CN-122018024-A - Frequency domain excitation complex resistivity fitting method

CN122018024ACN 122018024 ACN122018024 ACN 122018024ACN-122018024-A

Abstract

The invention discloses a frequency domain excitation complex resistivity fitting method, which relates to the technical field of geophysical exploration data processing, and comprises the specific steps of firstly collecting and preprocessing frequency domain excitation full-band complex resistivity data and outputting a standardized data set; the method comprises the steps of constructing a full-coupling mathematical model, calculating theoretical response values, determining parameters, establishing a forward operator, carrying out parameter sensitivity partitioning, setting constraint conditions, carrying out inversion fitting by adopting a self-adaptive partitioning iterative algorithm, and finally carrying out two-dimensional evaluation on quality, and outputting a final complex resistivity fitting result after correction.

Inventors

CHEN JIAN
MA LEI
Sheng Guangde
NONG WEIQUAN
Tan Dengpan

Assignees

国科（重庆）仪器有限公司

Dates

Publication Date: 20260512
Application Date: 20260228

Claims (10)

1. A frequency domain excitation complex resistivity fitting method is characterized by comprising the following specific steps: S1, full-band excitation data acquisition and preprocessing, namely acquiring full-band complex resistivity data of frequency domain excitation exploration, acquiring amplitude and phase actual measurement values of all frequency points, carrying out standardized preprocessing by combining construction parameters and geological priori information, and outputting a standardized complex resistivity data set; s2, full-coupling forward response calculation, namely, based on the standardized data set, constructing a full-coupling mathematical model containing an excitation effect and an electromagnetic coupling effect, calculating a full-frequency-band complex resistivity theoretical response value by solving the full-coupling mathematical model, determining a full-parameter set to be inverted, and establishing an integrated forward operator; S3, parameter sensitivity partitioning and constraint condition establishment, namely calculating the sensitivity of each parameter to be inverted in different frequency bands by utilizing the integrated forward algorithm sub-module, dividing continuous sub-frequency bands according to sensitivity distribution characteristics, setting a geological constraint interval of each parameter by combining geological priori information, and constructing a fitting weight matrix; S4, performing adaptive partition iterative inversion fitting, namely performing inversion fitting by adopting an adaptive partition iterative algorithm based on the standardized dataset, an integrated forward operator, a fitting weight matrix and a geological constraint interval, respectively and iteratively updating parameters in each sub-frequency band, checking whether the parameters after each iteration meet geological constraint and adaptively adjusting an iterative strategy, and outputting an optimal inversion parameter set and full-frequency band fitting response after convergence; And S5, performing two-dimensional quality evaluation on the optimal inversion parameter set and the full-frequency band fitting response, dividing the sub-frequency bands and constructing quantitative quality control indexes, judging the fitting residual error sources, performing targeted correction on the high residual error frequency bands, and outputting a final complex resistivity fitting result after verifying the geological validity of the parameters.
2. The frequency domain excitation complex resistivity fitting method according to claim 1 is characterized in that in the step S1, a frequency band for full-frequency band complex resistivity data acquisition of the frequency domain excitation exploration covers 0.001Hz to 100kHz, each octave is provided with at least 4 uniform frequency points, each measuring point is subjected to at least 4 groups of repeated observation, the standardized preprocessing comprises invalid frequency point elimination, noise suppression, elevation correction, topography correction, missing data completion and format unification, the invalid frequency point elimination adopts repeated observation relative error threshold judgment, the noise suppression adopts a 5-point sliding window median smoothing method, the elevation correction adopts a uniform half-space large model to complete resistivity amplitude normalization process, the topography correction adopts a finite element method to complete distortion correction process, and the missing data completion adopts a logarithmic linear interpolation method or a kriging interpolation method.
3. The frequency domain excitation complex resistivity fitting method according to claim 1, wherein in step S2, the integral forward response equation expression of the fully coupled mathematical model is: In the formula (I), in the formula (II), For complex resistivity theoretical response values at different angular frequencies, For the full set of parameters to be inverted, For the angular frequency corresponding to the acquisition frequency point one by one, In units of imaginary numbers, Is the zero-frequency resistivity of the material, In order for the polarization ratio to be high, As a function of the time constant, As the frequency-dependent coefficient of the frequency, In order to be a ground equivalent inductance, Is the equivalent capacitance to earth.
4. A frequency domain excitation complex resistivity fitting method as claimed in claim 3, in which in step S2 the full parameter set to be inverted consists of zero frequency resistivity Polarization rate Constant of time Frequency correlation coefficient Four excitation characteristic parameters and earth equivalent inductance Equivalent capacitance to earth The integrated forward operator is a calculation model which is constructed based on the integrated forward response equation, takes the total parameter set and angular frequency to be inverted as input and takes the complex resistivity theoretical response value as output, and is provided with boundary autonomous conditions that when And is also provided with When the integral forward response equation is degraded into a standard Cole-Cole model response equation.
5. The method for fitting frequency domain excitation complex resistivity according to claim 1, wherein in step S3, sensitivity of each parameter to be inverted in different frequency bands is calculated by adopting a partial derivative method, a complex resistivity response is calculated by frequency points, a partial derivative modulus value is used as a quantization index of parameter sensitivity of each parameter to be inverted, a continuous sub-frequency band is divided into three continuous non-overlapping frequency bands of a low-frequency excitation sensitive segment, a medium-frequency transition segment and a high-frequency electromagnetic coupling sensitive segment, the frequency band division is determined based on average sensitivity ratio of the excitation parameters to the electromagnetic coupling parameters, a fitting weight matrix is assigned according to the divided continuous sub-frequency bands, the assignment range of the excitation parameters in the low-frequency excitation sensitive segment is 0.9 to 1.0, the assignment range of the electromagnetic coupling parameters in the high-frequency electromagnetic coupling sensitive segment is 0.9 to 1.0, the assignment range of the excitation parameters in the medium-frequency electromagnetic coupling sensitive segment is 0 to 0.1, and the assignment of the parameters in the medium-frequency transition segment is linearly graded along with frequency logarithm.
6. The frequency domain excitation complex resistivity fitting method according to claim 1, wherein in the step S3, the specific range of the geological constraint interval is zero frequency resistivity: polarization ratio: time constant: Frequency correlation coefficient: ground equivalent inductance: Ground equivalent capacitance: 。
7. The method of fitting frequency domain excitation complex resistivity according to claim 1, wherein in step S4, the adaptive partitioning iterative algorithm adopts a frequency-dependent decoupling adaptive regularization fitting objective function expression as follows: In the formula (I), in the formula (II), In order to fit the objective function value, For the full set of parameters to be inverted, For the Hadamard product, For the fitting weight matrix constructed in step S3, For the measured complex resistivity vector corresponding to the normalized complex resistivity dataset output in step S1, The complex resistivity theoretical response vector for the integrated positive calculation sub-calculation established in step S2, For an adaptive damping factor that adjusts in real time with the fit residual, For a geology constrained regular matrix, As the initial value of the parameter to be inverted, The sign is calculated for the L2 norm.
8. The method is characterized in that in the step S4, the initial values of the parameters to be inverted are obtained from measured data of high sensitive frequency bands of corresponding parameters respectively, the initial values of the parameters of the excitation type are obtained through linear fitting of measured data of low-frequency excitation sensitive segments, the initial values of the parameters of the electromagnetic coupling type are obtained through analytic and solution calculation of measured data of high-frequency electromagnetic coupling sensitive segments, only the high-assignment parameters are updated in each sub-band in a multi-iteration process, boundary value correction is carried out on parameters exceeding a geological constraint interval after each iteration is completed, the adaptive damping factor is adjusted in real time along with the descending rate of fitting residual errors, and the iteration convergence condition is that the sum of squares of fitting residual errors is reduced below a preset precision threshold or the iteration times reach a preset maximum iteration times.
9. The frequency domain excitation complex resistivity fitting method according to claim 1, wherein in step S5, the two-dimensional residual quality control discrimination operator expression used for the two-dimensional quality evaluation is: In the formula (I), in the formula (II), A quality control judging index of the kth sub-frequency band divided by the full frequency band, Sub-band numbers divided for the full band, Is the quality control weight matrix of the kth sub-band, For the Hadamard product, Fitting a residual vector for the magnitude of the kth sub-band, Is the measured complex resistivity magnitude vector modulus value for the kth sub-band, The residual vector is fitted for the phase of the kth sub-band, The sign is calculated for the L1 norm, As the noise weight coefficient, The sign is calculated for the pearson correlation coefficient, Fitting a residual vector for the magnitude of the kth sub-band, A residual vector is fitted for the magnitudes of the k-1 th sub-band, The sign is calculated for the absolute value.
10. The method for fitting frequency domain excitation complex resistivity according to claim 1, wherein in step S5, the full-band sub-bands are divided according to a frequency logarithmic distribution rule, the number of sub-bands is not less than 5, the number of frequency points contained in each sub-band is not more than 2, the source discrimination of fitting residual errors is determined based on pearson correlation coefficients of adjacent frequency point fitting residual errors, the decision residual errors are mainly random noise when the correlation coefficients are smaller than 0.3, the decision residual errors are mainly systematic fitting deviation when the correlation coefficients are larger than or equal to 0.3, the targeted correction comprises local iteration correction corresponding to the systematic fitting deviation, sub-band weight adjustment corresponding to the random noise, and the geological validity verification is completed based on the matching degree of the fitting parameters and geological priori information.

Description

Frequency domain excitation complex resistivity fitting method Technical Field The invention relates to the technical field of geophysical exploration data processing, in particular to a frequency domain excitation complex resistivity fitting method. Background The frequency domain excitation electrical exploration is an important technical means for detecting the electrical characteristics of underground geologic bodies in the field of geophysical exploration, complex resistivity fitting is used as a core link of the technology, the result directly determines the interpretation precision of underground geologic structures, mineral resource distribution and hydrogeologic conditions, the technology performs parameter inversion fitting by collecting complex resistivity amplitude and phase data of underground media under different frequencies and combining mathematical models, and the geological information behind the data is mined, so that the technology is widely applied to the fields of mineral resource exploration, hydrogeologic investigation, engineering geological investigation and the like, in the actual exploration process, the electrical response of the underground medium simultaneously comprises an excitation effect and an electromagnetic coupling effect, and the performance characteristics of the two effects under different frequency bands are obviously different, so that higher requirements are put forward on the comprehensiveness and the accuracy of a complex resistivity fitting method, and in order to improve the matching degree of a fitting result and the actual geological condition, a complex resistivity fitting method capable of simultaneously considering the two effects and adapting to the full-band data characteristics is needed in the industry so as to solve the parameter inversion problem under the complex exploration scene. The traditional frequency domain excitation complex resistivity fitting method mainly uses a single effect as a core to construct a mathematical model, frequency domain response characteristics of the excitation effect and electromagnetic coupling effect are difficult to accurately characterize at the same time, deviation of fitting results is easy to occur due to lack of effect characterization, partial method tries to give consideration to both effects, but does not conduct differentiation processing on parameter sensitivity characteristics of different frequency bands, a unified fitting strategy of full frequency bands is adopted, each parameter cannot fully play a role in the high sensitive frequency bands, further precision of parameter inversion is insufficient, meanwhile, initial value selection of the traditional fitting algorithm lacks pertinence, effective constraint is not set in an iteration process, the condition that parameter iteration deviates from an actual geological range easily occurs, the iteration strategy is fixed, convergence speed is low, in addition, the traditional fitting quality evaluates how much single attention data matching degree, quantized quality control index distinguishing residual error sources are not constructed, fitting parameter validity is not verified by combining geological information, and partial fitting results meet data requirements, but practical geological interpretation value is not possessed. Disclosure of Invention The invention aims to make up the defects of the prior art, and provides a frequency domain excitation complex resistivity fitting method, which comprises the steps of firstly completing the acquisition and standardization pretreatment of full-frequency-band excitation data, then constructing a full-coupling mathematical model integrating excitation and electromagnetic coupling effects, building an integrated forward operator, analyzing parameter sensitivity to divide sub-frequency bands, setting geological constraints, constructing a fitting weight matrix, carrying out inversion fitting through a self-adaptive partition iterative algorithm, pertinently updating parameters of each sub-frequency band, dynamically adjusting the iterative strategy, finally judging residual sources and correcting through two-dimensional quality evaluation, and outputting fitting results after verifying the geological validity of the parameters. The invention provides a frequency domain excitation complex resistivity fitting method for solving the technical problems, which comprises the following specific steps: S1, full-band excitation data acquisition and preprocessing, namely acquiring full-band complex resistivity data of frequency domain excitation exploration, acquiring amplitude and phase actual measurement values of all frequency points, carrying out standardized preprocessing by combining construction parameters and geological priori information, and outputting a standardized complex resistivity data set; s2, full-coupling forward response calculation, namely, based on the standardized data set, constructing a full-c