Method for utilizing multi-point geological statistical structure to constrain direct current electric method data inversion

Abstract

The invention discloses a method for data inversion by utilizing a multipoint geological statistical structure constraint direct current electric method, which belongs to the field of geophysical exploration, and comprises the following steps: based on geological drilling data, establishing a model containing geological structure information by adopting a multipoint geological statistical algorithm, and constructing an underground stratum structure operator by utilizing the model; a structure operator is added to a regularization term, an initial resistivity model is given to calculate a data residual term, and an inversion objective function with structure constraint is formed; in the inversion process, a finite memory quasi-Newton optimization algorithm is adopted to carry out iterative optimization on a target function until the difference between forward modeling simulation data and actually measured data reaches a set threshold value, and constraint inversion is completed; and finally, outputting the resistivity inversion model. According to the method, the problems of fuzzy stratum boundary, reduced resolution and the like caused by regularization smooth constraint in a traditional method are reduced, and the method is suitable for subsurface stratum structure detection and fine imaging in a complex geological environment and has wide application value.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration, and in particular to a method for inverting DC electrical resistivity tomography data using multi-point geostatistical structures. Background Technology

[0002] With the rapid advancement of urban construction, the precision requirements for underground space exploration are constantly increasing, especially in areas such as urban infrastructure construction, active fault monitoring, and underground resource exploration, where the demand for high-resolution, non-destructive testing technologies is growing. Direct current resistivity (DCRS) is a geophysical exploration method for underground structures. It involves collecting DCRS data and then inverting this data to construct a resistivity model. DCRS technology offers flexible observation methods, high resolution, and strong anti-interference capabilities, giving it significant advantages in urban environments. However, in practical applications, the inversion problem is often ill-posed, meaning that the observation data is limited and contains noise, leading to instability in the inversion solution. Existing technologies mainly rely on mathematical regularization to optimize the solution, but these techniques only constrain the smoothness of the solution from a numerical perspective and fail to fully utilize the prior structural information of the underground medium contained in the drilling data, resulting in low resolution in the inversion results. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for inverting DC electrical resistivity tomography data using multi-point geostatistical structure constraints. This method introduces prior structural constraints during the inversion process, enabling the inversion solution to conform to geological structural characteristics while undergoing mathematical optimization, thereby improving the resolution and stability of the imaging.

[0004] The objective of this invention is achieved through the following technical solution: a method for inverting DC resistivity tomography data using multi-point geostatistical structure constraints, comprising the following steps:

[0005] Construction of underground stratigraphic structure operator: Based on geological drilling data, a multi-point geostatistical algorithm is used to stochastically model the underground spatial structure, generating a multi-point geostatistical model containing geological structure information, and constructing an underground stratigraphic structure operator based on the multi-point geostatistical model;

[0006] Establishment of the structural constraint inversion objective function: The structural operator is added to the regularization term, and the residual term of the initial resistivity model calculation data is given to form an inversion objective function with structural constraints;

[0007] Structural constraint inversion: The inversion objective function with structural constraints is iteratively optimized using a finite-memory quasi-Newton optimization algorithm until the difference between the forward simulation data and the measured data reaches the preset constraint condition, thus obtaining the inversion model;

[0008] Inversion model output: The inversion model is output for geological interpretation.

[0009] Furthermore, the multi-point geostatistical algorithm is a direct sampling algorithm, which uses a flexible and variable search neighborhood to determine data events, is suitable for non-homogeneous media, and has high computational efficiency.

[0010] Furthermore, the construction of the underground stratigraphic structure operator based on the multi-point geostatistical model specifically involves: dividing the multi-point geostatistical model into grids, calculating the information entropy of the lithology or physical property parameters corresponding to each grid, and constructing a normalized structure operator based on the information entropy.

[0011] Furthermore, the method of constructing the underground stratigraphic structure operator based on the multi-point geostatistical model further includes: constructing a structure operator matrix based on the structure operator, dynamically weighting the smoothness of the model according to the distribution of information entropy of lithological or physical property parameters in the multi-point geostatistical model, and reducing the weight of the smoothing constraint in areas with high information entropy values, wherein the areas with high information entropy values ​​include geological interfaces and structural abrupt change regions.

[0012] Furthermore, the regularization term is the difference between the resistivity inversion model and the reference model, constructed using the L2 norm, wherein the reference model is a uniform model whose resistivity value is the average resistivity of the probe area.

[0013] Furthermore, the data residual term represents the difference between the measured data and the forward simulation data, constructed using the L2 norm, where the measured data are the actual measured values ​​and the forward simulation data are the theoretical predicted values ​​corresponding to the current model.

[0014] Furthermore, the inversion objective function with structural constraints includes a data residual term and a structural constraint term. Overfitting is prevented by increasing the weight of the regularization term in the inversion objective function.

[0015] Furthermore, the structural constraint inversion process adopts a multi-iteration strategy for model updating. The termination condition is set as follows: the norm formed by the difference between the measured data and the forward simulation data is multiplied by the data weighting matrix. When its value is less than the set threshold or the rate of change meets the convergence condition, the iteration stops. The data weighting matrix is ​​used to characterize the importance of the observed values.

[0016] Furthermore, the structural constraint inversion process includes: updating the model parameters based on the information of the objective function gradient, and setting a parameter transformation relationship between the model parameters and the actual physical properties; the transformation relationship is a nonlinear function used to map the inverted parameters to the corresponding physical property values, thereby further constraining the range of physical property parameters.

[0017] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the method.

[0018] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described thereon.

[0019] The beneficial effects of this invention are as follows: This invention combines prior information on stratigraphic structure provided by drilling and other methods, establishes a model containing geological structure information based on multi-point geostatistics, and constructs an underground stratigraphic structure operator using this model. By adding the stratigraphic structure operator to the regularization term, the stratigraphic structure is effectively constrained during the DC resistivity tomography (DCS) data inversion process, thereby improving the resolution of the resistivity inversion model. The above-mentioned technical means effectively improve the resolution of DCS data inversion results, especially under conditions of low signal-to-noise ratio or uneven data coverage, while still maintaining good convergence and imaging quality. It reduces problems such as blurred stratigraphic boundaries and decreased resolution caused by regularization smoothing constraints in traditional methods. It is suitable for urban underground structure detection and fine imaging in complex geological environments, and has broad application value. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart of DC electrical resistivity tomography data inversion under multi-point geostatistical structure constraints.

[0022] Figure 2 These are schematic diagrams of inversion results from actual cases. The top diagram shows the inversion results without structural constraints, while the bottom diagram shows the inversion results with structural constraints. The burnt soil layer is shown in the light blue area of ​​the diagram. Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings. Unless otherwise specified, the features of the following embodiments and implementations can be combined with each other.

[0024] This invention provides a method for inverting DC electrical resistivity tomography data using multi-point geostatistical structure constraints, such as... Figure 1 As shown, it includes the following steps:

[0025] Construction of underground stratigraphic structure operator: Based on geological drilling data, a multi-point geostatistical algorithm is used to stochastically model the underground spatial structure, generating a multi-point geostatistical model containing geological structure information, and constructing an underground stratigraphic structure operator based on the multi-point geostatistical model.

[0026] Establishment of the structural constraint inversion objective function: The structural operator is added to the regularization term, and a uniform resistivity model with a resistivity of 30 ohm-meters is used as the initial model to calculate the residual term of the data, thus forming the inversion objective function with structural constraints.

[0027] Structural constraint inversion: The inversion objective function with structural constraints is iteratively optimized using a finite-memory quasi-Newton optimization algorithm until the difference between the forward simulation data and the measured data reaches the preset constraint condition, thus obtaining the inversion model;

[0028] Inversion model output: Output the above inversion model for geological interpretation.

[0029] The multi-point geostatistical algorithm is a direct sampling algorithm, which uses a flexible and variable search neighborhood to determine data events. It is suitable for non-homogeneous media and has high computational efficiency.

[0030] In one embodiment, the stratigraphic structure operator is structural information quantitatively extracted from a multi-point geostatistical model using information entropy. Specifically, assuming the multi-point geostatistical model contains N types of lithology or physical properties, the model is meshed, and the stratigraphic structure operator is used... Let represent the probability of the lithology or physical property corresponding to the i-th grid in a multi-point geostatistical model, then the information entropy of the lithology or physical property corresponding to that grid. for:

[0031] (1);

[0032] Using information entropy, a normalized structure operator is constructed. :

[0033] (2);

[0034] Based on structure operators Establish the structure operator matrix , The smoothness of the resistivity inversion model will be dynamically weighted according to the distribution of structural parameters. In regions with high information entropy values, the weight of the smoothing constraint will be reduced. These regions include geological interfaces and structural abrupt change areas, in order to obtain clear structural information.

[0035] In one embodiment, the regularization term of the structured operator The format is:

[0036] (3);

[0037] In equation (3), As a reference model, For smoothing matrices, Let be the structure operator matrix.

[0038] Define the data residuals of the constraint inversion objective function This is used to describe the difference between actual data and theoretical data from the model:

[0039] (4);

[0040] In equation (4), m is the resistivity inversion model. These are theoretical data generated by forward modeling. These are actual data obtained from measurements. For the DC method, m and ( ) respectively correspond to the resistivity of the model And apparent resistivity data. It is the inverse of the covariance matrix of the actual data, used to reduce the impact of large error data.

[0041] Combining equations (3) and (4), we define the objective function for multi-point geostatistical structure-constrained inversion. for,

[0042] (5);

[0043] In equation (5), , These represent the residual terms of the DC resistivity method data and the multi-point geostatistical structural constraint terms of the resistivity inversion model, respectively. During constraint inversion, the structural constraint terms in equation (5) can be weighted to adjust their weights.

[0044] The constrained inversion objective function (Equation (5)) is solved using the finite-memory quasi-Newton method. First, the gradient of the constrained inversion objective function with respect to the resistivity inversion model is calculated, and then the finite-memory quasi-Newton method is applied to transform the gradient into a search direction. and optimize step size Finally, the current resistivity inversion model is updated and iterated. The iterative calculation formula is as follows:

[0045] (6).

[0046] In one embodiment, the inversion process includes employing a multiple iterative update strategy and setting the following optimization convergence conditions:

[0047] .

[0048] in, Represents a data weighting matrix. Represents observation data, This represents forward simulation data. This indicates the number of data points.

[0049] In one embodiment, the inversion process includes parameter updates based on the gradient of the objective function, introducing a parameter transformation between the inversion parameters and the physical property (resistivity), with the transformation function as follows:

[0050] ;

[0051] , These are the minimum and maximum resistivity, respectively, used to ensure that any element of the inversion model vector... When the resistivity of the forward model changes, Constrained and Between. Because the resistivity values ​​vary over a large range, logarithmic coordinates were used to convert the resistivity parameters.

[0052] In one embodiment, the following specific experiments were conducted at the Liangzhu Ancient City Site in Hangzhou, Zhejiang Province, based on this method, including the following steps:

[0053] 1. Construction of Subsurface Stratigraphic Structure Operator: Based on geological drilling data, a model containing geological structural information is established using a multi-point geostatistical algorithm. This model is then used to construct the subsurface stratigraphic structure operator.

[0054] In this embodiment, the work area is located at the Liangzhu Ancient City Site in Hangzhou, Zhejiang Province. Drilling revealed a layer of burnt red soil approximately 0.2m thick and buried at a depth of about 2m, dating back to the Liangzhu period and presumably remnants of ancient architecture. The DC resistivity tomography (DCS) data acquisition electrode spacing was 0.5m, the survey line length was 24m, and data acquisition was performed using a Wenner device. To add structural constraints during the DCS data inversion process, two wells with a depth of 4m were drilled. A multi-point geostatistical method was used to calculate a model containing geological structures, and a stratigraphic structure operator was constructed using information entropy theory.

[0055] 2. Establishment of the structural constraint inversion objective function: Add the structural operator to the regularization term, calculate the residual term of the data given the initial model, and form an inversion objective function with structural constraints.

[0056] In this embodiment, the initial model adopted is a uniform model with a resistivity of 30 ohm-meters, and the initial model has a horizontal length of 24 meters and a vertical length of 4 meters.

[0057] 3. Structural Constraint Inversion: During the inversion process, the objective function is optimized by introducing structural constraint matrix operators into the inversion framework. These operators work together with traditional data terms and regularization terms to iteratively optimize the inversion process. The inversion process uses a finite-memory quasi-Newton method to iteratively optimize the objective function. A threshold value of 1 is set for the difference between the forward data and the measured data. When the difference between the forward data and the measured data reaches the set threshold value, the constraint inversion is completed.

[0058] In this embodiment, based on the acquisition method and drilling data, the inversion model size is selected as 24m × 4m, and the basic inversion grid is 0.1m × 0.1m. The initial inversion model adopts a uniform model with a uniformly distributed resistivity value of 30 ohm-meters.

[0059] The inversion process first uses the L-Curve method to determine the weights of the regularization term, with a final weight value of 100. Then, this weight is used as the weight of the regularization term in the structural constraint inversion objective function, and optimization inversion is performed simultaneously on both the structural constraint term and the data term. The inversion RMS error is then calculated using the system.

[0060] like Figure 2 As shown, the upper figure is the resistivity profile obtained by traditional inversion, and the lower figure is the resistivity profile corresponding to multi-point geostatistical structure-constrained inversion. From Figure 2 Comparing the results of the two inversion techniques, the thin layer of red-burnt soil was not displayed on the traditional inversion profile, while the multi-point geostatistical structure-constrained joint inversion technique was able to distinguish the thin layer of about 0.2m.

[0061] In summary, the DC electrical resistivity tomography (DCIP) data inversion method constrained by multi-point geostatistical structure can reduce the impact of traditional inversion regularization and smoothing constraints, and significantly improve the resolution of the inversion results while maintaining inversion accuracy. Compared with traditional inversion methods, the multi-point geostatistical structure constrained inversion technique is superior in terms of morphological characterization of subsurface thin-layer anomalies, accuracy of inverted physical property parameters, and accuracy of inverted thickness.

[0062] This invention also provides an electronic device, including a memory and a processor, wherein the memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the method for inverting DC electrical resistivity tomography data constrained by multi-point geostatistical structures as described in any embodiment.

[0063] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method for inverting DC electrical resistivity tomography data constrained by multi-point geostatistical structures as described in any embodiment.

[0064] The computer-readable storage medium can be an internal storage unit of any data processing device described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be any data processing device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data processing device and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0065] It will be understood by those skilled in the art that the above description is merely a preferred embodiment of the invention and is not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for inverting DC resistivity tomography data using multi-point geostatistical structure constraints, characterized in that, Includes the following steps: Construction of underground stratigraphic structure operator: Based on geological drilling data, a multi-point geostatistical algorithm is used to stochastically model the underground spatial structure, generating a multi-point geostatistical model containing geological structure information, and constructing an underground stratigraphic structure operator based on the multi-point geostatistical model; Establishment of the structural constraint inversion objective function: The structural operator is added to the regularization term, and the residual term of the initial resistivity model calculation data is given to form an inversion objective function with structural constraints; Structural constraint inversion: The inversion objective function with structural constraints is iteratively optimized using a finite-memory quasi-Newton optimization algorithm until the difference between the forward simulation data and the measured data reaches the preset constraint condition, thus obtaining the inversion model; Inversion model output: The inversion model is output for geological interpretation.

2. The method according to claim 1, characterized in that, The specific steps for constructing the underground stratigraphic structure operator based on the multi-point geostatistical model are as follows: the multi-point geostatistical model is divided into grids, the information entropy of the lithology or physical property parameters corresponding to each grid is calculated, and a normalized structure operator is constructed based on the information entropy.

3. The method according to claim 2, characterized in that, The method of constructing the underground stratigraphic structure operator based on the multi-point geostatistical model further includes: constructing a structure operator matrix based on the structure operator; dynamically weighting the smoothness of the model according to the distribution of information entropy of lithological or physical property parameters in the multi-point geostatistical model; reducing the weight of smoothing constraints in regions with high information entropy values; and the regions with high information entropy values ​​include geological interfaces and structural abrupt change regions.

4. The method according to claim 1, characterized in that, The regularization term represents the difference between the resistivity inversion model and the reference model, and is constructed using the L2 norm. The reference model is a uniform model whose resistivity value is the average resistivity of the probe region.

5. The method according to claim 4, characterized in that, The data residual term represents the difference between the measured data and the forward simulation data, constructed using the L2 norm. The measured data refers to the actual measured values, while the forward simulation data refers to the theoretical predicted values ​​corresponding to the current model.

6. The method according to claim 1, characterized in that, The inversion objective function with structural constraints includes a data residual term and a structural constraint term. Overfitting is prevented by increasing the weight of the regularization term in the inversion objective function.

7. The method according to claim 1, characterized in that, The structural constraint inversion process employs a multi-iteration strategy for model updates. The termination condition is set as follows: the norm formed by the difference between the measured data and the forward simulation data is multiplied by the data weighting matrix. When its value is less than a set threshold or the rate of change meets the convergence condition, the iteration stops. The data weighting matrix is ​​used to characterize the importance of the observed values.

8. The method according to claim 1, characterized in that, The structural constraint inversion process includes: updating the model parameters based on the information of the objective function gradient, and setting a parameter transformation relationship between the model parameters and the actual physical properties; the transformation relationship is a nonlinear function used to map the inverted parameters to the corresponding physical property values, and further constrain the range of physical property parameters.

9. An electronic device comprising a memory and a processor, characterized in that, The memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the method as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-8.

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