile is as follows Figure 10 As shown. Figure 10 In the inversion results, when the model data with large differences in layers and features are selected as the low-frequency model established by simulating the real logging curve as the initial model for inversion, the layer features of the inversion results do not correspond to the real model, and a hanging noodle phenomenon occurs, which is very different from the real model. When the low-frequency model established by joint sparse representation is used as the initial model for inversion, the vertical features of the inversion results correspond to the real model, but the lateral feature changes are roughly consistent with the real model, and there is still a big gap with the real model in the details. When the low-frequency model based on spatial structure and joint sparse representation is used as the initial model for inversion, the inversion results are closer to the real model. Although there is a certain gap with the real model, it is better than the previous two methods in terms of changes in lateral and vertical features, and the difference with the real model is smaller.

[0109] In order to test the performance of the method of the present invention in practical applications, the actual test data were selected as well logging data and seismic data from a work area in China. The data contained a total of 22 well logging data, and the actual available data range of each well logging data was 240ms. The method of the present invention was applied to actual post-stack seismic data and well logging curves.

[0110] There are 22 wells in this work area. After block splicing of the three elastic parameters and seismic data in the drilling data, a joint dictionary containing the characteristics of the entire work area was learned. Then, interpolation and joint sparse representation were performed to establish a low-frequency model, and finally the following was obtained: Figure 11 Low frequency model of . Figure 11 It can be seen from the results obtained only through joint sparse representation processing that the lateral characteristics of the interpolated low-frequency model are not obvious. For the logging of the same layer in the logging curve, there are extreme points and bull's eyes. However, the low-frequency model obtained by using joint sparse representation has more obvious lateral characteristics, and the lateral changes are consistent with the layers. Although the effect with the real well is reduced, the general area is located at the extreme points of the well. In order to more clearly verify the effectiveness of the established low-frequency model, the same round of inversion was performed on the established low-frequency model. Figure 11 is the inversion result. Figure 11 It can be seen from the inversion results that the low-frequency model established by the joint dictionary is effective. While solving the bull's eye effect, it strengthens the lateral characteristics of the inversion solution to a certain extent, and the detail information is more obvious.

[0111] In order to quantitatively measure the superiority of the low-frequency model establishment method based on spatial structure and joint sparse representation proposed in this invention over the traditional interpolation method for establishing low-frequency models, Figure 12 The following plots show the changes in blind well correlation when using different numbers of wells to build low-frequency models. The interpolation method for calculating blind wells is subject to significant uncertainty. This is not the case with using more wells, but rather depends on the spatial relationship between the current blind well and the other wells. If the blind wells used for testing differ significantly from or are far from the majority of the training set logging data, the calculated blind wells will be even more different from the actual logging data, with lower correlations and poorer reflection of the relative trends in the actual logging data. However, the opposite is true for blind wells established using spatial structure and joint sparse representation methods. As the number of logging data increases, the reconstructed blind wells better reflect the trends in the actual logging data and can maintain a relatively good performance even with fewer training set samples.

[0112] Figure 13The effects of the inverse distance weighted interpolation method, the joint sparse representation method proposed in this invention, and the low-frequency model established based on the spatial structure and the joint sparse representation method on inversion are given, and the relative errors between the inversion results and the true results of a total of 1000 traces on the entire profile are given. Figure 13 It can be seen that the relative error of the inversion results of the low-frequency model established by the interpolation method increases sharply in some channels. This may be due to the fact that the actual underground characteristics of these locations are very different from the logging data we selected for interpolation, resulting in a large difference between the low-frequency model and the actual low-frequency model, which in turn leads to very unsatisfactory inversion results. The error of the joint sparse representation method proposed in this invention is higher than that of the interpolation method in some logging locations. However, the error in the areas where the interpolation method increases sharply is maintained at a relatively stable value. The relative error based on spatial structure and joint sparse representation is generally lower than that of the interpolated low-frequency model. Not only does the error not increase sharply in some areas, but the relative error is also lower and more stable than the other two methods.

[0113] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the contents of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention.

Claims

1. A method for establishing a low-frequency model based on spatial structural features and joint sparse representation, characterized in that: The specific steps include: S01. Obtain seismic data S and existing well logging curves for the work area and perform block processing; S02. After normalizing the block processing results, perform joint dictionary D training and divide the joint dictionary D into logging curve dictionaries and Earthquake Data Dictionary ; S03. Using the earthquake data dictionary Perform joint sparse characterization to obtain the sparse coefficients of seismic data in the work area ; S04. Using the logging curve dictionary and the sparse coefficient Perform reconstruction processing to obtain the initial low-frequency model; S05. Construct an optimization solution process similar to the inversion process based on optimization theory and inversion theory; S06. Add the interpolation function as a regularization constraint to the optimization process to further reduce the size of the solution space; S07. Use the conjugate gradient descent algorithm to solve large-scale overdetermined equations, and perform sparse representation and sparse reconstruction on the solved low-frequency model; calculate the error between the reconstructed low-frequency model and the low-frequency model of the previous iteration ; And calculate the error between the reconstructed earthquake data and the real earthquake data ; S08. Repeat the process from step S05 to step S07 until the error and error If it remains stable, the iterative process is completed and the sparse coefficient is finally calculated. , and reconstruct the low-frequency model ; S09. Perform denormalization processing on the iterated low-frequency model data to restore the original low-frequency model format.

2. The method for establishing a low-frequency model based on spatial structural features and joint sparse representation according to claim 1, characterized in that: In step S02, all data for training the joint dictionary D are normalized to 0-1, and the joint dictionary D is trained using the K-SVD algorithm. The training of the joint dictionary D is represented as an energy minimization optimization problem, and the objective function is: ; ， Where A is a sparse coefficient matrix, It is a joint dictionary of the elastic three parameters of the well logging curve and seismic data training, expressed as follows: ， in, 、 、 、 dictionaries representing compressional wave velocity, shear wave velocity, density, and seismic data, respectively; is the sample data for training the joint dictionary. The sample data is formed by combining the sample data of the four parameters by taking small blocks and expressing it as follows: ， in, 、 、 、 A collection of sample patches representing compressional wave velocity, shear wave velocity, density, and seismic data, respectively.

3. The method for establishing a low-frequency model based on spatial structural features and joint sparse representation according to claim 1, characterized in that: In step S03, the orthogonal matching pursuit (OMP) algorithm is used to obtain the seismic data S and the seismic data dictionary. Sparse characterization can obtain the sparse coefficients of seismic data , as shown below: 。 4. The method for establishing a low-frequency model based on spatial structure features and joint sparse representation according to claim 1, characterized in that: In step S05, an iterative method is used to solve a stable sparse coefficient using multiple iterations. The objective function is expressed as follows: ， in, represents the low-frequency model to be solved, represents earthquake data, represents the sparse representation obtained from seismic data, Represent the small block matrices of the samples of P-wave velocity, S-wave velocity, density and seismic data, respectively. Indicates the weight of the initial sparsely reconstructed low-frequency model in the iterative process, Indicates the weight of introducing seismic data for correction in the iterative process, Indicates the initial low-frequency model is reconstructed using sparseness.

5. The method for establishing a low-frequency model based on spatial structural features and joint sparse representation according to claim 4, characterized in that: In step S06, the interpolation function is an interpolation low-frequency model. The interpolation low-frequency model with spatial characteristics is introduced into the iterative process of sparse representation as a constraint term, and the spatial structure information of the logging curve is introduced. The objective function is as follows: ， in, represents the low-frequency model obtained using the interpolation function, Indicates the weight of the interpolated low-frequency model during the iteration process.

6. A low-frequency model based on spatial structural features and joint sparse representation established by the model building method according to any one of claims 1 to 5.

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