A method for system error correction of frequency domain electromagnetic data

Abstract

The present application belongs to the field of geophysical prospecting, and particularly relates to a system error correction method for frequency domain electromagnetic data, comprising: collecting frequency domain electromagnetic data at a specified profile or survey area to obtain apparent resistivity values; obtaining underground resistivity information at two or more survey points of the profile or survey area where the frequency domain electromagnetic data is collected to obtain a depth-resistivity model vector; logarithmically transforming the apparent resistivity values to obtain logarithmic apparent resistivity; performing forward calculation on the depth-resistivity model vector to obtain theoretical apparent resistivity, and performing corresponding logarithmic transformation to obtain theoretical logarithmic apparent resistivity; constructing a stiffness matrix; constructing a right end vector matrix; solving a gain factor vector and an offset factor vector; correcting the logarithmic apparent resistivity to obtain corrected logarithmic apparent resistivity; and taking a natural exponent of the corrected logarithmic apparent resistivity to obtain a final correction result. The present application can effectively eliminate the influence of system error and improve the quality of frequency domain electromagnetic data.

Description

Technical Field

[0001] This invention belongs to the field of geophysical exploration, and specifically relates to a method for correcting systematic errors in frequency domain electromagnetic data. Background Technology

[0002] Frequency-domain electromagnetic methods are commonly used geophysical methods, widely applied in engineering geology, solid minerals, geothermal energy, groundwater, and environmental assessment. The quality of the data directly affects the accuracy of exploration results. Frequency-domain electromagnetic data is affected by various interference factors during acquisition, with systematic errors being one of them. Systematic errors refer to the instrument response of the electromagnetic sensor itself being mixed into the acquired data, causing deviations. Mitigating the impact of systematic errors is of practical significance for improving the effectiveness of frequency-domain electromagnetic exploration. Currently, research on systematic error correction methods for frequency-domain electromagnetic methods is limited.

[0003] Therefore, there is an urgent need to develop a systematic error correction method for frequency domain electromagnetic methods to solve the problem that systematic errors affect the exploration results of frequency domain electromagnetic data. Summary of the Invention

[0004] The purpose of this invention is to provide a method for correcting system errors in frequency domain electromagnetic data. This method can correct frequency domain electromagnetic data, effectively eliminate the influence of system errors on frequency domain electromagnetic data, and improve the quality of frequency domain electromagnetic data.

[0005] Technical solution to achieve the purpose of this invention:

[0006] A method for correcting systematic errors in frequency domain electromagnetic data, the method comprising:

[0007] Step 1: Collect frequency domain electromagnetic data in the specified profile or measurement area to obtain the apparent resistivity value;

[0008] Step 2: Obtain subsurface resistivity information at two or more measuring points in the profile or survey area where frequency domain electromagnetic data is collected, and obtain the depth-resistivity model vector.

[0009] Step 3: Perform a logarithmic transformation on the apparent resistivity value to obtain the logarithmic apparent resistivity;

[0010] Step 4: Perform forward modeling on the depth-resistivity model vector to obtain the theoretical apparent resistivity, and then perform the corresponding logarithmic transformation to obtain the theoretical logarithmic apparent resistivity;

[0011] Step 5: Construct the stiffness matrix A;

[0012] Step 6: Construct the right-hand vector matrix b;

[0013] Step 7: Solve for the gain factor vector g and the offset factor vector h;

[0014] Step 8: Correct the logarithmic apparent resistivity to obtain the corrected logarithmic apparent resistivity;

[0015] Step 9: Take the natural exponent of the corrected logarithmic apparent resistivity to obtain the final correction result.

[0016] The frequency domain electromagnetic data collected in step 1 includes data at each measurement point and at each frequency point.

[0017] The methods for acquiring frequency domain electromagnetic data in step 1 include: near-field source multi-frequency electromagnetic, magnetotelluric, and controllable source audio-visual magnetotelluric.

[0018] The methods for obtaining underground resistivity information in step 2 include: resistivity logging, DC resistivity sounding, ground-penetrating radar, or resistivity core measurement.

[0019] In step 4, the method for selecting the frequency domain electromagnetic data for acquisition is near-field source multi-frequency electromagnetic data. The one-dimensional forward modeling formula is as follows:

[0020]

[0021] In the formula, d is the theoretical apparent resistivity value, ρ is the transmit / receive distance of the near-field source multi-frequency electromagnetic instrument, t is the integral independent variable, r and u are variables related to the depth-resistivity model and frequency point obtained in step 3, and J represents the Bessel function.

[0022] Step 5 specifically involves: based on the logarithmic apparent resistivity value obtained in step 3, extracting the original frequency domain electromagnetic data at the corresponding measurement points in step 2, and constructing a stiffness matrix A, whose first column element is d. 0kj The subscript k represents the kth sampling point number, and the subscript j represents the jth frequency point; the second column is all -1.

[0023] Step 6 specifically involves: constructing a right-hand vector based on the theoretical logarithmic apparent resistivity value obtained in step 4, with elements d. kj , where the subscript k represents the kth sampling point number and the subscript j represents the jth frequency point.

[0024] Step 7 specifically involves calculating the correction factor vector x based on the following system of linear equations:

[0025] x=(A T A) -1 (A T b);

[0026] The first term of x is the gain factor g at the current frequency. j The gain factor g at each frequency point j Combined, they form a gain factor vector g;

[0027] The second term of x divided by the first term is the offset factor h of the current frequency point. j The offset factors of each frequency point are combined to form an offset factor vector h.

[0028] Step 8 specifically involves subtracting the offset factor at the corresponding frequency point from the logarithmic apparent resistivity value at each frequency point, and then multiplying it by the corresponding gain factor to obtain the corrected logarithmic apparent resistivity.

[0029] Step 9 specifically involves taking the natural exponent of the corrected logarithmic apparent resistivity obtained in step 8 to obtain the corrected apparent resistivity at each measurement point and at each frequency point, thereby obtaining the systematic error correction result of the frequency domain electromagnetic data of the specified profile or measurement area.

[0030] The beneficial technical effects of this invention are as follows:

[0031] 1. The present invention provides a method for correcting systematic errors in frequency domain electromagnetic data. It uses a known resistivity model of a local location for forward modeling, compares the measured response, and then obtains the correction coefficients, thereby extending the method to data from all locations.

[0032] 2. The present invention provides a systematic error correction method for frequency domain electromagnetic data. It uses logarithmic transformation to process the data to be corrected, and then performs inverse substitution after correction, thereby avoiding negative values ​​in the corrected data that do not conform to physical reality. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the embodiments.

[0034] This invention provides a method for correcting systematic errors in frequency domain electromagnetic data, which specifically includes the following steps:

[0035] Step 1: Collect frequency domain electromagnetic data in the specified profile or measurement area to obtain the apparent resistivity value.

[0036] In a specified profile or survey area, there are p measuring points. A frequency-domain electromagnetic instrument with n frequency points is used to collect raw data. Through data collection, the location information of several measuring points on the profile or in the survey area, as well as the measurement results at those points, can be obtained. This measurement result is the apparent resistivity value corresponding to a certain frequency point at a given measuring point, denoted as d0.

[0037] Methods for acquiring frequency domain electromagnetic data include: near-field source multi-frequency electromagnetic, magnetotelluric, and controlled-source audio-frequency magnetotelluric.

[0038] Step 2: Obtain underground resistivity information at two or more measuring points in the profile or survey area where frequency domain electromagnetic data is collected, and obtain the depth-resistivity model vector.

[0039] In the sampling points of the profile or survey area where frequency domain electromagnetic data is collected, select two or more sampling points to obtain subsurface resistivity information, and obtain the depth-resistivity model vector at a certain sampling point, denoted as m. k , where k is the position of the kth measuring point.

[0040] Methods for obtaining underground resistivity information include resistivity logging, DC resistivity sounding, ground-penetrating radar, or resistivity core measurement.

[0041] Step 3: Perform a logarithmic transformation on the frequency domain electromagnetic data from Step 1 to obtain the logarithmic apparent resistivity.

[0042] Take the natural logarithm of the apparent resistivity value obtained in step 1 to obtain the logarithmic apparent resistivity value, denoted as lnd0.

[0043] Step 4: Perform forward modeling on the depth-resistivity model vector from Step 2 to obtain the theoretical apparent resistivity, and then perform the corresponding logarithmic transformation to obtain the theoretical logarithmic apparent resistivity.

[0044] Based on the depth-resistivity model vector obtained in step 2, a one-dimensional forward modeling using the frequency domain electromagnetic method is performed. The specific forward modeling formula depends on the selected frequency domain electromagnetic method. The obtained theoretical apparent resistivity value is then divided by its natural logarithm to obtain the theoretical logarithmic apparent resistivity value, denoted as lnd.

[0045] Step 5: Construct the stiffness matrix A.

[0046] Based on the logarithmic apparent resistivity value obtained in step 3, the original frequency domain electromagnetic data at the corresponding measurement points in step 2 are extracted to construct a stiffness matrix A, whose first column element is d. 0kj The subscript k represents the kth sampling point number, and the subscript j represents the jth frequency point; the second column is all -1.

[0047] Step 6: Construct the right-hand vector matrix b.

[0048] Based on the theoretical logarithmic apparent resistivity value obtained in step 4, construct the right-hand vector, whose elements are d. kj , where the subscript k represents the kth sampling point number and the subscript j represents the jth frequency point.

[0049] Step 7: Solve for the gain factor vector g and the offset factor vector h.

[0050] Based on the stiffness matrix A obtained in step 6 and the right-hand vector b obtained in step 7, the correction factor vector x is obtained by solving according to the following formula:

[0051] x=(A T A) -1 (A T b)

[0052] In the formula, x is the correction factor vector. After solving, the first term of x is the gain factor g at the current frequency. j The second term of x divided by the first term is the offset factor h of the current frequency point. j The gain factor and offset factor at each frequency point are combined to form the gain factor vector g and the offset factor vector h.

[0053] Step 8: Correct the logarithmic apparent resistivity to obtain the corrected logarithmic apparent resistivity.

[0054] The logarithmic apparent resistivity value obtained in step 3 is corrected by subtracting the offset factor at the corresponding frequency point from the logarithmic apparent resistivity value at each frequency point, and then multiplying it by the corresponding gain factor.

[0055] Step 9: Take the natural exponent of the corrected logarithmic apparent resistivity to obtain the final correction result.

[0056] The natural exponent is taken from the corrected logarithmic apparent resistivity obtained in step 8 to obtain the corrected apparent resistivity at each frequency point at each measurement point, thereby obtaining the systematic error correction result of the frequency domain electromagnetic data of the specified profile or measurement area.

[0057] Example 1

[0058] Taking near-field source multi-frequency electromagnetic profile measurement data from a certain location in Shandong as an example, this invention provides a systematic error correction method for frequency domain electromagnetic data, which specifically includes the following steps:

[0059] Step 1: Collect frequency domain electromagnetic data in the specified profile or measurement area to obtain the apparent resistivity value.

[0060] A near-field source multi-frequency electromagnetic instrument with n frequency points is used to collect raw data at p measurement points on a specified profile. Through data collection, the location information of several measurement points on the profile or in the measurement area, as well as the measurement results at those points, can be obtained. This measurement result is the apparent resistivity value corresponding to a certain frequency point at a given measurement point, denoted as d0.

[0061] Step 2: Obtain underground resistivity information at two measuring points in the profile or survey area where frequency domain electromagnetic data is collected, and obtain the depth-resistivity model vector.

[0062] In the profile or measurement area where frequency domain electromagnetic data is collected, select two or more measurement points to conduct DC resistivity depth sounding, and obtain the depth-resistivity model vector at a certain measurement point, denoted as m. k , where k is the position of the kth measuring point.

[0063] Step 3: Perform a logarithmic transformation on the frequency domain electromagnetic data from Step 1 to obtain the logarithmic apparent resistivity.

[0064] Take the natural logarithm of the apparent resistivity value obtained in step 1 to obtain the logarithmic apparent resistivity value, denoted as lnd0.

[0065] Step 4: Perform forward modeling on the depth-resistivity model vector from Step 2 to obtain the theoretical apparent resistivity, and then perform the corresponding logarithmic transformation to obtain the theoretical logarithmic apparent resistivity.

[0066] Based on the depth-resistivity model vector obtained in step 2, a one-dimensional forward modeling using the frequency domain electromagnetic method is performed. The specific forward modeling formula is the one-dimensional forward modeling formula for near-field source multi-frequency electromagnetic methods:

[0067]

[0068] In the formula, d is the theoretical apparent resistivity value, ρ is the transmit / receive distance of the near-field source multi-frequency electromagnetic instrument, t is the integral independent variable, r and u are variables related to the depth-resistivity model and frequency point obtained in step 3, and J represents the Bessel function.

[0069] The formula for calculating r is:

[0070]

[0071] In the formula:

[0072]

[0073]

[0074]

[0075]

[0076] u i =(m 2 -iωμ i σ i ) 1 / 2 i = 0, 1, ..., n

[0077] In the formula, i is the current stratigraphic number, n is the total number of layers, ω is the angular frequency, μ is the magnetic permeability, σ is the layer conductivity, and l is the layer thickness.

[0078] The theoretical apparent resistivity value is obtained by taking the natural logarithm of the natural logarithm to obtain the theoretical logarithmic apparent resistivity value, denoted as lnd.

[0079] Step 5: Construct the stiffness matrix A.

[0080] Based on the logarithmic apparent resistivity value obtained in step 3, the original frequency domain electromagnetic data at the corresponding measurement points in step 2 are extracted to construct a stiffness matrix A, whose first column element is d. 0kjThe subscript k represents the kth sampling point number, and the subscript j represents the jth frequency point; the second column is all -1.

[0081] Step 6: Construct the right-hand vector matrix b.

[0082] Based on the theoretical logarithmic apparent resistivity value obtained in step 4, construct the right-hand vector, whose elements are d. kj , where the subscript k represents the kth sampling point number and the subscript j represents the jth frequency point.

[0083] Step 7: Solve for the gain factor vector g and the offset factor vector h.

[0084] Based on the stiffness matrix A obtained in step 6 and the right-hand vector b obtained in step 7, the solution x of the linear equation system is calculated using the following formula:

[0085] x=(A T A) -1 (A T b)

[0086] In the formula, x is the correction factor vector. After solving, the first term of x is the gain factor g at the current frequency. j The second term of x divided by the first term is the offset factor h of the current frequency point. j The gain factor and offset factor at each frequency point are combined to form the gain factor vector g and the offset factor vector h.

[0087] Step 8: Correct the logarithmic apparent resistivity to obtain the corrected logarithmic apparent resistivity.

[0088] The logarithmic apparent resistivity value obtained in step 3 is corrected by subtracting the offset factor at the corresponding frequency point from the logarithmic apparent resistivity value at each frequency point, and then multiplying it by the corresponding gain factor.

[0089] Step 9: Take the natural exponent of the corrected logarithmic apparent resistivity to obtain the final correction result.

[0090] The natural exponent is taken from the corrected logarithmic apparent resistivity obtained in step 8 to obtain the corrected apparent resistivity at each measurement point and at each frequency point, thereby obtaining the system error correction result of the near-field source multi-frequency electromagnetic data of the specified profile.

[0091] The accuracy of the systematic error correction results for the near-field source multi-frequency electromagnetic data of the specified profile obtained in this embodiment is significantly improved compared to the uncorrected result, and there are no negative values ​​that do not conform to physical reality. Inversion interpretation of this data can yield imaging results that conform to the actual situation. Without correction, the data accuracy will be severely affected when the systematic error is large, leading to detection failure.

[0092] The present invention has been described in detail above with reference to the embodiments. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention. All contents not described in detail in the present invention can be derived from existing technologies.

Claims

1. A method for correcting systematic errors in frequency domain electromagnetic data, characterized in that, The method includes: Step 1: Collect frequency domain electromagnetic data in the specified profile or measurement area to obtain the apparent resistivity value; Step 2: Obtain subsurface resistivity information at two or more measuring points in the profile or survey area where frequency domain electromagnetic data is collected, and obtain the depth-resistivity model vector. Step 3: Perform a logarithmic transformation on the apparent resistivity value to obtain the logarithmic apparent resistivity; Step 4: Perform forward modeling on the depth-resistivity model vector to obtain the theoretical apparent resistivity, and then perform the corresponding logarithmic transformation to obtain the theoretical logarithmic apparent resistivity; Step 5: Construct the stiffness matrix A; Step 6: Construct the right-hand vector matrix b; Step 7: Solve for the gain factor vector g and the offset factor vector h; Step 8: Correct the logarithmic apparent resistivity to obtain the corrected logarithmic apparent resistivity; Step 9: Take the natural exponent of the corrected logarithmic apparent resistivity to obtain the final correction result.

2. The method for correcting system errors in frequency domain electromagnetic data according to claim 1, characterized in that, The frequency domain electromagnetic data collected in step 1 includes data at each measurement point and at each frequency.

3. The method for correcting systematic errors in frequency domain electromagnetic data according to claim 1, characterized in that, The methods for acquiring frequency domain electromagnetic data in step 1 include: near-field source multi-frequency electromagnetic, magnetotelluric, and controllable source audio-visual magnetotelluric.

4. The method for correcting system errors in frequency domain electromagnetic data according to claim 1, characterized in that, The methods for obtaining underground resistivity information in step 2 include: resistivity logging, DC resistivity sounding, ground-penetrating radar, or resistivity core measurement.

5. A method for correcting system errors in frequency domain electromagnetic data according to claim 1, characterized in that, In step 4, the method for selecting the frequency domain electromagnetic data for acquisition is near-field source multi-frequency electromagnetic data. The one-dimensional forward modeling formula is as follows: In the formula, d is the theoretical apparent resistivity value, ρ is the transmit / receive distance of the near-field source multi-frequency electromagnetic instrument, t is the integral independent variable, r and u are variables related to the depth-resistivity model and frequency point obtained in step 3, and J represents the Bessel function.

6. A method for correcting system errors in frequency domain electromagnetic data according to claim 5, characterized in that, Step 5 specifically involves: based on the logarithmic apparent resistivity value obtained in step 3, extracting the original frequency domain electromagnetic data at the corresponding measurement points in step 2, and constructing a stiffness matrix A, whose first column element is d. 0kj The subscript k represents the kth sampling point number, and the subscript j represents the jth frequency point; the second column is all -1.

7. A method for correcting system errors in frequency domain electromagnetic data according to claim 6, characterized in that, Step 6 specifically involves: constructing a right-hand vector based on the theoretical logarithmic apparent resistivity value obtained in step 4, with elements d. kj , where the subscript k represents the kth sampling point number and the subscript j represents the jth frequency point.

8. A method for correcting system errors in frequency domain electromagnetic data according to claim 7, characterized in that, Step 7 specifically involves calculating the correction factor vector x based on the following system of linear equations: x=(A T A) -1 (A T b); The first term of x is the gain factor g at the current frequency. j The gain factor g at each frequency point j Combined, they form a gain factor vector g; The second term of x divided by the first term is the offset factor h of the current frequency point. j The offset factors of each frequency point are combined to form an offset factor vector h.

9. A method for correcting system errors in frequency domain electromagnetic data according to claim 8, characterized in that, Step 8 specifically involves subtracting the offset factor at the corresponding frequency point from the logarithmic apparent resistivity value at each frequency point, and then multiplying it by the corresponding gain factor to obtain the corrected logarithmic apparent resistivity.

10. A method for correcting systematic errors in frequency domain electromagnetic data according to claim 9, characterized in that, Step 9 specifically involves taking the natural exponent of the corrected logarithmic apparent resistivity obtained in step 8 to obtain the corrected apparent resistivity at each measurement point and at each frequency point, thereby obtaining the systematic error correction result of the frequency domain electromagnetic data of the specified profile or measurement area.

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