CN-122021108-A - Resistivity three-dimensional inversion method based on groundwater seepage parameter constraint

CN122021108ACN 122021108 ACN122021108 ACN 122021108ACN-122021108-A

Abstract

The invention discloses a resistivity three-dimensional inversion method based on groundwater seepage parameter constraint, which relates to resistivity inversion, and comprises the following steps of establishing a three-dimensional model and determining model parameters; the method comprises the steps of inputting an initial model and observation data, carrying out forward numerical computation by adopting finite difference to obtain a model electric field value, comparing the electric field value obtained by forward modeling with the observation data to obtain a data error, calculating a crossed gradient item of a model resistance and hydrologic parameters in a physical space, establishing an objective function, calculating the gradient of the objective function, obtaining a searching step length and a searching direction in a forward modeling mode by taking a nonlinear conjugate gradient method as an inversion method, judging whether a linear searching convergence condition is converged, entering the next step if the linear searching convergence condition is converged, otherwise updating the model, returning to forward modeling computation, calculating a data root mean square error, ending iteration if the linear searching convergence condition is converged, otherwise updating the step length and the searching direction, calculating the model updating quantity, and returning to forward modeling computation.

Inventors

FENG BINGHUI
WANG KAIXUAN
SU KUN
WANG HAIGEN
Dai Youxu
DU SHUAI
LI PENG
ZHU FENGBIN
Zhai Rujia
WANG GUOQUAN
GE XIANGWEI

Assignees

中国地质调查局烟台海岸带地质调查中心

Dates

Publication Date: 20260512
Application Date: 20251218

Claims (6)

1. The resistivity three-dimensional inversion method based on groundwater seepage parameter constraint is characterized by comprising the following steps of: S1, building a three-dimensional model and determining model parameters; S2, inputting an initial model and observation data; S3, forward modeling numerical calculation is carried out by adopting finite difference to obtain a model electric field value, and the electric field value obtained by forward modeling is compared with observed data to obtain a data error; s4, calculating a cross gradient term of the model resistance and the hydrologic parameter in a physical property space; S5, establishing an objective function, calculating the gradient of the objective function, and obtaining a searching step length and a searching direction in a pseudo-forward mode by taking a nonlinear conjugate gradient method as an inversion method; S6, judging whether the linear search convergence condition is converged, if so, entering the next step, otherwise, updating the model, and returning to the step S3; And S7, calculating the root mean square error of the data, ending iteration if convergence, otherwise updating the step length and the searching direction, calculating the updating quantity of the model, and returning to the step S3.
2. The method of three-dimensional inversion of resistivity based on groundwater seepage parameter constraints of claim 1, wherein step S1 comprises: The three-dimensional model is built by dividing the entire simulation area into Grid of, here order Representative node To the point of Is used for the distance of (a), Representative node To the point of Is used for the distance of (a), Representative node To the point of Is a distance of (2); wherein, the numerical value change range of i is 1 to im-1, the numerical value change range of j is 1 to jm-1, the numerical value change range of k is 1 to km-1, and the electric field value is taken at the grid node position.
3. The method of three-dimensional inversion of resistivity based on groundwater seepage parameter constraints of claim 1, wherein step S3 comprises: The electric field value is obtained by the following equation (1): (1) Wherein the method comprises the steps of Representing the electrical conductivity of the subsurface medium, , , Is the coordinates of the point of power supply a.
4. The three-dimensional inversion method of resistivity based on groundwater seepage parameter constraint of claim 1, wherein the cross gradient term in S4 is: (2) wherein t represents the cross-gradient, Represented as a groundwater permeability coefficient gradient, Expressed as a resistivity gradient.
5. The three-dimensional inversion method of resistivity based on groundwater seepage parameter constraint according to claim 1, wherein the objective function in step S5 is: (3) Wherein, the Three-dimensional inversion objective function representing resistivity method added to cross gradient term constraint term, wherein Representing observed data, F (m) representing forward calculation, The L represents the Laplace matrix, which consists of second partial derivatives, and the advantage of adopting a second partial derivative operator is that the obtained model is the smoothest; Representing a given initial model vector of the model, , As the number of weights to be used, Is used for balancing the data items and model items in inversion, For balancing the specific gravity occupied by the cross gradient term; When (when) When the model part is dominant, the inversion focuses on the smoothness of the model, when When the data part is dominant, inversion focuses on fitting the data.
6. The three-dimensional inversion method of resistivity based on groundwater seepage parameter constraint according to claim 1, wherein the objective function is biased towards the model transpose to obtain an objective function gradient, and the expression is: (4) Wherein, the Represents the gradient of the objective function, J represents the Jacobian matrix, i represents the number of inversion iterations, Representing the vector of data residuals and, A partial derivative matrix that is a cross gradient; (5) to obtain the model update amount It is necessary to calculate the search direction p and the step a, (6) The search direction p is solved with the following equation: (7) When the 1 st inversion iteration is performed, When the iteration number is greater than 1, the expression is as shown in (8): (8) For the vector in equation (7) Using gradients And a preconditioning factor C; (9) the expression for the preconditioning factor in equation (9) can be written as: (10) Is a constant scalar in the inversion process, and is obtained by solving a linear equation set Vector; The expression of step a in formula (6) is: (11) Let the target gradient function (4) (12) Order the (13) K is a symmetrical matrix, and the two sides of the matrix (12) are transposed first to be changed into: (14) in the formula (14), the coefficient matrix is moved to the left to be changed into a form similar to a forward equation set, v is obtained by using 'quasi forward' calculation, and then a target gradient function is obtained; In the order (11) (15) Wherein M is the number of model units, N is the number of observed data, x is a one-dimensional array with length M, and the following steps: (16) From the above equation, the coefficient matrix is shifted to the left to be similar to the forward equation set, and the solution to q is completed through the pseudo forward, so as to obtain the step length a.

Description

Resistivity three-dimensional inversion method based on groundwater seepage parameter constraint Technical Field The invention relates to the technical field of resistivity inversion, in particular to a three-dimensional resistivity inversion method based on groundwater seepage parameter constraint. Background The direct current resistivity method is a common prospecting method in geophysics, and has a wider application range. Because the underground geologic bodies are often complex and changeable, inversion research is performed in a three-dimensional mode in order to better recover the structural information of the underground target body. The three-dimensional inversion problem is often underdetermined and nonlinear, if linear inversion is adopted, the problem that inversion is trapped in local minima often occurs, in order to avoid the trouble, the inversion is carried out by adopting a nonlinear conjugate gradient method, and the method does not need to solve a sensitivity matrix, but solves the product of the sensitivity or the transpose thereof and another vector, so that the operation time can be effectively reduced. When the underground geologic body is comprehensively interpreted, the inversion result of a single method is difficult to obtain a unified geologic model, and the underground geologic body is interpreted by combining different methods. The cross gradient method is a joint inversion method with a wider application range, the method only needs that physical parameters have similarity in spatial distribution, the groundwater seepage parameters can be obtained through observation well pumping tests, the groundwater content of the groundwater body and the resistivity of the geologic body are greatly correlated, and the groundwater seepage parameters are applied to resistivity inversion by utilizing the correlation of the two in spatial physical properties. In view of the problems and defects in the existing resistivity inversion method, the application provides a resistivity three-dimensional inversion method based on groundwater seepage parameter constraint. Disclosure of Invention The invention provides a resistivity three-dimensional inversion method based on groundwater seepage parameter constraint, which is a resistivity nonlinear conjugate gradient three-dimensional inversion method added with groundwater seepage parameter constraint and has the characteristics of high efficiency and high speed. According to an aspect of the present disclosure, there is provided a resistivity three-dimensional inversion method based on groundwater seepage parameter constraints, the method comprising the steps of: S1, building a three-dimensional model and determining model parameters; S2, inputting an initial model and observation data; S3, forward modeling numerical calculation is carried out by adopting finite difference to obtain a model electric field value, and the electric field value obtained by forward modeling is compared with observed data to obtain a data error; s4, calculating a cross gradient term of the model resistance and the hydrologic parameter in a physical property space; S5, establishing an objective function, calculating the gradient of the objective function, and obtaining a searching step length and a searching direction in a pseudo-forward mode by taking a nonlinear conjugate gradient method as an inversion method; S6, judging whether the linear search convergence condition is converged, if so, entering the next step, otherwise, updating the model, and returning to the step S3; And S7, calculating the root mean square error of the data, ending iteration if convergence, otherwise updating the step length and the searching direction, calculating the updating quantity of the model, and returning to the step S3. In one possible implementation, step S1 includes: The three-dimensional model is built by dividing the entire simulation area into Grid of, here orderRepresentative nodeTo the point ofIs used for the distance of (a),Representative nodeTo the point ofIs used for the distance of (a),Representative nodeTo the point ofIs a distance of (2); wherein, the numerical value change range of i is 1 to im-1, the numerical value change range of j is 1 to jm-1, the numerical value change range of k is 1 to km-1, and the electric field value is taken at the grid node position. In one possible implementation, step S3 includes: The electric field value is obtained by the following equation (1): (1) Wherein the method comprises the steps of Representing the electrical conductivity of the subsurface medium,,,Is the coordinates of the point of power supply a. In one possible implementation, the cross gradient term in S4 is:(2) wherein t represents the cross-gradient, Represented as a groundwater permeability coefficient gradient,Expressed as a resistivity gradient. In one possible implementation, the objective function in step S5 is:(3) Wherein, the Three-dimensional inversion objective func