Random projection based petrophysical parameter inversion of potential field data

Abstract

The application discloses a kind of based on random projection's physical property parameter inversion method of potential field data, comprising the following steps: S1: measured potential field data is obtained, according to survey area and depth range is profiled in underground space, sensitivity matrix in inversion is calculated based on potential field data forward theory, and then the forward calculation relationship of full space is established;S2: random projection matrix is designed, and sensitivity matrix is projected to multiple low-dimensional subspace, and the subspace forward calculation relationship is established;S3: based on the regularization equation of subspace forward calculation relationship, and the physical property parameter in subspace is solved using conjugate gradient algorithm;S4: the final physical property parameter inversion result is obtained by the weighted average calculation of multiple physical property parameters in subspace.The physical property parameter inversion method of potential field data based on random projection has higher depth resolution and inversion reliability, and improves the practicability of physical property inversion method in actual data processing.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of earth science, and particularly provides a random projection-based physical property parameter inversion method for potential field data. BACKGROUND

[0002] The gravity and magnetic exploration is a method of measuring the gravity field and magnetic field anomaly data in a certain area, then inverting and interpreting the obtained measured data, so as to quantitatively or qualitatively analyze the density or magnetic susceptibility distribution of the underground medium. Compared with the seismic, electromagnetic and other geophysical methods, the gravity and magnetic exploration method has the characteristics of low cost, high efficiency and high horizontal resolution. At present, the literatures on the linear inversion of potential field data are mainly based on the Tikhonov regularization theory, but there are problems such as difficulty in selecting parameters, difficulty in constraining prior information, and the demand for joint inversion of multi-source geophysical data. The constraint joint inversion of the profile interpretation results of the seismic or electromagnetic data also needs to establish an effective potential field plane data inversion method. For the large-scale potential field data collected in the two-dimensional plane, it is an urgent problem to develop a potential field data physical property parameter inversion method with high resolution and accuracy. SUMMARY

[0003] In view of this, the present application aims at the deficiencies of the prior art, and provides a random projection-based physical property parameter inversion method for potential field data, so as to improve the accuracy and resolution of the potential field data physical property inversion result.

[0004] The technical scheme provided by the present application is as follows: a random projection-based physical property parameter inversion method for potential field data, comprising the following steps:

[0005] 1. The random projection-based physical property parameter inversion method for potential field data, characterized in that it comprises the following steps:

[0006] S1: obtaining the measured potential field data, performing the underground space profiling according to the survey area and the depth range, and calculating the sensitivity matrix in the inversion based on the potential field data forward theory S , and then establishing the forward calculation relationship of the whole space:

[0007] (1)

[0008] In the formula, d represents the column vector of the observation data, wherein M represents the number of observation data; m is the model parameter column vector, wherein N represents the number of profiling grids; S is the sensitivity matrix of the type, and ;

[0009] S2: design random projection matrix The sensitivity matrix with the dimension of N is projected into Q groups of low-dimensional subspaces, a subspace forward calculation relationship is established, and the sensitivity matrix in the jth subspace is The expression is:

[0010] (2)

[0011] In the formula, is the jth group of random projection matrix established;

[0012] Further, a subspace forward calculation relationship is established:

[0013] (3)

[0014] S3: based on the subspace forward calculation relationship, a regularization equation is established,

[0015] (4)

[0016] And the conjugate gradient algorithm is used to solve the subspace physical property parameter . is a weight factor, mainly to balance and The weight size of the two items, the value range is 0~1;

[0017] S4: the final physical property parameter inversion result is obtained through weighted average calculation of the physical property parameters in multiple subspaces: m

[0018] (5)

[0019] In the formula, is the construction times of the random projection matrix, is the jth random projection matrix constructed based on random projection.

[0020] The physical property parameter inversion method of the potential field data based on random projection provided by the application solves the problems existing in the existing physical property inversion method of the potential field data based on Tikhonov regularization, establishes a potential field data inversion method based on random projection, randomly projects the sensitivity matrix in the whole space into a low-dimensional subspace, the random projection strategy breaks the spatial arrangement relationship of the original sensitivity matrix, and further avoids the "skin effect" problem in the traditional inversion process, and the solving process in the low-dimensional subspace makes the inversion problem a well-posed problem, and a more stable inversion result can be obtained. In addition, this strategy can effectively combine the information such as stratified and spatial distribution of geological bodies obtained by seismic or electromagnetic methods, realize joint inversion of multi-source geophysical data, and provide a possibility for further expansion of the method. ​

[0021] This invention provides a method for inverting physical property parameters from potential field data based on random projection. By using sparse projection, the underdetermined problem in physical property inversion is transformed into a well-posed problem for solution, improving the stability of the iterative inversion solution. This method solves for physical property parameters through multiple random projection inversion calculations, obtaining reliable three-dimensional distribution results of physical properties. It avoids problems such as difficult parameter selection and low depth resolution in traditional physical property inversion calculations, improving the reliability of geological body physical property parameter inversion and providing technical support for fields such as comprehensive geothermal resource exploration and mineral resource exploration. Attached Figure Description

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0023] Figure 1 A flowchart of the method for inverting physical property parameters of potential field data based on random projection provided by the present invention;

[0024] Figure 2 This is a spatial distribution map of the superimposed anomalies in the embodiment;

[0025] Figure 3 This is a diagram showing the inversion results of potential field data property parameters based on random projection.

[0026] Figure 4 This is a diagram showing the inversion results of potential field data property parameters based on random projection under the constraint of stratigraphic information. Detailed Implementation

[0027] The present invention will be further explained below with reference to specific implementation schemes, but this explanation does not limit the scope of the invention.

[0028] like Figure 1 As shown, this invention provides a method for inverting physical property parameters of potential field data based on random projection, comprising the following steps:

[0029] S1: Acquire measured potential field data, divide the underground space according to the survey area and depth range, and calculate the sensitivity matrix for inversion based on the forward modeling theory of potential field data. S This leads to the establishment of forward modeling relationships across the entire space:

[0030] (1)

[0031] In the formula, d A column vector representing the observed data. , where M represents the number of observation data; m It is a column vector of model parameters. ,in N Indicates the number of meshes; S yes sensitivity matrix of type 2, and ;

[0032] S2: Design a random projection matrix Project the sensitivity matrix of dimension N into Q groups of low-dimensional subspaces, establish the subspace forward calculation relationship, and the sensitivity matrix in the jth subspace is The expression is:

[0033] (2)

[0034] In the formula, is the jth group of random projection matrix established;

[0035] Further establish the subspace forward calculation relationship:

[0036] (3)

[0037] S3: Based on the subspace forward calculation relationship, establish the regularization equation,

[0038] (4)

[0039] And use the conjugate gradient algorithm to solve the subspace physical property parameter ; is a weight factor, mainly to balance And The weight size of the two, the value range is 0~1;

[0040] S4: Through the weighted average calculation of the physical property parameters In multiple subspaces, the final physical property parameter inversion result is obtained: m

[0041] (5)

[0042] In the formula, is the construction times of the random projection matrix, is the jth random projection matrix constructed based on random projection.

[0043] Embodiment:

[0044] Take the potential field anomaly data caused by the deep and shallow superimposed prism model as an example, determine the spatial distribution of physical properties by the random projection-based potential field data physical property parameter inversion method, wherein, Figure 2 is the spatial distribution of deep and shallow superimposed anomalies.

[0045] The specific steps are as follows:

[0046] ​S1: According to the measurement area (x direction is 30 kilometers) and the depth range (depth direction is 20 kilometers), the underground space is profiled, and the sensitivity matrix in the inversion is calculated based on the forward theory of potential field data S , and the forward calculation relationship of the whole space is established:

[0047] (1)

[0048] In the formula, d represent the column vector of the observation data, where M represents the number of observation data, and the sampling interval is 1 kilometer, so M is equal to 30, m is the model parameter column vector, where N N represents the number of profile grids, and N is equal to 600, S is the sensitivity matrix of the type , and ;

[0049] S2: Design a random projection matrix , project the sensitivity matrix with dimension N to Q groups of low-dimensional subspaces, Q is 30, establish the subspace forward calculation relationship, and the sensitivity matrix in the jth subspace is The expression is:

[0050] (2)

[0051] In the formula, is the jth group of random projection matrix established;

[0052] and the subspace forward calculation relationship is established:

[0053] (3)

[0054] S3: Based on the subspace forward calculation relationship, the regularization equation is established,

[0055] (4)

[0056] In the formula, is the jth group of objective function established;

[0057] The least squares QR decomposition method is used to minimize the objective function, and the subspace physical property parameter is obtained;

[0058] S4: Through the weighted average calculation of the physical property parameters in multiple subspaces, the final physical property parameter inversion result is obtained: m

[0059] (5)​

[0060] Figure 3 For the physical property distribution results after the superposition of multiple random projections, it can be seen that the method in this paper can also invert the physical property distribution of the deep prism without the constraint of the depth weighting function.

[0061] Figure 4 For the physical property inversion results after adding the horizon information constraint, it can be seen that the addition of the prior horizon information such as the earthquake / magnetic field can provide the reliability of the physical property inversion results of the potential field data.

[0062] The embodiments of the present application are described in detail above in combination with the drawings, but the present application is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the purpose of the present application.

Claims

1. A method for petrophysical parameter inversion of potential field data based on random projection, characterized in that, The method comprises the following steps: S1: Obtain measured potential field data, divide the underground space according to the survey area and depth range, and calculate the sensitivity matrix in inversion based on the forward theory of potential field data S , and further establish the forward calculation relationship of the whole space: (1) wherein d is a column vector representing the observation data, where M represents the number of observation data; m is a column vector of model parameters, wherein N denotes the number of the partitioned grids; S is a sensitivity matrix of the form ; S2: design a random projection matrix The sensitivity matrix with dimension N is projected into Q groups of low-dimensional subspaces to establish a subspace forward calculation relationship. The sensitivity matrix in the jth group of subspaces is The expression is: (2) In the formula, is the jth group of random projection matrix established; Further, the subspace forward calculation relationship is established: (3) S3: establishing a regularization equation based on the subspace forward calculation relationship, (4) And the conjugate gradient algorithm is used to solve the property parameters in the subspace ; is a weight factor, mainly to balance and the weight size of the two items, the value range is 0~1; S4: Calculate the final petrophysical parameter inversion result by weighted average calculation of the petrophysical parameters in multiple subspaces m :​ (5) In the formula, is the number of times of construction of the random projection matrix, is the random projection matrix constructed based on the random projection for the jth time.

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