An efficient inversion algorithm for large-scale geophysical data

Abstract

The present invention discloses an efficient inversion algorithm for large-scale geophysical data, including using observation data constraint downsampling based on information monitoring to reduce the number of observation data involved in inversion before inversion, so as to achieve a preliminary reduction in the scale of the inversion problem. The inversion algorithm is based on the Gauss-Newton iteration algorithm, and uses the preconditioned conjugate gradient method to solve the model update direction, and uses the inversion-verification mode to update the physical property model. On the basis of the downsampled data set, the number of observation data involved in the iteration is further reduced, so as to achieve a secondary reduction in the scale of the inversion problem, thereby achieving efficient and low memory usage inversion of large-scale data. The present invention does not require all data to participate in the inversion, keeps the inversion accuracy unchanged, can save more storage requirements and time consumption, and combines data downsampling and training-verification iteration mode to achieve rapid inversion of large-scale geophysical data.

Description

Technical Field

[0001] The present invention relates to the field of geophysical field acquisition technology, and in particular to an efficient inversion algorithm for large-scale geophysical data. Background Art

[0002] In recent years, geophysical field acquisition technology has made great progress, and the amount of observation data that can be obtained is often as high as several Gb or more, which leads to low inversion efficiency and a sharp increase in memory requirements when inverting large-scale geophysical data, greatly restricting the progress of subsequent geological interpretation. Therefore, improving the inversion efficiency of large-scale data and reducing memory requirements while ensuring the inversion effect are of practical significance for shortening the interpretation cycle.

[0003] Scholars have conducted relevant research on large-scale geophysical inversion problems. A more direct method is to improve computer hardware configuration and use parallel computing on clusters to perform large-scale data inversion. From an algorithmic perspective, the core problem of large-scale data inversion is the sharp increase in memory requirements caused by large-scale data, which cannot be met by computer equipment and also increases the time consumption of inversion. Scholars have also conducted research around this perspective. From the perspective of model parameters, wavelet compression and other methods can be used to convert model parameters into transform domain data with spatial sparse characteristics for inversion; there are also strategies for random data set inversion from a data perspective to perform inversion of multiple sub-problems and take the average of the sub-problem results as the final inversion result.

[0004] Using all observation data to reconstruct the distribution of underground physical properties greatly reduces the inversion efficiency in large-scale data situations and easily leads to memory crashes during inversion.

[0005] Some inversion methods, such as CPU / GPU parallel inversion, rely on the availability of computer clusters and increase the difficulty of inversion algorithm development and the cost of use;

[0006] Some model space methods require complex transformation processing of model parameter vectors and sensitivity matrices, which increases the computational cost. In addition, the processing of model constraints (such as sparse constraints) cannot be directly reflected in the physical parameters, which limits the inversion effect.

[0007] Other methods based on data downsampling cannot guarantee the integrity of the data information after downsampling. They often use the weighted average of the inversion results of multiple downsampling data sets to approximate the final inversion result, and the resolution of the inversion result cannot be guaranteed.

[0008] In view of the above problems, the present invention provides an efficient inversion algorithm for large-scale geophysical data that can save more storage requirements and time consumption. Summary of the invention

[0009] The present invention provides a large-scale geophysical data efficient inversion algorithm which can save more storage requirements and time consumption.

[0010] The purpose of the present invention is to provide an efficient inversion algorithm for large-scale geophysical data, the inversion algorithm comprising observation data constrained downsampling based on information monitoring, a Gauss-Newton inversion iterative algorithm and an inversion-verification mode inversion iterative algorithm.

[0011] Furthermore, the specific calculation steps of observation data constraint downsampling based on information monitoring are as follows:

[0012] Step 1: Regularize the observation data to obtain spatially uniformly distributed observation data;

[0013] Step 2: Use the boundary recognition method to obtain underground geological structure information, use the corresponding measurement point data at the boundary as a constraint, initialize the downsampled data set ds, and use the remaining data as the redundant data set dr. It should be emphasized that the characteristic information contained in the observation data can be used as a constraint to initialize the downsampled data set ds;

[0014] Step 3: monitor the information change in the downsampled data set ds, use the downsampled data set ds to predict the redundant data set dr, use the prediction error to measure the information change in the downsampled data set ds, and the prediction is implemented by an interpolation algorithm based on Taylor polynomials;

[0015] Step 4: Add the point with the largest prediction error into the downsampled data set ds, update the redundant data set dr, and return to step 3 to continue execution;

[0016] Step 5: When the prediction error of dr is less than the noise level of the data, the downsampling ends and the ds dataset is used as the final downsampled dataset.

[0017] Furthermore, the specific calculation steps of the Gauss-Newton inversion iterative algorithm are as follows:

[0018] Step 1: Obtain the gridding parameters and down-sampling data set of the underground inversion area;

[0019] Step 2: The algorithm uses the Tikhonov regularization method to reduce the non-uniqueness of the solution. The overall objective function is:

[0020]

[0021] Among them, φ d is the data fitting difference, which measures the fitting degree between the observed data and the predicted data of the solution model, φ m is a model constraint term, which is used to add model prior information, μ is a regularization parameter, which is used to adjust the relative weight of data fitting difference and model constraint term in iteration, φ d The expression is:

[0022] φ d =||W d (d obs -F(m))|| 2

[0023] φ m The expression is:

[0024] φ m =||W m (mm ref ))|| 2

[0025] Among them, W d is the data weighting matrix, d obs is the observed data, m is the solution model, F is the forward operator, different geophysical data have different forms, W m is the model weight matrix, m ref is the reference model;

[0026] Step 3: Use the Gauss-Newton iteration method to minimize the objective function. At the kth iteration, use the following formula to update the solution model:

[0027]

[0028] Step 4: Use the preconditioned conjugate gradient method to obtain the update direction △m of the model. The conjugate gradient method is between the steepest descent method and the Newton method. It uses the first-order derivative to approximate the Hessian matrix and can efficiently solve large linear equations.

[0029] Step 5. After obtaining the update direction of the solution model, it is also necessary to determine the update step size. If the step size is too large, the inversion iteration may not converge. If the step size is too small, the inversion iteration converges slowly. The Armijo method is used to determine the update step size:

[0030] m k+1 =m k +α△m

[0031]

[0032] Step 6. The iterative convergence condition in the inversion is related to the noise level of the observed data. Under the Gaussian noise assumption, the expected value of the data fitting error is the number of observed data. The convergence condition is set to stop the iteration when the data fitting error is less than 1.5 times the number of data.

[0033] Furthermore, the specific calculation steps of the inversion-verification mode inversion iterative algorithm are as follows:

[0034] Step 1: Randomly select 5% of the data from the optimal subset as the inversion subset, and another 5% of the data as the verification subset;

[0035] Step 2: Use the inversion subset to iteratively update the solution model, and the updating process adopts the Gauss-Newton iteration method;

[0036] Step 3: Use the validation subset to evaluate whether the updated solution model is valid. If the data fitting error of the validation subset decreases after the model is updated, the current solution model is valid. Use the validation subset to replace the inversion subset, and re-select 5% of the data as a new validation subset. If the data fitting error of the validation subset increases after the model is updated, it means that the current solution model is invalid. In this case, combine the validation subset and the inversion subset to form a new inversion subset, and re-select 10% of the data as a new validation subset.

[0037] Step 4: When the data fitting error of the validation subset is less than the convergence threshold, the inversion ends.

[0038] The present invention has the following advantages: the present invention takes into account the redundant characteristics of geophysical data, downsamples the observation data based on the inherent characteristics of the data, uses an interpolation algorithm to monitor information changes in real time during the data downsampling process, and achieves effective dimensionality reduction of the data, thereby compressing the scale of the inversion problem; secondly, based on the Gauss-Newton method, the inversion adopts an inversion-verification mode to iteratively update the model, which reduces the memory requirements of matrix operations in the inversion and improves the inversion efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flowchart of the present invention. DETAILED DESCRIPTION

[0040] The present invention provides an efficient inversion algorithm for large-scale geophysical data. The inversion algorithm includes observation data constrained downsampling based on information monitoring, a Gauss-Newton inversion iterative algorithm and an inversion-verification mode inversion iterative algorithm.

[0041] In this embodiment, the specific calculation steps of observation data constraint downsampling based on information monitoring are as follows:

[0042] Step 1: Regularize the observation data to obtain spatially uniformly distributed observation data;

[0043] Step 2: Use the boundary recognition method to obtain underground geological structure information, use the corresponding measurement point data at the boundary as a constraint, initialize the downsampled data set ds, and use the remaining data as the redundant data set dr. It should be emphasized that the characteristic information contained in the observation data can be used as a constraint to initialize the downsampled data set ds;

[0044] Step 3: monitor the information change in the downsampled data set ds, use the downsampled data set ds to predict the redundant data set dr, use the prediction error to measure the information change in the downsampled data set ds, and the prediction is implemented by an interpolation algorithm based on Taylor polynomials;

[0045] Step 4: Add the point with the largest prediction error into the downsampled data set ds, update the redundant data set dr, and return to step 3 to continue execution;

[0046] Step 5: When the prediction error of dr is less than the noise level of the data, the downsampling ends and the ds dataset is used as the final downsampled dataset.

[0047] In this embodiment, the specific calculation steps of the Gauss-Newton inversion iterative algorithm are as follows:

[0048] Step 1: Obtain the gridding parameters and down-sampling data set of the underground inversion area;

[0049] Step 2: The algorithm uses the Tikhonov regularization method to reduce the non-uniqueness of the solution. The overall objective function is:

[0050]

[0051] Among them, φ d is the data fitting difference, which measures the fitting degree between the observed data and the predicted data of the solution model, φ m is a model constraint term, which is used to add model prior information, μ is a regularization parameter, which is used to adjust the relative weight of data fitting difference and model constraint term in iteration, φ d The expression is:

[0052] φ d =||W d (d obs -F(m))|| 2

[0053] φ m The expression is:

[0054] φ m =||W m (mm ref ))|| 2

[0055] Among them, W d is the data weighting matrix, d obs is the observed data, m is the solution model, F is the forward operator, different geophysical data have different forms, W m is the model weight matrix, m ref is the reference model;

[0056] Step 3: Use the Gauss-Newton iteration method to minimize the objective function. At the kth iteration, use the following formula to update the solution model:

[0057]

[0058] Step 4: Use the preconditioned conjugate gradient method to obtain the update direction △m of the model. The conjugate gradient method is between the steepest descent method and the Newton method. It uses the first-order derivative to approximate the Hessian matrix and can efficiently solve large linear equations.

[0059] Step 5. After obtaining the update direction of the solution model, it is also necessary to determine the update step size. If the step size is too large, the inversion iteration may not converge. If the step size is too small, the inversion iteration converges slowly. The Armijo method is used to determine the update step size:

[0060] m k+1 =m k +α△m

[0061]

[0062] Step 6. The iterative convergence condition in the inversion is related to the noise level of the observed data. Under the Gaussian noise assumption, the expected value of the data fitting error is the number of observed data. The convergence condition is set to stop the iteration when the data fitting error is less than 1.5 times the number of data.

[0063] In this embodiment, the specific calculation steps of the inversion-verification mode inversion iterative algorithm are as follows:

[0064] Step 1: Randomly select 5% of the data from the optimal subset as the inversion subset, and another 5% of the data as the verification subset;

[0065] Step 2: Use the inversion subset to iteratively update the solution model, and the updating process adopts the Gauss-Newton iteration method;

[0066] Step 3: Use the validation subset to evaluate whether the updated solution model is valid. If the data fitting error of the validation subset decreases after the model is updated, the current solution model is valid. Use the validation subset to replace the inversion subset, and re-select 5% of the data as a new validation subset. If the data fitting error of the validation subset increases after the model is updated, it means that the current solution model is invalid. In this case, combine the validation subset and the inversion subset to form a new inversion subset, and re-select 10% of the data as a new validation subset.

[0067] Step 4: When the data fitting error of the validation subset is less than the convergence threshold, the inversion ends.

[0068] Although the specific implementation of the present invention is described in detail in conjunction with the drawings, it should not be understood as limiting the scope of protection of this patent. Within the scope described in the claims, various modifications and variations that can be made by those skilled in the art without creative work still fall within the scope of protection of this patent.

Claims

1. An efficient inversion algorithm for large-scale geophysical data, characterized by: The inversion algorithm includes observation data constrained downsampling based on information monitoring, Gauss-Newton inversion iteration algorithm and inversion-verification mode inversion iteration algorithm; The specific calculation steps of the observation data constraint downsampling based on information monitoring are as follows: Step 1: Regularize the observation data to obtain spatially uniformly distributed observation data; Step 2: Use the boundary recognition method to obtain underground geological structure information, use the corresponding measurement point data at the boundary as a constraint, initialize the downsampled data set ds, and use the remaining data as the redundant data set dr. It should be emphasized that the characteristic information contained in the observed data is used as a constraint to initialize the downsampled data set ds; Step 3: monitor the information change in the downsampled data set ds, use the downsampled data set ds to predict the redundant data set dr, use the prediction error to measure the information change in the downsampled data set ds, and the prediction is implemented by an interpolation algorithm based on Taylor polynomials; Step 4: Add the point with the largest prediction error into the downsampled data set ds, update the redundant data set dr, and return to step 3 to continue execution; Step 5: When the prediction error of dr is less than the noise level of the data, the downsampling ends and the ds data set is used as the final downsampled data set; The specific calculation steps of the Gauss-Newton inversion iterative algorithm are as follows: Step 1: Obtain the gridding parameters and down-sampling data set of the underground inversion area; Step 2: The algorithm uses the Tikhonov regularization method to reduce the non-uniqueness of the solution. The overall objective function is: Among them, φ d is the data fitting difference, which measures the fitting degree between the observed data and the predicted data of the solution model, φ m is a model constraint term, which is used to add model prior information, μ is a regularization parameter, which is used to adjust the relative weight of data fitting difference and model constraint term in iteration, φ d The expression is: φ m The expression is: Among them, W d is the data weighting matrix, d obs is the observed data, m is the solution model, F is the forward operator, different geophysical data have different forms, W m is the model weight matrix, m ref is the reference model; Step 3: Use the Gauss-Newton iteration method to minimize the objective function. At the kth iteration, use the following formula to update the solution model: Step 4: Use the preconditioned conjugate gradient method to obtain the update direction △m of the model. The conjugate gradient method is between the steepest descent method and the Newton method. It uses the first-order derivative to approximate the Hessian matrix and efficiently solves large linear equations. Step 5. After obtaining the update direction of the solution model, it is also necessary to determine the update step size. If the step size is too large, the inversion iteration may not converge. If the step size is too small, the inversion iteration converges slowly. The Armijo method is used to determine the update step size: Step 6. The iterative convergence condition in the inversion is related to the noise level of the observed data. Under the Gaussian noise assumption, the expected value of the data fitting error is the number of observed data. The convergence condition is set to stop the iteration when the data fitting error is less than 1.5 times the number of data.

2. The large-scale geophysical data efficient inversion algorithm according to claim 1, characterized in that: The specific calculation steps of the inversion-verification mode inversion iterative algorithm are as follows: Step 1: Randomly select 5% of the data from the optimal subset as the inversion subset, and another 5% of the data as the verification subset; Step 2: Use the inversion subset to iteratively update the solution model, and the updating process adopts the Gauss-Newton iteration method; Step 3: Use the validation subset to evaluate whether the updated solution model is valid. If the data fitting error of the validation subset decreases after the model is updated, the current solution model is valid. Use the validation subset to replace the inversion subset, and reselect 5% of the data as a new validation subset. If the data fitting error of the validation subset increases after the model is updated, it means that the current solution model is invalid. In this case, combine the validation subset and the inversion subset to form a new inversion subset, and reselect 10% of the data as a new validation subset. Step 4: When the data fitting error of the validation subset is less than the convergence threshold, the inversion ends.

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