Full-zone apparent resistivity calculation method of multi-source excited controlled source electromagnetic method in frequency domain

Abstract

The application belongs to the field of geophysical exploration, and particularly discloses a frequency domain full-area apparent resistivity calculation method of multi-source excitation controlled source electromagnetic method x and H z , and then the amplitude formula of E x and H z is obtained, weighted superposition is performed to obtain the amplitude formula of E x and H z under the condition of multi-source excitation uniform half space, and then the iteration formula of E x and H z full-area apparent resistivity is obtained; the normalized amplitude of the transmitting current of E x and H z measured by the observation point is obtained, weighted is performed to obtain the superposition amplitude formula of E x and H z of the observation point, an initial apparent resistivity is given, the superposition amplitude of E x and H z of the observation point and the initial apparent resistivity are substituted into the iteration formula, and iteration calculation is performed to obtain the frequency domain E x and H z full-area apparent resistivity of the multi-source excitation controlled source electromagnetic method. The application fills the blank of the frequency domain full-area apparent resistivity calculation of the multi-source excitation controlled source electromagnetic method, and effectively promotes the development of electromagnetic exploration technology. The application is suitable for the calculation of the frequency domain full-area apparent resistivity of the multi-source excitation controlled source electromagnetic method.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of geophysical exploration, and relates to a controlled source electromagnetic method, in particular to a full-area apparent resistivity calculation method in frequency domain of multi-source excitation controlled source electromagnetic method. BACKGROUND

[0002] The controlled source electromagnetic method refers to a kind of electromagnetic exploration method for transmitting electric current of multiple frequencies to the underground through a ground wire source, observing electric field or magnetic field components on the ground, and studying the electrical distribution of the earth based on the observed electric field or magnetic field to solve related geological problems. The multi-source excitation multi-coverage controlled source electromagnetic method is a new observation method developed on the basis of conventional single-source excitation, which has higher sensitivity to target bodies and better focusing, effectively improving the exploration effect. However, the calculation of full-area apparent resistivity of multi-source excitation multi-coverage observation data is currently in a blank state, which restricts the analysis and interpretation of multi-source excitation multi-coverage controlled source electromagnetic method data. SUMMARY

[0003] The purpose of the present application is to provide a full-area apparent resistivity calculation method in frequency domain of multi-source excitation controlled source electromagnetic method to fill the blank of full-area apparent resistivity calculation of multi-source excitation multi-coverage controlled source electromagnetic method and effectively promote the development of electromagnetic exploration technology.

[0004] In order to achieve the above-mentioned purpose, the technical method adopted by the present application is as follows:

[0005] The full-area apparent resistivity calculation method in frequency domain of multi-source excitation controlled source electromagnetic method includes the calculation of full-area apparent resistivity of horizontal electric field component and the calculation of full-area apparent resistivity of vertical magnetic field component. The calculation method of full-area apparent resistivity of horizontal electric field component in frequency domain of multi-source excitation controlled source electromagnetic method includes the following steps:

[0006] S1, a rectangular coordinate system is established, the horizontal electric field component on the ground under the condition of single-source excitation uniform half-space is calculated, and then the amplitude of the normalized transmission current is taken to obtain the amplitude formula of the horizontal electric field component on the ground under the condition of single-source excitation uniform half-space;

[0007] S2, according to the amplitude formula of the horizontal electric field component on the ground under the condition of single-source excitation uniform half-space, weighted superposition is performed to obtain the amplitude formula of the horizontal electric field component on the ground under the condition of multi-source excitation uniform half-space;

[0008] S3, according to the amplitude formula of the horizontal electric field component on the ground under the condition of multi-source excitation uniform half-space, the iteration formula of full-area apparent resistivity based on the horizontal electric field component of multi-source excitation controlled source electromagnetic method is obtained;

[0009] S4, normalize the transmitting current of the horizontal electric field component measured by the observation point under multi-source excitation, take the amplitude, and then weight according to the weighting coefficient of the weighted stacking in step S2 to obtain a stacking amplitude formula of the horizontal electric field component of the observation point under multi-source excitation.

[0010] S5, given an initial apparent resistivity, substitute the stacking amplitude of the horizontal electric field component of the observation point under multi-source excitation and the initial apparent resistivity into the iterative formula in step S3 to perform iterative calculation to obtain the full-area apparent resistivity of the frequency domain horizontal electric field component of the multi-source excitation controlled source electromagnetic method.

[0011] The method for calculating the full-area apparent resistivity of the frequency domain vertical magnetic field component of the multi-source excitation controlled source electromagnetic method comprises the following steps:

[0012] N1, establish a rectangular coordinate system, calculate the ground vertical magnetic field component under single-source excitation uniform half-space condition, then normalize the transmitting current to take the amplitude to obtain an amplitude formula of the ground vertical magnetic field component under single-source excitation uniform half-space condition;

[0013] N2, according to the amplitude formula of the ground vertical magnetic field component under single-source excitation uniform half-space condition, weighted stacking is performed to obtain an amplitude formula of the ground vertical magnetic field component under multi-source excitation uniform half-space condition;

[0014] N3, according to the amplitude formula of the ground vertical magnetic field component under multi-source excitation uniform half-space condition, an iterative formula of the full-area apparent resistivity of the multi-source excitation controlled source electromagnetic method based on the vertical magnetic field component is obtained;

[0015] N4, normalize the transmitting current of the vertical magnetic field component measured by the observation point under multi-source excitation to take the amplitude, and then weight according to the weighting coefficient of the weighted stacking in step N2 to obtain a stacking amplitude formula of the vertical magnetic field component of the observation point under multi-source excitation;

[0016] N5, given an initial apparent resistivity, substitute the stacking amplitude of the vertical magnetic field component of the observation point under multi-source excitation and the initial apparent resistivity into the iterative formula in step N3 to perform iterative calculation to obtain the full-area apparent resistivity of the frequency domain vertical magnetic field component of the multi-source excitation controlled source electromagnetic method.

[0017] As a limitation: in step S1, the rectangular coordinate system takes the center of the transmitting source as the coordinate origin, and the direction of the transmitting source as the x-axis direction, and the vertical direction as the y direction.

[0018] As a further limitation: in step S1, the calculation formula of the ground horizontal electric field component under single-source excitation uniform half-space condition is:

[0019]

[0020] In the formula, E xfor the horizontal electric field component, x is the horizontal coordinate of the observation point, I is the transmitting current, p is the earth resistivity, I is the half length of the transmitting source, r1 is the distance from the observation point to one end of the transmitting source, r2 is the distance from the observation point to the other end of the transmitting source, for the electromagnetic wave propagation constant in the earth, w is the circular frequency, m0 is the magnetic permeability in the air, r is the distance from the observation point to the discrete dipole dl;

[0021] The formula for taking the amplitude of the normalized transmitting current is:

[0022]

[0023] In the above formula, Amp represents taking the amplitude operation on a complex number, and the kernel part in the above formula is

[0024]

[0025] The amplitude formula of the horizontal electric field component on the ground under the condition of single-source excitation of a uniform half space is:

[0026]

[0027] The amplitude formula of the horizontal electric field component on the ground under the condition of multi-source excitation of a uniform half space in step S2 is:

[0028]

[0029] In the above formula, E xcore_i is the kernel part in the amplitude formula of the horizontal electric field component of the i-th transmitting source after normalization of the transmitting current, is the weighting coefficient of the i-th transmitting source, R i , and R j are the vertical distances from the observation point to the i-th transmitting source and the j-th transmitting source respectively, and p represents the number of transmitting sources;

[0030] The iteration formula of the full-zone apparent resistivity based on the horizontal electric field component in the multi-source excitation controlled source electromagnetic method in step S3 is:

[0031]

[0032] The formula for the superposition amplitude of the horizontal electric field component on the observation point under multi-source excitation in step S4 is:

[0033]

[0034] In the above formula, A Ei is the amplitude of the horizontal electric field component measured by the observation point under the excitation of the i-th transmitting source after normalization of the transmitting current, and A E is the superposition amplitude of the horizontal electric field component on the observation point under multi-source excitation.

[0035] As a further limitation: the condition for stopping the iterative calculation in step S5 is that the relative error of the apparent resistivity value obtained for two consecutive times is less than a set value, or a prescribed number of iterations is reached.

[0036] As another limitation: in step N1, the rectangular coordinate system takes the center of the transmitter as the coordinate origin, and the direction of the transmitter as the x-axis direction, and the vertical direction as the y direction.

[0037] As a further limitation: in step N1, the formula for calculating the vertical magnetic field component on the ground under the condition of single-source excitation of a homogeneous half-space is:

[0038]

[0039] In the formula, H z is the vertical magnetic field component, y is the longitudinal coordinate of the observation point, I is the transmitting current, p is the earth resistivity, l is the half length of the transmitting source, is the electromagnetic wave propagation constant in the earth, w is the circular frequency, μ0 is the magnetic permeability in the air, and r is the distance from the observation point to the discrete dipole dl;

[0040] The formula for taking the amplitude of the normalized transmitting current is:

[0041]

[0042] In the above formula, Amp represents the amplitude operation on a complex number, and the kernel part in the above formula is

[0043]

[0044] Therefore, the amplitude formula for the vertical magnetic field component on the ground under the condition of single-source excitation of a homogeneous half-space is:

[0045]

[0046] The amplitude formula for the vertical magnetic field component on the ground under the condition of multi-source excitation of a homogeneous half-space in step N2 is:

[0047]

[0048] In the above formula, H zcore_i is the kernel part in the amplitude formula of the vertical magnetic field component of the i-th transmitting source after the transmitting current is normalized, is the weighting coefficient of the i-th transmitting source, R i , R j are the vertical distances from the observation point to the i-th transmitting source and the j-th transmitting source respectively, and p represents the number of transmitting sources.

[0049] The iterative formula for the full-zone apparent resistivity based on the vertical magnetic field component in the controlled source electromagnetic method under multi-source excitation in step N3 is:

[0050]

[0051] The formula of the superimposed amplitude of the vertical magnetic field component of the observation point under the multi-source excitation in step N4 is:

[0052]

[0053] In the above formula, A Hi is the normalized amplitude of the emission current of the vertical magnetic field component of the observation point under the excitation of the i-th emission source, A H is the superimposed amplitude of the vertical magnetic field component of the observation point under the multi-source excitation.

[0054] As a further limitation: the condition for stopping the iterative calculation in step N5 is that the relative error of the apparent resistivity value obtained for two consecutive times is less than a set value, or a specified number of iterations is reached.

[0055] Compared with the prior art, the beneficial effects obtained by the present application are:

[0056] The present application provides a multi-source excitation controlled source electromagnetic method frequency domain full-area apparent resistivity calculation method, which superimposes the weighted amplitude expression of the horizontal electric field component E x of each source and the vertical magnetic field component H z to construct a multi-source weighted superimposed full-area apparent resistivity iterative calculation formula, and then obtains the multi-source excitation controlled source electromagnetic method frequency domain horizontal electric field component E x full-area apparent resistivity and vertical magnetic field component H z full-area apparent resistivity, which fills the gap of the multi-source excitation controlled source electromagnetic method frequency domain full-area apparent resistivity calculation, and effectively promotes the development of electromagnetic exploration technology.

[0057] The present application is suitable for the calculation of the multi-source excitation controlled source electromagnetic method frequency domain full-area apparent resistivity. BRIEF DESCRIPTION OF DRAWINGS

[0058] The present application will be described in further detail below in combination with the drawings and specific embodiments.

[0059] Figure 1 is the rectangular coordinate system for the single-source excitation ground electromagnetic response calculation of the embodiment of the present application;

[0060] Figure 2 is the schematic diagram of the observation device of the four-source excitation four-time coverage controlled source electromagnetic method of the embodiment of the present application;

[0061] Figure 3 is the horizontal electric field component E x amplitude and vertical magnetic field component Hz Amplitude vs. frequency of electromagnetic wave;

[0062] Figure 4 Forward obtained horizontal electric field component E for A2B2 source excitation at Sta. 1 observation point of the embodiment of the present invention x Amplitude and vertical magnetic field component H z Amplitude vs. frequency of electromagnetic wave;

[0063] Figure 5 Forward obtained horizontal electric field component E for A3B3 source excitation at Sta. 1 observation point of the embodiment of the present invention x Amplitude and vertical magnetic field component H z Amplitude vs. frequency of electromagnetic wave;

[0064] Figure 6 Forward obtained horizontal electric field component E for A4B4 source excitation at Sta. 1 observation point of the embodiment of the present invention x Amplitude and vertical magnetic field component H z Amplitude vs. frequency of electromagnetic wave;

[0065] Figure 7 Forward obtained horizontal electric field component E for A1B1 source excitation at Sta. 3 observation point of the embodiment of the present invention x Amplitude and vertical magnetic field component H z Amplitude vs. frequency of electromagnetic wave;

[0066] Figure 8 Forward obtained horizontal electric field component E for A2B2 source excitation at Sta. 3 observation point of the embodiment of the present invention x Amplitude and vertical magnetic field component H z Amplitude vs. frequency of electromagnetic wave;

[0067] Figure 9 Forward obtained horizontal electric field component E for A3B3 source excitation at Sta. 3 observation point of the embodiment of the present invention x Amplitude and vertical magnetic field component H z Amplitude vs. frequency of electromagnetic wave;

[0068] Figure 10 Forward obtained horizontal electric field component E for A4B4 source excitation at Sta. 3 observation point of the embodiment of the present invention x Amplitude and vertical magnetic field component H z Amplitude vs. frequency of electromagnetic wave;

[0069] Figure 11 Horizontal electric field component E for Sta. 1 observation point of the embodiment of the present invention x Full zone apparent resistivity and vertical magnetic field component H zFull-area apparent resistivity curve chart;

[0070] Figure 12 Horizontal electric field component E of observation point Sta.3 of the embodiment of the present application x Full-area apparent resistivity and vertical magnetic field component H z Full-area apparent resistivity curve chart. DETAILED DESCRIPTION

[0071] The present application will be further described in conjunction with the embodiments. However, those skilled in the art should understand that the present application is not limited to the following embodiments, and any improvement and equivalent change made on the basis of the specific embodiments of the present application are within the scope of protection of the present application.

[0072] Embodiment A frequency-domain full-area apparent resistivity calculation method of multi-source excitation controlled source electromagnetic method

[0073] A frequency-domain full-area apparent resistivity calculation method of multi-source excitation controlled source electromagnetic method, the calculation of full-area apparent resistivity includes the calculation of horizontal electric field component full-area apparent resistivity and the calculation of vertical magnetic field component full-area apparent resistivity, the frequency-domain horizontal electric field component full-area apparent resistivity calculation method of multi-source excitation controlled source electromagnetic method includes the following steps:

[0074] S1, establish a rectangular coordinate system, as shown in Figure 1 , take the center of the transmitting source as the coordinate origin, take the direction of the transmitting source as the x-axis direction, and take the vertical direction as the y direction. The observation point is M(x, y). The horizontal electric field component on the ground under the condition of single-source excitation uniform half-space is calculated, and then the amplitude is taken after normalization of the transmitting current to obtain the amplitude formula of the horizontal electric field component on the ground under the condition of single-source excitation uniform half-space.

[0075] The calculation formula of the horizontal electric field component on the ground under the condition of single-source excitation uniform half-space is:

[0076]

[0077] In the formula, E x is the horizontal electric field component, x is the horizontal coordinate of the observation point, I is the transmitting current, p is the earth resistivity, l is the half length of the transmitting source, r1 is the distance from the observation point to one end of the transmitting source, r2 is the distance from the observation point to the other end of the transmitting source, is the electromagnetic wave propagation constant in the earth, w is the circular frequency, μ0 is the magnetic permeability in the air, and r is the distance from the observation point to the discrete dipole dl.

[0078] The formula for taking the amplitude after normalization of the transmitting current is:

[0079]

[0080] In the formula, Amp represents taking the amplitude of a complex number, and the kernel part in the formula is

[0081]

[0082] The amplitude formula of the horizontal electric field component on the ground under the condition of single-source excitation of a uniform half-space is:

[0083]

[0084] S2, according to the amplitude formula of the horizontal electric field component on the ground under the condition of single-source excitation of a uniform half-space, weighted stacking is performed to obtain the amplitude formula of the horizontal electric field component on the ground under the condition of multi-source excitation of a uniform half-space; the amplitude formula of the horizontal electric field component on the ground under the condition of multi-source excitation of a uniform half-space is:

[0085]

[0086] In the formula, E xcore_i is the kernel part in the amplitude formula of the horizontal electric field component on the ground under the condition of single-source excitation of a uniform half-space after normalization of the transmission current, is a weighting coefficient of the i th transmission source, R i and R j are the vertical distances from the observation point to the i th transmission source and the j th transmission source respectively, and p represents the number of transmission sources;

[0087] S3, according to the amplitude formula of the horizontal electric field component on the ground under the condition of multi-source excitation of a uniform half-space, an iteration formula of the full-zone apparent resistivity based on the horizontal electric field component in the method of multi-source controlled source electromagnetic method is obtained; the iteration formula of the full-zone apparent resistivity based on the horizontal electric field component in the method of multi-source controlled source electromagnetic method is:

[0088]

[0089] S4, the transmission current of the horizontal electric field component measured by the observation point under multi-source excitation is normalized to take the amplitude, and then weighted according to the weighting coefficient of the weighted stacking in step S2 to obtain a stacking amplitude formula of the horizontal electric field component of the observation point under multi-source excitation; the stacking amplitude formula of the horizontal electric field component of the observation point under multi-source excitation is:

[0090]

[0091] In the formula, A Ei is the amplitude of the horizontal electric field component measured by the observation point under the excitation of the i th transmission source after normalization of the transmission current, and A E is the stacking amplitude of the horizontal electric field component of the observation point under multi-source excitation;

[0092] S5, given an initial apparent resistivity, the superposition amplitude of the horizontal electric field component of the observation point under multi-source excitation and the initial apparent resistivity are substituted into the iterative formula in step S3, and iterative calculation is carried out until the relative error of the apparent resistivity values obtained by two consecutive times is less than a set value, or the number of iterations reaches a predetermined number, to obtain the full-area apparent resistivity of the horizontal electric field component in the frequency domain of the multi-source excitation controlled source electromagnetic method;

[0093] The method for calculating the full-area apparent resistivity of the vertical magnetic field component in the frequency domain of the multi-source excitation controlled source electromagnetic method comprises the following steps:

[0094] N1, a rectangular coordinate system is established, the center of the transmitting source is taken as the coordinate origin, the direction of the transmitting source is taken as the x-axis direction, and the vertical direction is taken as the y direction. The vertical magnetic field component on the ground under the condition of single-source excitation of a uniform half-space is calculated, and then the amplitude of the normalized transmitting current is taken to obtain the amplitude formula of the vertical magnetic field component on the ground under the condition of single-source excitation of a uniform half-space. The calculation formula of the vertical magnetic field component on the ground under the condition of single-source excitation of a uniform half-space is:

[0095]

[0096] In the formula, H z is the vertical magnetic field component, y is the longitudinal coordinate of the observation point, I is the transmitting current, p is the earth resistivity, l is the half length of the transmitting source, is the electromagnetic wave propagation constant in the earth, w is the circular frequency, μ0 is the magnetic permeability in the air, and r is the distance from the observation point to the discrete dipole dl;

[0097] The formula for taking the amplitude of the normalized transmitting current is:

[0098]

[0099] In the above formula, Amp represents the amplitude operation on a complex number, and the kernel part in the above formula is

[0100]

[0101] Therefore, the amplitude formula of the vertical magnetic field component on the ground under the condition of single-source excitation of a uniform half-space is:

[0102]

[0103] N2, according to the amplitude formula of the vertical magnetic field component on the ground under the condition of single-source excitation of a uniform half-space, weighted superposition is carried out to obtain the amplitude formula of the vertical magnetic field component on the ground under the condition of multi-source excitation of a uniform half-space. The amplitude formula of the vertical magnetic field component on the ground under the condition of multi-source excitation of a uniform half-space is:

[0104]

[0105] In the formula, H zcore_iThe amplitude formula of the vertical magnetic field component of the i-th transmitting source after the transmitting current is normalized, The weighting coefficient of the i-th transmitting source, R i , R j The vertical distance from the observation point to the i-th transmitting source and the j-th transmitting source, respectively, and p represents the number of transmitting sources.

[0106] N3, according to the amplitude formula of the vertical magnetic field component of the ground under the condition of multi-source excitation of a uniform half space, an iteration formula of the full-area apparent resistivity based on the vertical magnetic field component of multi-source excitation controlled source electromagnetic method is obtained; the iteration formula of the full-area apparent resistivity based on the vertical magnetic field component of multi-source excitation controlled source electromagnetic method is:

[0107]

[0108] N4, the transmitting current of the vertical magnetic field component measured by the observation point under multi-source excitation is normalized to take the amplitude, and then the weighting coefficient of the weighted stacking in step N2 is weighted to obtain the stacking amplitude formula of the vertical magnetic field component of the observation point under multi-source excitation; the stacking amplitude formula of the vertical magnetic field component of the observation point under multi-source excitation is:

[0109]

[0110] In the above formula, A Hi The amplitude of the transmitting current of the vertical magnetic field component measured by the observation point under the excitation of the i-th transmitting source after normalization, A H The stacking amplitude of the vertical magnetic field component of the observation point under multi-source excitation;

[0111] N5, given an initial apparent resistivity, the stacking amplitude of the vertical magnetic field component of the observation point under multi-source excitation and the initial apparent resistivity are substituted into the iteration formula in step N3, and iterative calculation is performed until the relative error of the apparent resistivity values obtained by two consecutive times is less than a set value, or the prescribed number of iterations is reached, to obtain the full-area apparent resistivity of the frequency domain vertical magnetic field component of the multi-source excitation controlled source electromagnetic method.

[0112] This embodiment adopts a five-layer geoelectric model, and the resistivities of the first layer to the fifth layer are 100 Ω·m, 10 Ω·m, 100 Ω·m, 10 Ω·m, and 100 Ω·m, respectively. The thicknesses of the first layer to the fourth layer are 400 m, 100 m, 3000 m, and 500 m, respectively. Four transmitting sources are set, and the observation device schematic diagram of four-source excitation four times covering the controlled source electromagnetic method is as shown in Figure 2As shown in the figure, A1B1, A2B2, A3B3, and A4B4 are four grounded conductor sources, each 10000m in length, with a transmitting current of 100A. Sta.0 to Sta.5 represent six measuring points. The four sources A1B1, A2B2, A3B3, and A4B4 respectively excite the sample, covering the measuring area four times. The horizontal electric field component E generated by each source is recorded at measuring points Sta.0 to Sta.5. x and the vertical magnetic field component H z .

[0113] This embodiment uses two observation points, Sta.1 and Sta.3, as examples to verify the frequency domain full-area apparent resistivity calculation method of the multi-source excited controllable source electromagnetic method. The horizontal electric field component E is modeled forward at the two observation points, Sta.1 and Sta.3. x and the vertical magnetic field component H z The horizontal electric field component E obtained by forward modeling the source A1B1-A4B4 at observation point Sta.1 x Amplitude and vertical magnetic field component H z The curves of amplitude versus electromagnetic wave frequency are shown below. Figures 3-6 As shown, the horizontal electric field component E obtained from the forward modeling of the source A1B1-A4B4 at observation point Sta.3 is... x Amplitude and vertical magnetic field component H z The curves of amplitude versus electromagnetic wave frequency are shown below. Figures 7-10 As shown, following the frequency domain full-area apparent resistivity calculation method of the multi-source excited controllable source electromagnetic method in this embodiment, the horizontal electric field component E at observation points Sta.1 and Sta.3 is calculated. x Apparent resistivity and vertical magnetic field component H of the whole region z The apparent resistivity of the entire region is determined when the horizontal electric field component E at the Sta.1 observation point is obtained twice consecutively. x The iteration stops when the relative error of the apparent resistivity across the entire region is less than 0.01%, and the iteration stops when the vertical magnetic field component H of the Sta.1 observation point is obtained twice consecutively. z The iteration stops when the relative error of apparent resistivity across the entire region is less than 0.01%, and the horizontal electric field component E at the Sta.1 observation point is obtained. x Apparent resistivity and vertical magnetic field component H of the whole region z Apparent resistivity of the entire region, such as Figure 11 As shown, when the horizontal electric field component E at the Sta.3 observation point is obtained twice consecutively... x The iteration stops when the relative error of the apparent resistivity across the entire region is less than 0.01%, and the iteration stops when the vertical magnetic field component H of the Sta.3 observation point is obtained twice consecutively. z The iteration stops when the relative error of apparent resistivity across the entire region is less than 0.01%, and the horizontal electric field component E at the Sta.3 observation point is obtained. x Apparent resistivity and vertical magnetic field component H of the whole region zThe full-area apparent resistivity, as shown in Figure 12 The results show that the electromagnetic field response and the full-area apparent resistivity obtained by the forward calculation are correct, and thus the calculation method of the full-area apparent resistivity of the multi-source excited controlled source electromagnetic method in the frequency domain is reliable.

Claims

1. A frequency domain full-zone apparent resistivity calculation method for multi-source excited controlled source electromagnetic method, characterized in that, The calculation of the apparent resistivity of the whole area includes the calculation of the apparent resistivity of the whole area of the horizontal electric field component and the calculation of the apparent resistivity of the whole area of the vertical magnetic field component, and the calculation method of the apparent resistivity of the whole area of the horizontal electric field component of the multi-source excitation controlled source electromagnetic method in the frequency domain comprises the following steps: S1, a rectangular coordinate system is established, the horizontal electric field component on the ground under the condition of single-source excitation and uniform half space is calculated, and then the amplitude of the horizontal electric field component on the ground under the condition of single-source excitation and uniform half space is obtained after the transmitting current is normalized; S2, according to the amplitude formula of the horizontal electric field component on the ground under the condition of single-source excitation and uniform half space, weighted stacking is performed to obtain the amplitude formula of the horizontal electric field component on the ground under the condition of multi-source excitation and uniform half space; S3, according to the amplitude formula of the horizontal electric field component on the ground under the condition of multi-source excitation and uniform half space, the iteration formula of the apparent resistivity of the whole area of the horizontal electric field component based on the multi-source excitation controlled source electromagnetic method is obtained; S4, the amplitude of the horizontal electric field component is obtained after the transmitting current of the horizontal electric field component measured by the observation point under the multi-source excitation is normalized, and then the weighted stacking amplitude formula of the horizontal electric field component of the observation point under the multi-source excitation is obtained according to the weighting coefficient of the weighted stacking in step S2; S5, an initial apparent resistivity is given, the weighted stacking amplitude of the horizontal electric field component of the observation point under the multi-source excitation and the initial apparent resistivity are substituted into the iteration formula in step S3, and then iterative calculation is performed to obtain the apparent resistivity of the whole area of the horizontal electric field component of the multi-source excitation controlled source electromagnetic method in the frequency domain; The calculation method of the apparent resistivity of the whole area of the vertical magnetic field component of the multi-source excitation controlled source electromagnetic method in the frequency domain comprises the following steps: N1, a rectangular coordinate system is established, the vertical magnetic field component on the ground under the condition of single-source excitation and uniform half space is calculated, and then the amplitude of the vertical magnetic field component on the ground under the condition of single-source excitation and uniform half space is obtained after the transmitting current is normalized; N2, according to the amplitude formula of the vertical magnetic field component on the ground under the condition of single-source excitation and uniform half space, weighted stacking is performed to obtain the amplitude formula of the vertical magnetic field component on the ground under the condition of multi-source excitation and uniform half space; N3, according to the amplitude formula of the vertical magnetic field component on the ground under the condition of multi-source excitation and uniform half space, the iteration formula of the apparent resistivity of the whole area of the vertical magnetic field component based on the multi-source excitation controlled source electromagnetic method is obtained; N4, the amplitude of the vertical magnetic field component is obtained after the transmitting current of the vertical magnetic field component measured by the observation point under the multi-source excitation is normalized, and then the weighted stacking amplitude formula of the vertical magnetic field component of the observation point under the multi-source excitation is obtained according to the weighting coefficient of the weighted stacking in step N2; N5, an initial apparent resistivity is given, the weighted stacking amplitude of the vertical magnetic field component of the observation point under the multi-source excitation and the initial apparent resistivity are substituted into the iteration formula in step N3, and then iterative calculation is performed to obtain the apparent resistivity of the whole area of the vertical magnetic field component of the multi-source excitation controlled source electromagnetic method in the frequency domain.

2. The full-area apparent resistivity calculation method in frequency domain for multi-source excited controlled source electromagnetic method according to claim 1, characterized in that, In step S1, the rectangular coordinate system takes the center of the transmitting source as the coordinate origin and takes the direction of the transmitting source as the x-axis direction, and the vertical direction is the y direction.

3. The full-area apparent resistivity calculation method in frequency domain for multi-source excited controlled source electromagnetic method according to claim 2, characterized in that, In step S1, the calculation formula of the horizontal electric field component on the ground under the condition of single-source excitation and uniform half space is: where E is the electric field, x is the horizontal coordinate of the observation point, I is the transmitted current, p is the earth resistivity, I is the half length of the transmitter, r1 is the distance from the observation point to one end of the transmitter, r2 is the distance from the observation point to the other end of the transmitter, x is the electromagnetic wave propagation constant in the earth, w is the circular frequency, μ0 is the magnetic permeability in air, and r is the distance from the observation point to the discrete dipole dl. is the electromagnetic wave propagation constant in the earth, w is the circular frequency, μ0 is the magnetic permeability in air, and r is the distance from the observation point to the discrete dipole dl. The formula for taking the amplitude after the transmitting current is normalized is: In the formula, Amp represents the amplitude operation on a complex number, and the kernel part in the formula is The amplitude formula of the horizontal electric field component on the ground under the condition of single-source excitation of a homogeneous half-space is: The amplitude formula of the horizontal electric field component on the ground under the condition of multi-source excitation of a homogeneous half-space in step S2 is: In the above formula, E xcore_i is the core part of the amplitude formula after the horizontal electric field component of the i-th transmitting source is normalized by the transmitting current, is the weighted coefficient of the i-th transmitting source, R i , R j are the vertical distances from the observation point to the i-th transmitting source and the j-th transmitting source, respectively, and p represents the number of transmitting sources. The iteration formula of the full-area apparent resistivity based on the horizontal electric field component under the condition of multi-source excitation of a controllable source electromagnetic method in step S3 is: The formula of the superposition amplitude of the horizontal electric field component of an observation point under the condition of multi-source excitation in step S4 is: In the above formula, A Ei is the normalized amplitude of the emission current of the horizontal electric field component measured at the observation point for the i-th emission source excitation E is the superimposed amplitude of the horizontal electric field component at the observation point for the multi-source excitation.

4. The full-area apparent resistivity calculation method in frequency domain for multi-source excited controlled source electromagnetic method according to claim 3, characterized in that, The iteration calculation stopping condition in step S5 is that the relative error of the apparent resistivity values obtained continuously for two times is less than a set value, or a prescribed iteration number is reached.

5. The frequency domain full-zone apparent resistivity calculation method of multi-source excited controlled source electromagnetic method according to any one of claims 1-4, characterized in that, In step N1, the rectangular coordinate system takes the center of the transmitting source as the coordinate origin, takes the direction of the transmitting source as the x-axis direction, and takes the vertical direction as the y direction.

6. The full-area apparent resistivity calculation method in frequency domain for multi-source excited controlled source electromagnetic method according to claim 5, characterized in that, The calculation formula of the vertical magnetic field component on the ground under the condition of single-source excitation of a homogeneous half-space in step N1 is: where H z is the vertical magnetic field component, y is the ordinate of the observation point, I is the transmitting current, p is the earth resistivity, l is the half length of the transmitter, is the electromagnetic wave propagation constant in the earth, w is the circular frequency, μ0 is the magnetic permeability in air, r is the distance from the observation point to the discrete dipole dl; The formula for taking the amplitude of the normalized transmitting current is: In the above formula, Amp represents the amplitude operation on a complex number, and the kernel part in the above formula is The amplitude formula of the vertical magnetic field component on the ground under the condition of single-source excitation of a homogeneous half-space is: The amplitude formula of the vertical magnetic field component on the ground under the condition of multi-source excitation of a homogeneous half-space in step N2 is: In the above formula, H zcore_i is the core part of the amplitude formula of the vertical magnetic field component of the i-th transmitting source after normalization by the transmitting current, is the weighting coefficient of the i-th transmitting source, R i , R j are the vertical distances from the observation point to the i-th transmitting source and the j-th transmitting source, respectively, and p represents the number of transmitting sources. The iteration formula of the full-area apparent resistivity based on the vertical magnetic field component under the condition of multi-source excitation of a controllable source electromagnetic method in step N3 is: The formula of the superposition amplitude of the vertical magnetic field component of an observation point under the condition of multi-source excitation in step N4 is: In the above formula, A Hi is the normalized amplitude of the vertical magnetic field component measured at the observation point for the i-th source excitation H is the superimposed amplitude of the vertical magnetic field component at the observation point for the multi-source excitation.

7. The full-area apparent resistivity calculation method in frequency domain for multi-source excited controlled source electromagnetic method according to claim 6, characterized in that, The iteration calculation stopping condition in step N5 is that the relative error of the apparent resistivity values obtained continuously for two times is less than a set value, or a prescribed iteration number is reached.

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