CN116859469A - Magnetic field frequency gradient apparent resistivity measurement method and system based on horizontal couple source - Google Patents

Magnetic field frequency gradient apparent resistivity measurement method and system based on horizontal couple source Download PDF

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CN116859469A
CN116859469A CN202310817850.XA CN202310817850A CN116859469A CN 116859469 A CN116859469 A CN 116859469A CN 202310817850 A CN202310817850 A CN 202310817850A CN 116859469 A CN116859469 A CN 116859469A
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magnetic field
apparent resistivity
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汤井田
罗志亮
周聪
肖晓
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Central South University
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    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
    • G01V3/08—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation operating with magnetic or electric fields produced or modified by objects or geological structures or by detecting devices
    • G01V3/083—Controlled source electromagnetic [CSEM] surveying
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    • G01—MEASURING; TESTING
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    • G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
    • G01V3/08—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation operating with magnetic or electric fields produced or modified by objects or geological structures or by detecting devices
    • G01V3/083—Controlled source electromagnetic [CSEM] surveying
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Abstract

The application discloses a magnetic field frequency gradient apparent resistivity measurement method and a magnetic field frequency gradient apparent resistivity measurement system based on a horizontal couple source. Based on an analytical expression of a magnetic field frequency gradient generated by a horizontal couple source on the surface of a uniform half space, calculating a frequency difference value of radial magnetic field intensity and tangential magnetic field intensity through a difference algorithm, suppressing a primary field, and highlighting a secondary field; and the field value frequency gradient of the uniform half space is used for equivalent practical field value frequency difference, and the solution of apparent resistivity is realized by adopting a numerical iteration method. The method for extracting apparent resistivity by calculating the magnetic field frequency gradient can realize electromagnetic sounding under the condition of small induction number and effectively reflect deep electrical structures.

Description

Magnetic field frequency gradient apparent resistivity measurement method and system based on horizontal couple source
Technical Field
The application belongs to the technical field of geophysical exploration, and particularly relates to a magnetic field frequency gradient apparent resistivity measurement method and system based on a horizontal couple source.
Background
The frequency domain controllable source electromagnetic sounding method generally utilizes a transmitter to supply alternating current with a certain transmitting frequency to the underground through a grounding wire (horizontal electric dipole) or a non-grounding loop (vertical magnetic dipole), lays measuring points outside a certain transmitting-receiving distance, receives an electric field and/or a magnetic field after being transmitted by the ground through a receiver, and finally calculates apparent resistivity according to the electromagnetic field according to a certain method, wherein the apparent resistivity can reflect objective electrical changes of the underground. The change rule of the conductivity from shallow to deep underground can be obtained by sequentially changing the frequency. The most commonly used frequency domain controllable source electromagnetic sounding method at present mainly comprises a controllable source audio magnetotelluric method (CSAMT) and a wide area electromagnetic method (WFEM), and has the advantages of high efficiency, strong anti-interference capability and the like.
The controllable source audio magnetotelluric method (CSAMT) adopts a definition method of apparent resistivity in magnetotelluric method, measures mutually orthogonal horizontal electric field and horizontal magnetic field at measuring points, and calculates the Carniya apparent resistivity. Over a sufficiently large transceiver distance (far zone), the electromagnetic waves generated by the artificial source may be approximated as planar electromagnetic waves, where the carnian apparent resistivity of the CSAMT may reflect electrical changes in the subsurface. However, in the transition area and the near area, the artificial source electromagnetic field cannot be approximated by plane waves, and at this time, the CSAMT apparent resistivity curve in the equi-spaced double-logarithmic coordinates will show a linear change at low frequency, and the objective electrical properties of the underground cannot be reflected without relation to the underground resistivity.
Wide area electromagnetic methods (WFEM) can measure only a single electromagnetic field component, fit an observed electric or magnetic field with a uniform half-space resistivity model, and find apparent resistivity through continuous iterative searches. The wide area apparent resistivity is obtained according to an analysis expression of an electromagnetic field without any approximation, so that a apparent resistivity sounding curve is not distorted in a non-wave area and the change of an underground electrical structure can be well reflected in a whole area. However, under the condition of small induction number, the proportion of the secondary field with depth measurement capability to the total field is too small, and only a few parts per million is needed, so that in an actual noisy observation environment, effective secondary field information cannot be obtained under the condition of small induction number, and frequency electromagnetic depth measurement is realized, and a wide-area electromagnetic method still needs a larger receiving and transmitting distance or can only obtain limited detection depth.
Disclosure of Invention
Aiming at the problem that the current frequency domain controllable source electromagnetic exploration method cannot make electromagnetic sounding under a small induction number and calculate apparent resistivity which objectively reflects underground electrical information, the application provides a magnetic field frequency gradient apparent resistivity measurement method and system based on a horizontal couple source.
In order to achieve the technical purpose, the application adopts the following technical scheme:
a magnetic field frequency gradient apparent resistivity measurement method based on a horizontal couple source, comprising:
when a horizontal couple source paved on the ground surface is electrified, a current signal is changed, a radial magnetic field and a tangential magnetic field are continuously collected at a measuring point at a distance r from the horizontal couple source, and the radial magnetic field intensity H is obtained by utilizing time-frequency conversion r And tangential magnetic field strength
Respectively calculating radial magnetic field intensity H r And tangential magnetic field strengthDifferential value as a function of frequency->
Will beSubstituting the calculated apparent resistivity into a function analysis expression of the magnetic field frequency gradient and the resistivity, calculating the apparent resistivity corresponding to each frequency by adopting a numerical iteration method, and selecting a calculation result under a small induction number as the apparent resistivity obtained by final measurement; wherein, the function analysis expression of the magnetic field frequency gradient and the apparent resistivity is as follows:
wherein: idL is the polar moment of the horizontal couple source, where I represents the current intensity and dL is the length of the horizontal couple source; k is the number of complex waves, and the number of complex waves,i represents an imaginary unit, ω represents angular frequency ω=2pi f, μ represents permeability, and f is a time-varying current frequency of the horizontal couple source; />The observation angle of the measuring point; i 0 And I 1 The first virtual volume Bessel functions of 0 order and 1 order respectively, K 0 And K 1 The virtual volume Bessel functions of the second class are respectively 0 order and 1 order; sigma is conductivity, is the apparent resistivity ρ calculated iteratively a Is the reciprocal of (2);
the inductances are defined as p=r/δ, where r is the transmit-receive distance and δ is the skin depth.
Further, a dichotomy is used to solve for apparent resistivity in the function analytical expression.
Further, the horizontal couple source is a grounded long wire, and the electric dipole moment is in the x direction.
Further, the apparent resistivity of the magnetic field frequency gradient with the frequency change on different measuring points is obtained by moving the measuring points, and then the apparent resistivity of the magnetic field frequency gradient in the whole region is obtained.
Further, a current signal is fed into a horizontal couple source paved on the ground surface, and is an alternating current with determined emission frequency.
Further, the frequency of the current signal is sequentially changed on the same measuring point, so that the magnetic field frequency gradient apparent resistivity of the measuring point based on different current frequencies is correspondingly obtained, and further, the frequency detection curve of the measuring point, namely the frequency-magnetic field frequency gradient apparent resistivity curve, is obtained.
Further, the distance r between the measuring point and the horizontal thermocouple source refers to the distance between the dipole of the horizontal thermocouple source and the measuring point.
Further, a magnetic field sensor is used for collecting a radial magnetic field and a tangential magnetic field at the measuring point.
A magnetic field frequency gradient apparent resistivity measurement system based on a horizontal galvanic source, comprising: a horizontal thermocouple source, a receiver and a processor;
the horizontal couple source is paved on the ground surface, and generates a magnetic field after a current signal is turned on;
the receiver comprises a tangential magnetic field acquisition module and a radial magnetic field acquisition module which are respectively used for acquiring a radial magnetic field and a tangential magnetic field, so as to obtain the radial magnetic field intensity H r And tangential magnetic field strength
The processor is used for realizing the following calculation and obtaining the apparent resistivity:
respectively calculating radial magnetic field intensity H r And tangential magnetic field strengthDifferential value as a function of frequency->
Will beSubstituting the magnetic field frequency gradient and the resistivity into a function analysis expression, and calculating apparent resistivity corresponding to each frequency by adopting a numerical iteration method; wherein, the function analysis expression of the magnetic field frequency gradient and the resistivity is as follows:
wherein: idL is the polar moment of the horizontal couple source, where I represents the current intensity and dL is the length of the horizontal couple source; k is the number of complex waves, and the number of complex waves,representing imaginary units, ω representing angular frequency ω=2pi f, μ representing permeability, f being the time-varying current frequency of the horizontal couple source; />The observation angle of the measuring point; i 0 And I 1 The first virtual volume Bessel functions of 0 order and 1 order respectively, K 0 And K 1 The virtual volume Bessel functions of the second class are respectively 0 order and 1 order; sigma is the iteratively calculated apparent resistivity ρ a Is the reciprocal of (2);
the inductances are defined as p=r/δ, where r is the transmit-receive distance and δ is the skin depth.
Further, the receiving and transmitting distance r and the observation angleAnd calculating by recording the coordinates of the horizontal couple source and the measuring point. Advantageous effects
According to the magnetic field frequency gradient apparent resistivity measurement method based on the horizontal couple source, the tangential magnetic field and the radial magnetic field are measured, the apparent resistivity is calculated by utilizing the derived magnetic field frequency derivative analysis formula and adopting a numerical iteration method, and the method is suitable for apparent resistivity measurement of any receiving and transmitting distance, and theoretically, no non-wave area distortion exists, so that the method has the capability of detecting an underground deep electrical structure under a small receiving and transmitting distance.
In addition, the application is used for measuring the measuring point with small receiving and transmitting distance, electromagnetic field signals can be greatly enhanced, the signal to noise ratio is high, the anti-interference capability is strong, the power requirement on a transmitter is small, and the portable and large-depth frequency sounding can be realized.
In addition, numerical simulation proves that the obtained magnetic field frequency gradient apparent resistivity has the characteristic of the apparent resistivity of a wave region when the receiving and transmitting distance is large, deep information can be reflected in the middle and short receiving and transmitting distances, and near source distortion of the apparent resistivity curve in the traditional controllable source audio magnetotelluric method does not exist.
Drawings
FIG. 1 is a schematic diagram of an apparatus used in the implementation of an embodiment of the present application.
FIG. 2 is a graph of the relative error between the uniform half-space magnetic field frequency gradient resolution and the magnetic field frequency difference, where (a) is H r Frequency gradient resolution and frequency differential relative error, (b) isThe frequency gradient analysis solution and the frequency difference relative error.
FIG. 3 shows the frequency gradient of the normalized field value as a function of the inductance, (a) isA curve of the response number, (b) is +.>The curve of the response number indicates +.>Both have binaryzation.
FIG. 4 shows H for different transmission/reception distances under two-layer medium condition r A frequency gradient apparent resistivity curve contrast chart, (a) is the calculation result of apparent resistivity when r/h=0.1, and (b) is the calculation result of apparent resistivity when r/h=1.
FIG. 5 shows the transmission/reception distance under the condition of two layers of mediumA frequency gradient apparent resistivity curve contrast chart, (a) is the calculation result of apparent resistivity when r/h=0.1, and (b) is the calculation result of apparent resistivity when r/h=1.
Detailed Description
The following describes in detail the embodiments of the present application, which are developed based on the technical solution of the present application, and provide detailed embodiments and specific operation procedures, and further explain the technical solution of the present application.
The application provides a magnetic field frequency gradient apparent resistivity measuring method and system based on a horizontal couple source. The theoretical formula derivation process of tangential magnetic field and radial magnetic field based on the uniform half-space model is as follows:
since the definition of apparent resistivity is obtained by field fitting in a uniform half-space, the present application first shows a field value formula in a uniform half-space. Under this condition, the tangential magnetic field at the surface siteWith radial magnetic field H r The displacement current term is ignored, as the displacement current is much smaller than the conduction current in practical cases, as represented by the following equation. The application derives the frequency gradient analysis value of the magnetic field from the formula:
where IdL is the electric dipole moment, where I represents the current strength, dL is the length of the horizontal electric dipole source,for complex wave number, i represents imaginary number unit, ω represents angular frequency ω=2pi f, μ represents permeability, and f is time-varying current frequency of horizontal couple source; r is the distance between the measuring point and the horizontal couple source, < >>To measureObservation angle of the point; i 0 And I 1 The first virtual volume Bessel functions of 0 order and 1 order respectively, K 0 And K 1 The virtual volume Bessel functions of the second class are 0 order and 1 order respectively.
Will H r 、The in-phase component and the quadrature component of the (b) are subjected to series expansion under a small induction number, and the series expansion expression of the Bessel function according to the imaginary volume is obtained. Only the first two items are written here:
wherein H is r Andthe previous In, Q represent the In-phase component and quadrature component, respectively. As can be seen from the above, no matter H r Or->The first of the in-phase component is irrelevant to the electrical structure (the change condition of resistivity) of the underground medium, is a primary field of a horizontal magnetic field, and does not have the property of frequency sounding; h r And->The second term of the in-phase component is proportional to the conductivity sigma. H r And->All terms of the orthogonal component series expansion are related to the conductivity sigma and the frequency f, and have the characteristic of frequency sounding.
The following relationship is satisfied between the virtual volume Bessel function of the integer order and the Bessel function of the first type:
the expression of the first type of Bessel function is:
the derivation can be obtained:
the derivative properties of the first class of bessel functions are:
0 th order, 1 st order first order imaginary volume Bessel function derivative:
I′ 0 (x)＝[J 0 (ix)]′＝iJ 0 ′(ix)＝-iJ 1 (ix)＝I 1 (x)
0 th order, 1 st order, second order imaginary volume Bessel function derivative:
based on the above derived conclusions, it can be finally obtainedIs of the analytical formula:
the expansion of the progression at small inductance of the magnetic field frequency gradient is still performed in the same manner as before
With H as previously shown r 、The comparison of the series expansion can obviously show that each expression carries the electrical information of the underground medium after the frequency derivative is calculatedAnd has the characteristic of frequency sounding, so that the influence of primary fields can be eliminated from measured data.
Will beTo->Normalizing and converting into a relation with the induction number to obtain normalized radial magnetic field frequency gradient response:
therein () N Representing a normalization operation;
will beTo->Normalizing and converting into a relation with the induction number to obtain a normalized tangential magnetic field frequency gradient response:
in the frequency domain electromagnetic method, the induction number is defined as p=r/δ. Where r is the transmit-receive distance and delta is the skin depth. Ikr can be converted into (1+i) P according to the relation between the skin depth and the complex wave number (the complex wave number obtained under the condition of neglecting displacement current), so that a relation between the normalized magnetic field gradient value and the induction number is obtained.
According to the numerical simulation result of the normalized field value gradient, the existence of the binary phenomenon can be intuitively seen. The numerical solution of apparent resistivity is solved by adopting an iteration method or an inverse cubic spline interpolation method, and the methods all require that the field or the field gradient has monotonicity along with the change of the induction number. Because of the existence of binarycity, the solution of the whole area can not be carried out like the wide area apparent resistivity, and the iteration value which is required and limited under the condition of small induction number is selected as the apparent resistivity value.
Different frequencies are input from a field source, magnetic field values under different frequencies are collected, frequency difference is carried out on the magnetic field values by using a difference algorithm, and the difference step length is set to be a given frequency interval. And carrying out numerical iteration calculation at each frequency point. Such as frequency f 1 The corresponding measured field value gradient value is grad 1 One producedSubstituting it into the expression of the uniform half space becomes a factor of apparent resistivity ρ 1 Is a nonlinear transcendental equation of (c). Adopting a dichotomy to perform iterative solution continuously, setting the maximum iteration times and the solution precision, and obtaining the apparent resistivity rho when the frequency point 1 Is a value of (2). And calculating frequency points by frequency points to obtain apparent resistivity values under different frequencies, and drawing a sounding curve.
When the apparent resistivity is solved by adopting a dichotomy method, setting each parameter of the lamellar model in a program, calculating the magnetic field frequency gradient of the lamellar model under certain frequency, adopting a uniform half-space model for equivalence, enabling the field value gradient calculated by the uniform half-space model under the frequency to be equal to lamellar, obtaining an overrun equation about the resistivity, and solving by adopting an iteration method.
Through the process, the apparent resistivity of any measuring point under a certain frequency can be calculated, wherein the apparent resistivity of all measuring points in a design area under a certain frequency can be calculated by adopting the same mode by changing the positions of the measuring points, and the apparent resistivity of the same measuring point under different frequencies can be calculated by adopting the same mode by changing the frequency.
In the practical application process, firstly, working parameters are generally designed, and according to the target exploration depth, the working parameters are setAnd (5) calculating the appropriate transceiving distance and transmitting frequency range. A horizontal long lead (horizontal couple source) is laid on the ground surface, and the central position of the couple source is used as the origin of coordinates. Determining the electric dipole moment, adopting GPS to record the position of a transmitter, feeding current waveforms such as square waves or pseudo-random multi-frequency square waves, and recording the transmitted current waveform and current intensity I; then, measuring points are arranged on the ground surface, when the transmitter stably works, magnetic field sensors in corresponding directions are paved according to the positions of the field sources to obtain a measured magnetic field value sequence, coordinates of a transmitting dipole and an observation point are recorded, and a transmitting-receiving distance r and an observation angle are calculated
Simulation and calculation:
FIG. 2 is a graph of relative error between a uniform half-space magnetic field frequency gradient analytical solution and a magnetic field frequency differential, and the parameters taken during calculation are: the electric dipole moment 1A m, the resistivity of the uniform half space is 1000 omega m, and the emission frequency of the electric dipole source is 0.01Hz. It can be seen that the calculated values are consistent with the theoretical values. The numerical simulation result shows that the method is correct by using the derived frequency gradient analysis solution, and also shows that the method can meet the calculation accuracy by adopting a differential algorithm, and can be used for the differential calculation of the magnetic field frequency of the layered medium.
FIG. 3 is normalizedNumerical simulation results, it can be seen that +.>The method has obvious binaryzation, and the calculation result under a small induction number is required to be selected when the apparent resistivity is calculated.
FIG. 4 shows the resistivity of the bottom layer for different transmission/reception distances and different resistivities of the bottom layer under the condition of two layers of mediumMagnetic field frequency gradient apparent resistivity curve. The model parameters are the transmission/reception distance r=120m, 1200m, the resistivity of the first layer medium is 100 Ω·m,the second layer medium has resistivity of 2Ω·m,10Ω·m,20Ω·m,500Ω·m,1000Ω·m,5000 Ω·m, the first layer thickness is 1200m, (a) r/h=0.1->Comparison of the calculated apparent resistivity with (b) r/H=1 +.>And comparing the calculated results of the apparent resistivity with a graph. The abscissa is the ratio of skin depth to the thickness of the first layer, the ordinate is the ratio of apparent resistivity to the resistivity of the first layer of the model, and the curve represents the significance that the apparent resistivity at the corresponding depth can be obtained for each frequency. The curves of different colors represent the calculation results under different bottom layer resistivity models, and the corresponding relation between each curve of different colors and the bottom layer resistivity is marked on the graph. As can be seen from fig. 4, the apparent resistivity described in the present application reflects the change of the subsurface resistivity at different transmission/reception distances, and is not similar to the distortion of the apparent resistivity, which increases linearly at low frequencies. The sounding curve is sensitive to the low-resistance layer, and can well distinguish different resistivity models, but the response to the high-resistance layer is very weak. As can be seen by comparing fig. 4 (a) and fig. 4 (b), the magnetic field frequency gradient apparent resistivity can be electrically measured with a small transmission/reception distance, and increasing the transmission/reception distance helps to make the curve tail branch more approximate to the actual resistivity.
FIG. 5 shows the resistivity of the bottom layer for different transmission/reception distances and different resistivities of the bottom layer under the condition of two layers of mediumMagnetic field frequency gradient apparent resistivity curve. All parameters are equal to->The calculated parameters of apparent resistivity are the same. Fig. 5 (a) r/h=0.1 +.>Calculation result contrast chart of apparent resistivityFig. 5 (b) is r/h=1 +.>And comparing the calculated results of the apparent resistivity with a graph. The abscissa is the ratio of skin depth to the thickness of the first layer, the ordinate is the ratio of apparent resistivity to the resistivity of the first layer of the model, and the curve represents the significance that the apparent resistivity at the corresponding depth can be obtained for each frequency. The curves of different colors represent the calculation results under different bottom layer resistivity models, and the corresponding relation between each curve of different colors and the bottom layer resistivity is marked on the graph. As can be seen from fig. 5, the apparent resistivity described in the present application reflects the change of the subsurface resistivity at different transmission/reception distances, and is not similar to the distortion of the apparent resistivity, which increases linearly at low frequencies. The sounding curve is sensitive to the low-resistance layer, and can well distinguish different resistivity models, but the response to the high-resistance layer is very weak. As can be seen by comparing fig. 5 (a) and fig. 5 (b), the magnetic field frequency gradient apparent resistivity can be electrically measured under a small transmission-reception distance, and increasing the transmission-reception distance is helpful for making the curve tail branch more approximate to the actual resistivity.
In summary, the present application provides a solution for calculating apparent resistivity for small sensing numbers, which can be used for deep electrical structure detection at short transmission/reception distances.
The above embodiments are preferred embodiments of the present application, and various changes or modifications may be made thereto by those skilled in the art, which should be construed as falling within the scope of the present application as claimed herein, without departing from the general inventive concept.

Claims (10)

1. A magnetic field frequency gradient apparent resistivity measurement method based on a horizontal couple source, comprising:
when a horizontal couple source paved on the ground surface is electrified, a current signal is changed, a radial magnetic field and a tangential magnetic field are continuously collected at a measuring point at a distance r from the horizontal couple source, and the radial magnetic field intensity H is obtained by utilizing time-frequency conversion r And tangential magnetic field strength
Respectively calculating radial magnetic field intensity H r And tangential magnetic field strengthDifferential value as a function of frequency->
Will beSubstituting the calculated apparent resistivity into a function analysis expression of the magnetic field frequency gradient and the resistivity, calculating the apparent resistivity corresponding to each frequency by adopting a numerical iteration method, and selecting a calculation result under a small induction number as the apparent resistivity obtained by final measurement; wherein, the function analysis expression of the magnetic field frequency gradient and the apparent resistivity is as follows:
wherein: idL is the polar moment of the horizontal couple source, where I represents the current intensity and dL is the length of the horizontal couple source; k is the number of complex waves, and the number of complex waves,i represents an imaginary unit, ω represents angular frequency ω=2pi f, μ represents permeability, and f is a time-varying current frequency of the horizontal couple source; />The observation angle of the measuring point; i 0 And I 1 The first virtual volume Bessel functions of 0 order and 1 order respectively, K 0 And K 1 The virtual volume Bessel functions of the second class are respectively 0 order and 1 order; sigma is conductivity, is the apparent resistivity ρ calculated iteratively a Is the reciprocal of (2);
the inductances are defined as p=r/δ, where r is the transmit-receive distance and δ is the skin depth.
2. The method of claim 1, wherein the apparent resistivity in the analytical expression is solved by using a dichotomy.
3. The method of claim 1, wherein the horizontal couple source is a grounded long wire and the dipole moment is in the x-direction.
4. The method for measuring magnetic field frequency gradient apparent resistivity according to claim 1, wherein magnetic field frequency gradient apparent resistivity with frequency variation at different measuring points is obtained by moving the measuring points, and further magnetic field frequency gradient apparent resistivity of the whole region is obtained.
5. The method of measuring apparent resistivity of magnetic field frequency gradients in accordance with claim 1, wherein the signal of current flowing from a horizontal galvanic source placed on the earth is an alternating current of determined emission frequency.
6. The method for measuring the apparent resistivity of the magnetic field frequency gradient according to claim 5, wherein the frequencies of the incoming current signals are sequentially changed on the same measuring point, the apparent resistivity of the magnetic field frequency gradient of the measuring point based on different current frequencies is correspondingly obtained, and then a frequency detection curve of the measuring point, namely a frequency-magnetic field frequency gradient apparent resistivity curve, is obtained.
7. The method of claim 1, wherein the distance r between the measuring point and the horizontal thermocouple source is the distance between the dipole of the horizontal thermocouple source and the measuring point.
8. The method of claim 1, wherein the radial magnetic field and the tangential magnetic field are acquired at the measurement point using a magnetic field sensor.
9. A magnetic field frequency gradient apparent resistivity measurement system based on a horizontal galvanic source, comprising: a horizontal thermocouple source, a receiver and a processor;
the horizontal couple source is paved on the ground surface, and generates a magnetic field after a current signal is turned on;
the receiver comprises a tangential magnetic field acquisition module and a radial magnetic field acquisition module which are respectively used for acquiring a radial magnetic field and a tangential magnetic field, so as to obtain the radial magnetic field intensity H r And tangential magnetic field strength
The processor is used for realizing the following calculation and obtaining the apparent resistivity:
respectively calculating radial magnetic field intensity H r And tangential magnetic field strengthDifferential value as a function of frequency->
Will beSubstituting the calculated apparent resistivity into a function analysis expression of the magnetic field frequency gradient and the resistivity, calculating the apparent resistivity corresponding to each frequency by adopting a numerical iteration method, and selecting a calculation result under a small induction number as the apparent resistivity obtained by final measurement; wherein, the function analysis expression of the magnetic field frequency gradient and the resistivity is as follows:
wherein: idL is the polar moment of the horizontal couple source, where I represents the current intensity and dL is the length of the horizontal couple source; k is the number of complex waves, and the number of complex waves,i represents an imaginary unit, ω represents angular frequency ω=2pi f, μ represents permeability, and f is a time-varying current frequency of the horizontal couple source; />The observation angle of the measuring point; i 0 And I 1 The first virtual volume Bessel functions of 0 order and 1 order respectively, K 0 And K 1 The virtual volume Bessel functions of the second class are respectively 0 order and 1 order; sigma is the iteratively calculated apparent resistivity ρ a Is the reciprocal of (2);
the inductances are defined as p=r/δ, where r is the transmit-receive distance and δ is the skin depth.
10. The magnetic field frequency gradient apparent resistivity measurement system of claim 1, wherein the transmit-receive distance r and the observation angleAnd calculating by recording the coordinates of the horizontal couple source and the measuring point.
CN202310817850.XA 2023-07-05 2023-07-05 Magnetic field frequency gradient apparent resistivity measurement method and system based on horizontal couple source Pending CN116859469A (en)

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