CN114076988B - Wave number apparent resistivity measuring method based on horizontal electric dipole source - Google Patents
Wave number apparent resistivity measuring method based on horizontal electric dipole source Download PDFInfo
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- G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
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- 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
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Abstract
The invention discloses a method and a device for measuring wave number apparent resistivity based on a horizontal electric dipole source and a readable storage medium, wherein the method is realized by using a method of measuring wave number apparent resistivity on the earth surfaceLaying grounded horizontal electric dipole source and supplying current, and measuring horizontal electric dipole source
Comparing the two components, eliminating the part incapable of being solved, obtaining a unitary quartic equation of the parameter x related to the wave number, and measuring the obtained horizontal electric dipole source
And substituting the two components into the equation, resolving four roots of the equation, and selecting a reasonable root according to the phase to calculate the apparent resistivity of the wave number. The method selects the grounded horizontal electric dipole source as the field source, effectively overcomes the limitation of the frequency domain magnetic source in practical application, does not need iterative calculation in the process of obtaining the wave number apparent resistivity, is suitable for any receiving and transmitting distance and any frequency except for the minimum receiving and transmitting distance, does not have any distortion in low frequency, can reflect the objective change rule of the electrical property of the underground medium, and further expands the detection depth.
Description
Technical Field
The invention belongs to the technical field of exploration geophysics, and particularly relates to a method and a device for measuring apparent resistivity of wave number based on a horizontal electric dipole source and a readable storage medium.
Background
The land frequency domain controllable source electromagnetic method has the advantages of high efficiency, strong anti-interference capability, high resistance, sensitivity and the like, and is widely applied to the fields of deep resource exploration, underground water resources, environment, engineering investigation and the like. In the controlled source electromagnetic method, the electromagnetic field generated by a grounded electric dipole or an ungrounded magnetic dipole can be used to reflect changes in the conductivity of the subsurface. The wave number apparent resistivity is an effective tool for converting electromagnetic field measurement data into underground conductivity distribution, can more visually reflect an underground electrical structure than an electromagnetic field component, is convenient for quality control of field data, and can immediately provide knowledge of a primary electrical structure.
However, as a mainstream artificial source electromagnetic surveying technique, the controlled source audio magnetotelluric method (CSAMT) requires observation in an area where the transmission and reception distances are much larger than the survey depth. The most classical apparent resistivity definition in the frequency domain controllable source method is the ratio form of an orthogonal electric field and a magnetic field in the controllable source audio frequency magnetotelluric method, the mode uses the Carniya apparent resistivity in the magnetotelluric method for reference, utilizes the characteristic of approximate plane waves under the far zone condition, and requires the receiving and transmitting distance to meet the following requirements: approximately five times the skin depth. When the receiving and transmitting distance is reduced (in a transition region and a near region), the assumption that plane waves of the artificial source electromagnetic field are not satisfied any more, and at the moment, a CSAMT apparent resistivity curve is increased by 45 degrees at low frequency, obvious distortion occurs, and underground conductivity change cannot be directly reflected.
The wide area electromagnetic method (WFEM) adopts an accurate electric field expression to obtain the apparent resistivity of the whole area, and the measuring area is expanded to a partial transition area, so that the frequency depth measurement can be carried out under a closer receiving and transmitting distance. At present, only one electric field component is mainly measured on a measuring point by a wide-area electromagnetic method, and then the wide-area apparent resistivity is calculated by a method recorded in a new method for defining the whole-area apparent resistivity in horizontal couple source frequency sounding of Shang Jingtian and He Jishan, namely, an observed electric field or magnetic field is fitted by using a uniform half-space resistivity model, and the apparent resistivity is obtained through continuous iterative search. The calculation method still needs iterative solution to measure the azimuth angle of the area
Must be between 60 and 120 degrees. In addition, because the attenuation of the field generated by the magnetic source in the frequency domain along with the increase of the receiving and transmitting distance is far larger than that of the electric source, the strength of the field is weaker and difficult to measure, and the magnetic source method is difficult to detect a high-resistivity target, the frequency domain magnetic source has larger application limitation in practical application. Therefore, an analytical solving method suitable for the apparent resistivity of the electric dipole source needs to be found, and the measurement area is further enlarged.
Disclosure of Invention
The invention aims to provide a method for solving the problems that the functions of the electric field and the apparent resistivity in a uniform half-space model contain transcendental functions, iterative search is needed for solving, the whole-region apparent resistivity cannot be directly analyzed and calculated by a field value, and the application limitation exists in a magnetic source methodMethod, device and readable storage medium for measuring apparent resistivity based on wave number of horizontal electric dipole source by combining tangential electric field and two components (H) of vertical magnetic field of horizontal electric dipole source z ,
) The method is converted into a unitary quartic equation related to the wave number of the electromagnetic field, and the part which cannot be analyzed is eliminated in the conversion process, so that the process of solving the unitary quartic equation does not need iteration. And then the invention solves the four roots of the unitary quartic equation by analysis, and selects reasonable roots according to the phase to calculate the apparent resistivity of the wave number. The whole process of the invention does not need iterative calculation, is suitable for any transceiving distance and any frequency except for the minimum transceiving distance, has no distortion at low frequency, and can reflect the objective change rule of the electrical property of the underground medium.
In one aspect, the invention provides a method for measuring apparent resistivity of wave number based on a horizontal electric dipole source, which comprises the following steps:
step 1: laying a grounded horizontal electric dipole source on the ground surface and supplying current; and laying measuring points on the surface of the earth, recording the transmitting-receiving distance r of the measuring points, and measuring the tangential electric field E φ And a vertical magnetic field H z ；
Step 2: the receiving and transmitting distance r and the tangential electric field E are measured φ And a vertical magnetic field H z Substituting a unitary quartic equation analytic parameter x;
ax 4 +(3a+b)x 3 +(3a+b+2)x 2 +3x+3＝0
wherein the content of the first and second substances,
x = ikr, a, b are coefficients of a univariate polynomial,
respectively represent the normalized tangential electric field E φ And a vertical magnetic field H z K is the wave number of the electromagnetic wave, i represents the unit of imaginary number;
the unary quartic equation is based on the tangential electric field E of a horizontal electric dipole source φ And a vertical magnetic field H z Two component formulas of (a);
and step 3: calculating the apparent resistivity of the wave number based on the parameter x;
wherein a parameter x with a phase between 0 and 90 is selected to calculate the wave number apparent resistivity.
According to the electromagnetic field theory of uniform half-space,
thus impedance
The phase of Z in uniform half-space is 45 degrees using the arctan function. In the layered medium, the phase is not equal to 45 degrees, and is different from the phase of the uniform half space. In the case of a layered medium in the electromagnetic method, the phase change generally does not exceed 45 degrees around the phase change of the uniform half-space, and therefore, the phase of Z is in the interval of 0 to 90 degrees to select a reasonable x. The invention summarizes a universal selection means based on the theory, thereby quickly determining reasonable x for calculating the apparent resistivity of the wave number.
Optionally, the tangential electric field E φ And a vertical magnetic field H z The normalization formula of (a) is as follows:
wherein y is the coordinate of the measuring point, ω is the angular frequency, μ is the vacuum permeability, I is the intensity of the current supplied, and ds is the length of the horizontally long wire of the horizontal electric dipole source.
Optionally, the calculation formula of the apparent resistivity of the wave number is as follows:
in the formula, ρ a Representing apparent resistivity at said measurement point corresponding to a certain frequency, Z being expressed as complexThe intermediate parameter of the numbers, phi, denotes the phase, im (Z) denotes the imaginary part of the intermediate parameter Z, re (Z) denotes the real part of the intermediate parameter Z, omega is the angular frequency and mu is the vacuum permeability.
Optionally, the method further comprises: and sequentially changing the frequency, calculating the apparent resistivity of the wave number under each frequency on the corresponding measuring point according to the mode of the steps S2 to S3, and drawing a frequency-wave number apparent resistivity curve.
Optionally, the method further comprises: and moving the measuring points in sequence, changing the frequency of each measuring point in sequence, and calculating the apparent resistivity of the wave number at each frequency of the corresponding measuring point in the manner of the steps S2-S3, thereby obtaining the frequency-apparent resistivity curve of all the measuring points.
In a second aspect, the present invention provides a measuring apparatus based on the above method, which includes: a horizontal electric dipole source, a transmitter, a receiver and a processor;
wherein, the horizontal electric dipole source is laid on the ground surface and connected with the transmitter, and the transmitter supplies current to the horizontal electric dipole source;
the receiver is arranged on the measuring point and records measuring data, and at least comprises a tangential electric field measuring module and a vertical magnetic field measuring module, wherein the tangential electric field measuring module is used for measuring a tangential electric field E φ The vertical magnetic field measurement module is used for measuring a vertical magnetic field H z ；
The processor is connected with the receiver and used for acquiring measurement data and transmitting and receiving distance r and tangential electric field E in the measurement data φ And a vertical magnetic field H z Substituting a unitary quartic equation analytic parameter x; and calculating the apparent resistivity of the wave number based on the parameter x.
In a third aspect, the present invention provides a readable storage medium storing a computer program for invocation by a processor to implement:
obtaining measurement data on a measurement point, and then transmitting and receiving distance r and tangential electric field E in the measurement data φ And a vertical magnetic field H z Substituting a unitary quartic equation analytic parameter x; calculating a parameter x with a phase between 0 and 90Obtaining wave number apparent resistivity, wherein the measurement data is acquired after a grounded horizontal electric dipole source is laid on the ground surface and current is supplied;
the unary quartic equation is based on the tangential electric field E of a horizontal electric dipole source φ And a vertical magnetic field H z The two component formula of (a) is derived as follows:
ax 4 +(3a+b)x 3 +(3a+b+2)x 2 +3x+3＝0
wherein, the first and the second end of the pipe are connected with each other,
x = ikr, a, b are coefficients of a univariate polynomial,
respectively represent the normalized tangential electric field E φ And a vertical magnetic field H z K is the electromagnetic wave number, and i represents the imaginary unit.
Advantageous effects
1. The method for measuring wave number apparent resistivity based on the horizontal electric dipole source provided by the invention takes the grounded horizontal electric dipole source as a field source, is directly coupled with the ground, and supplies current far exceeding a magnetic source to the ground, so that an electromagnetic field signal is far stronger than the magnetic source, and the method has strong anti-interference capability and has larger detection depth and anti-interference capability than the magnetic source. The magnetic source method only generates horizontal current and belongs to an induction type field source, so that the method is almost ineffective for a high-resistance object. In addition, the current supplied underground by the invention contains vertical components, so the invention has a detection effect far superior to a geoelectric electromagnetic method and a magnetic source method for a high-resistance layer target, and the invention utilizes a grounded horizontal electric dipole source as a field source, thereby effectively overcoming the limitation and obstacle of the frequency domain magnetic source in practical application.
2. The invention provides a wave number apparent resistivity measuring method based on a horizontal electric dipole source, which takes a grounded horizontal electric dipole source as a field source and utilizes a tangential electric field E of the horizontal electric dipole source φ And a vertical magnetic field H z Deducing a unitary four times with the unresolvable portion eliminatedThe equation finds the analytic solving method suitable for the apparent resistivity of the horizontal electric dipole source on one hand, and on the other hand, the analytic process does not need iterative search, the electromagnetic field wave number and the apparent resistivity are obtained through analytic operation, the method is suitable for any frequency and transmitting-receiving distance except the minimum transmitting-receiving distance, the result is accurate, no distortion exists, and therefore the method has the capability of detecting the underground deep electrical structure under the small transmitting-receiving distance.
3. The invention provides a method for measuring wave number apparent resistivity based on a horizontal electric dipole source, which provides a universal method for selecting proper root x to calculate the wave number apparent resistivity, so that reasonable x can be quickly determined and used for calculating the wave number apparent resistivity.
Drawings
FIG. 1 is a schematic view of a measurement apparatus provided by an embodiment of the present invention;
fig. 2 is a schematic diagram of wave number-dependent resistivity and phase curves corresponding to four different roots calculated under the conditions that the resistivity is set to 100 Ω · m and the transmission-reception distance is 2000m in a uniform half space, where (a) is a graph of the wave number-dependent resistivity corresponding to the four different roots, and (b) is a graph of the phase curves corresponding to the four different roots;
FIG. 3 is a graph showing the apparent resistivity and phase frequency curves of a D-type model (p) for different transmission distances under two layers of media 1 ,ρ 2 )＝(100Ωm,10Ωm),h 1 =2000m, graph (a) is the calculation result of the apparent resistivity frequency curve, and graph (b) is the calculation result of the phase frequency curve;
FIG. 4 is a graph of apparent resistivity and phase frequency for two layers of media in a G-type model, the G-type model (ρ) 1 ,ρ 2 )＝(10Ωm,1000Ωm),h 1 =2000m, graph (a) is the calculation result of the apparent resistivity frequency curve, and graph (b) is the calculation result of the phase frequency curve;
FIG. 5 is a schematic diagram showing the calculation results of apparent resistivities of the wave numbers of different intermediate layer thicknesses in a K-type three-layer medium, wherein the geoelectrical model is K-type (the intermediate resistivity is higher than that of the first layer and the third layer), the resistivity of the first layer is 10 Ω & m, the thickness of the first layer is 1000m, the resistivity of the second layer is 1000 Ω & m, the thickness of the layer is 500m, and the resistivity of the third layer is 10 Ω & m; graph (a) is the calculation result of the apparent resistivity frequency curve, and graph (b) is the calculation result of the phase frequency curve;
FIG. 6 is a graph showing the calculation results of wave numbers of resistivities of different intermediate layer thicknesses of an H-type earth model (the intermediate resistivity is lower than that of the first layer and the third layer), the earth model is H-type (the intermediate resistivity is lower than that of the first layer and the third layer), the resistivity of the first layer is 100 Ω & m, the thickness of the first layer is 1000m, the resistivity of the second layer is 10 Ω & m, the thickness of the layer is 500m, and the resistivity of the third layer is 100 Ω & m. Graph (a) is the calculation result of the apparent resistivity frequency curve, and graph (b) is the calculation result of the phase frequency curve;
FIG. 7 is a graph showing the measured wave number apparent resistivity, the wide area apparent resistivity and the controllable source audio magnetotelluric apparent resistivity of a measuring point with a certain azimuth angle of 45 degrees in Anhui. The square symbols are the results of wave number apparent resistivity, and the circular curve is the result of wide area apparent resistivity with the receiving and transmitting distance; the right triangle is the apparent resistivity result of the controllable source audio magnetotelluric method.
FIG. 8 is a graph comparing the vertical magnetic field generated by a magnetic dipole source and the vertical magnetic field generated by a grounded horizontal electric dipole source.
Detailed Description
The present invention will be further described with reference to the following examples.
The invention provides a method and a device for measuring wave number apparent resistivity based on a horizontal electric dipole source and a readable storage medium, aiming at the problem that the function of electric field and apparent resistivity in a uniform half-space model contains transcendental function, and the whole region apparent resistivity cannot be directly analyzed and calculated by a field value by means of iterative search solution. Wherein, a grounded horizontal electric dipole source is paved on the earth surface, the tangential electric field and the vertical magnetic field of the horizontal electric dipole source are measured and collected at a measuring point, and the tangential electric field E of the horizontal electric dipole source is based φ And a vertical magnetic field H z The two component formulas of the electromagnetic field wave number and the apparent resistivity are used for deducing a unitary quartic equation, eliminating the part which cannot be analyzed, further analyzing the unitary quartic equation to obtain a parameter x related to the electromagnetic field wave number, and selecting a proper parameter x to calculate the electromagnetic field wave number, the apparent resistivity and the phase position.
The invention takes the following quartic equation as an example to briefly describe the derivation process of the quartic equation in a single unit in the embodiment:
under a layered medium (assuming N layers of medium, each layer having a conductivity of σ) i Layer thickness of h i ) The tangential electric field and the vertical magnetic field at the surface measurement point are obtained by the following formula (the formula is used for simulating the response values of the electric field and the magnetic field of the actual measurement point in the following description):
in the above formula
For reflection coefficient, Y, of electromagnetic waves of TE polarization mode at a survey point on the earth's surface 0 Indicating the intrinsic admittance of the air layer,
represents the comprehensive admittance of all resistance layers below the i layer, and the expression is
Wherein the content of the first and second substances,
intrinsic admittance of the ith layer;
can be calculated from the conductivity of each layer, since the conductivity in air is zero, u 0 λ, μ is the vacuum permeability, λ is an intermediate parameter;
the reflection coefficient of the TM polarization mode is shown,
the surface resistance of the i-th layer is shown,
the intrinsic impedance of the ith layer is represented, wherein,
represents the admittance ratio of the ith layer,
J 1 (λr),J 0 and (lambdar) is a first-order and zero-order Bessel function, and the electromagnetic field response of the surface of the laminated medium can be obtained by integrating the integral parameter lambdar from zero to an infinite interval. The first term in the integral in the magnetic field formula is a field generated by a current-carrying wire, does not carry geoelectrical information, and only has field source information; the second term is r TE The integral of the coefficient from zero to infinity contains earth resistivity information. The electric field formula is influenced not only by the TE mode but also by the TM mode. Theoretically, the TM mode is generated by the vertical current density in the earth, so that the electric field component of the earth's surface is closely related to the vertical current density, and the vertical current component generates a strong accumulated charge when it encounters a layer interface, so that recording the electric field component may make the device more sensitive to high-resistance layer targets.
In deriving the apparent resistivity of the electric dipole, a uniform half-space condition is used, which means that if the subsurface is uniform half-space, the apparent resistivity obtained by substituting the electric and magnetic fields measured at the surface into this equation will be equal to the true resistivity of the subsurface. When the underground resistivity is in layered or three-dimensional distribution, the apparent resistivity obtained by substituting the electric field and the magnetic field measured on the earth surface into the formula can still reflect the underground resistivity distribution. At high frequencies, apparent resistivity reflects shallow information, and as frequency decreases, apparent resistivity will gradually reflect deep information. Therefore, the apparent resistivity derived herein using uniform half-space is equally applicable to complex media.
Considering a vertical magnetic field and a tangential electric field generated by an electric dipole field source on the earth surface under the quasi-static approximation of a uniform half space, wherein the two components do not contain a complex virtual-vector Bessel function, the uniform half space conductivity is sigma, the receiving and transmitting distance is r, and the transmitting electric dipole moment Ids is the product of current and the length ds of a transmitting lead, the electromagnetic field expression at the measuring point of the uniform half space is as follows for the horizontal electric dipole source:
in the above formula, E φ 、H z Respectively representing a tangential electric field and a vertical magnetic field; p is the apparent resistivity and is the resistivity,
is the azimuth angle.
Is the wave number of the uniform half-space, ω is the angular frequency, which is equal to 2 π f, f is the frequency, μ is the vacuum permeability, σ is the electrical conductivity, e -ikr The function is an exponential function, the expression contains the product of the exponential function and the normal function, and the expression does not have the inverse function of analytical solution.
To resolve k analytically, the measured electric field is first measured
And a magnetic field H z And (4) normalization is carried out:
h at the measurement point z And E φ After normalization and item shifting transformation, the following can be obtained:
eliminating the two above formulas by dividing after term shifting -ikr The following can be obtained:
order to
x = ikr, yielding:
ax 4 +(3a+b)x 3 +(3a+b+2)x 2 +3x+3＝0.
in the above formula, a and b can be directly obtained from an electric field and a magnetic field, for known transceiving distance and frequency and transmitting polar moment, the obtained x is only related to the resistivity, and the apparent resistivity of each transceiving distance at each frequency can be directly obtained. For a general complex coefficient unary quartic equation, four complex roots can be obtained by solving by using matlab symbols. Therefore, when the root is selected to calculate the apparent resistivity, the invention judges according to the phase, and selects the root with the phase between 0 and 90 to calculate the apparent resistivity, and the argument is as follows:
the equator apparatus was used for the experiment, with a uniform half-space resistivity of 100 Ω · m and a transmission/reception distance of 2000 m. The results of the four apparent resistivities calculated using the wavenumber apparent resistivity method described above are shown in fig. 2. As can be seen from the figure, only four roots are changed into two roots at a low frequency, the four roots are different at a medium frequency, three roots appear from the medium frequency to a high frequency, and two roots appear when the frequency is continuously increased. In the first and last branch curves, two apparent resistivities meet the requirement, and only one root in the phase meets the requirement, which is consistent with the phenomenon reflected by the approximate expression. It can be seen that 2 nd and 3,4 each have a portion of the frequency band corresponding to the true apparent resistance. The phase at 45 degrees is a true phase curve (consistent with the uniform half-space theory result), so when selecting the apparent resistivity, the judgment is carried out according to the phase, and the root of which the phase is between 0 and 90 is selected to calculate the apparent resistivity.
After selecting the appropriate root x, the apparent resistivity and phase of the measured point can be found using the following formula:
therefore, according to the theoretical contents, the change curve of apparent resistivity and phase along with frequency at any position can be analyzed and calculated, and the earth information at any position can be extracted.
Based on this, the present embodiment provides a method for measuring apparent resistivity based on wave number of a horizontal electric dipole source, which includes the following steps:
step 1: laying a grounded horizontal electric dipole source on the ground surface and supplying current; laying measuring points on the surface of the earth, recording the receiving and transmitting distances r of the measuring points, and measuring the tangential electric field E φ And a vertical magnetic field H z 。
As shown in fig. 1, a horizontally long wire is laid on the ground surface, the current intensity is I, the length of the wire is ds, and alternating current such as pseudo-random waveforms containing multiple frequencies is supplied to a coil through a transmitter; arranging a receiver (measuring point) outside the vicinity of the perpendicular bisector of the HED, recording the transceiving distance r of the measuring point, and the azimuth angle of the measuring point relative to the field source
Emission current I, horizontal long wire length ds. Measuring tangential electric field E using non-polarizing electrodes φ Measuring the vertical magnetic field H by using magnetic probes or air-core coils z 。
Step 2: the receiving and transmitting distance r and the tangential electric field E are measured φ And a vertical magnetic field H z Substituting a unitary quartic equation analytic parameter x;
and step 3: and calculating the apparent resistivity and phase of the wave number based on the parameter x.
The calculation process of each part can refer to the above theoretical formula.
Example 2:
the embodiment 2 of the invention provides a device based on the measuring method, which comprises a horizontal electric dipole source, a transmitter, a receiver and a processor, wherein the horizontal electric dipole source is connected with the transmitter;
wherein, the horizontal electric dipole source is laid on the ground surface and connected with the transmitter, and the transmitter supplies current to the horizontal electric dipole source;
the receiver is arranged on the measuring point and records measuring data, and at least comprises a tangential electric field measuring module and a vertical magnetic field measuring module, wherein the tangential electric field measuring module is used for measuring a tangential electric field E φ The vertical magnetic field measurementThe module is used for measuring the vertical magnetic field H z . In this embodiment, non-polarized electrodes are used to measure the tangential electric field emitted by the magnetic source, and magnetic probes or air coils are used to measure the perpendicular magnetic field.
The processor is connected with the receiver and used for acquiring measurement data and transmitting and receiving distance r and tangential electric field E in the measurement data φ And a vertical magnetic field H z Substituting a unitary quartic equation analytic parameter x; and calculating the apparent resistivity and phase of the wave number based on the parameter x.
The specific implementation process of each module, especially the algorithm process involved in the processor, may refer to the relevant description of embodiment 1.
Example 3:
the present invention provides a readable storage medium storing a computer program for invocation by a processor to implement:
obtaining measurement data on a measurement point, and then transmitting and receiving distance r and tangential electric field E in the measurement data φ And a vertical magnetic field H z Substituting a unitary quartic equation analytic parameter x; and calculating the apparent resistivity and phase of the wave number based on the parameter x.
It will be appreciated that the measurement data obtained is obtained with reference to example 1, i.e. collected after laying a grounded horizontal electric dipole source at the surface and supplying current.
The specific implementation process of each step refers to the explanation of the foregoing method.
The readable storage medium is a computer readable storage medium, which may be an internal storage unit of the controller according to any of the foregoing embodiments, for example, a hard disk or a memory of the controller. The readable storage medium may also be an external storage device of the controller, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like provided on the controller. Further, the readable storage medium may also include both an internal storage unit of the controller and an external storage device. The readable storage medium is used for storing the computer program and other programs and data required by the controller. The readable storage medium may also be used to temporarily store data that has been output or is to be output.
Based on such understanding, the technical solution of the present invention essentially or partly contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned readable storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
Simulation and verification:
(1) Laying a grounded long lead on the ground surface, wherein the grounded end is AB, recording the length ds of the AB, positioning the position of a field source AB by adopting a differential positioning method, supplying current waveforms such as square waves or pseudo-random multi-frequency square waves and the like into the lead, and recording the emission current waveform and the current intensity I;
(2) And collecting data. Measuring points are distributed on the ground surface, when a transmitter works stably, the positions of the measuring points are recorded to obtain a transmitting-receiving distance r, measuring electrodes M, N in corresponding directions are laid according to the position of a field source, the distance of MN is d, a measured time domain voltage sequence is obtained, and then a time domain tangential electric field E is obtained φ ＝V MN And d. The magnetic field is measured by a special magnetic sensor to obtain time domain magnetic field data. The apparent resistivity method needs to record the phases of an electric field and a magnetic field, in actual work, a receiver is adopted to record the transmitting current, the recording time is synchronous with the GPS time, and the receiver at a measuring point needs to record the transmitting current and simultaneously receive the data of the magnetic field and the electric field.
(3) And (5) calculating apparent resistivity of wave number. Converting the receiver data from time domain to frequency domain to obtain the electric field, magnetic field and current in frequency domain, and recording AB length ds, current intensity I and azimuth angle
And substituting to solve a unitary quadratic equation to directly calculate the apparent resistivity of the wave number.
Fig. 3 to fig. 6 are numerical simulation calculation results of a series of layered models, wherein parameters of the layered media are illustrated in the attached drawings, and electromagnetic field values of measuring points under the layered media are calculated by formulas under the layered media. FIG. 7 is a comparison of the results of the wave number apparent resistivity and the Carniya apparent resistivity of the measured data at a location in Anhui province.
Fig. 3 (a) is a calculation result of the apparent wave number resistivity under the condition of two layers of media of the D-type model, the abscissa is frequency, the ordinate is apparent resistivity, and the curve represents the meaning that the apparent wave number resistivity at the corresponding depth can be obtained at each frequency; fig. 3 (b) shows the calculation result of the wave number phase in the two-layer medium condition of the D-type model. The square symbol is the result when the transmitting-receiving distance is 3000m, and the circular curve is the result when the transmitting-receiving distance is 5000 m; the lower triangular symbol is the result with the transceiving distance of 7000 m; the right triangle is the result of wave number apparent resistivity and wave number phase when the transmitting-receiving distance is 10000 m; the black solid line is the apparent resistivity result of the magnetotelluric method.
As can be seen from FIG. 3, the apparent resistivity of the wave number described in the present invention can reflect the change of the underground resistivity under different transceiving distances, and the phenomenon of the distortion of the resistivity is not observed. When the receiving and transmitting distance is large, the wave number apparent resistivity is similar to a geoelectromagnetic method curve, and when the receiving and transmitting distance is short, the asymptote of the low-frequency wave number apparent resistivity is not equal to the bottom layer apparent resistivity, but can still reflect the information of the shallow bottom layer. Indicating that the wave number apparent resistivity can proceed without distortion in the whole region. The low resistance layer causes a phase reduction. As the transmission/reception distance increases, the sensitivity to the second layer also becomes greater.
Fig. 4 (a) is a calculation result of the apparent wave number resistivity under the two-layer medium condition of the G-type model, the abscissa is frequency, the ordinate is the apparent wave number resistivity, and the curve represents the meaning that the apparent wave number resistivity at the corresponding depth can be obtained at each frequency; fig. 4 (b) shows the calculation result of the wave number phase under the two-layer medium condition of the G-type model.
As can be seen from fig. 4, apparent resistivity and phase curve of the magnetotelluric method start to oppose high resistance of the second layer at lower frequency, apparent resistivity of wave number can respond to the second layer at higher frequency, and apparent resistivity of wave number has better effect than that of the magnetotelluric method for resolving the high-resistance substrate because of higher frequency, short wavelength and high resolution.
Fig. 5 (a) is a calculation result of the wave number apparent resistivity under the condition of two layers of media of the K-type model, the abscissa is frequency, the ordinate is the wave number apparent resistivity, and the curve represents the meaning that the wave number apparent resistivity at the corresponding depth can be obtained at each frequency; fig. 5 (b) shows the calculation result of the wave number phase under the two-layer medium condition of the K-type model.
As can be seen in fig. 5, for the middle high resistance layer in the tri-layer dielectric, the apparent resistivity and phase curve of the magnetotelluric method is nearly close to that of the first layer, with no significant response to the high resistance layer of the middle layer. The wave number apparent resistance and the phase thereof have obvious response to the high-resistance layer in the middle frequency band, so the response of the wave number apparent resistivity and the phase is far stronger than that of the MT method.
Fig. 6 (a) is a calculation result of the wave number apparent resistivity under the condition of the two layers of media of the H-type model, the abscissa is frequency, the ordinate is the wave number apparent resistivity, and the curve represents the meaning that the wave number apparent resistivity at the corresponding depth can be obtained at each frequency; fig. 6 (b) shows the calculation result of the wave number phase under the condition of the two-layer medium of the H-type model.
As seen in fig. 6, the apparent resistivity and phase of the magnetotelluric method have similar curve response characteristics to the apparent resistivity of the wavenumber for the intermediate low-resistance layer in the tri-layer medium. It is demonstrated that the magnetotelluric method and the wavenumber apparent resistivity method have a comparable effect for the intermediate low-resistance layer.
As seen from fig. 7, when the azimuth angle is 45 degrees, the wide-area apparent resistivity calculated by using the x component of the electric field and the carney apparent resistivity of the controlled-source audio frequency magnetotelluric method are significantly distorted, wherein the distortion of the phase of the controlled-source audio frequency magnetotelluric method is particularly serious, and the wave number apparent resistivity and the phase curve thereof of the present invention are smooth and have no distortion.
FIG. 8 shows the measured vertical magnetic field components of a horizontal electric dipole source and a vertical magnetic dipole at the same current (1A) and the same transmission-reception distance (3400 m).
As can be seen from fig. 8, the magnetic field generated by the electric dipole in the measured data is significantly larger than the perpendicular magnetic field of the perpendicular magnetic dipole. The magnetic field signal generated by the vertical magnetic dipole is weak, and smooth and reliable measured data are difficult to obtain. The electric dipole can obtain reliable magnetic field data and effectively calculate the wave number apparent resistivity.
The new apparent resistivity is consistent with the MT response. The phase sensitivity of this method to high resistivity objects is much higher than MT and the sensitive region is mainly centered on the medium offset. Furthermore, this apparent resistivity is not affected by the azimuth angle.
The results show that for the layered medium, the apparent resistivity and the phase of the wave number obtained by the method are consistent with the magnetotelluric sounding curve when the receiving and transmitting distances are large, and the wave region apparent resistivity characteristic is achieved. When the receiving and transmitting distance is equivalent to the abnormal depth, the wave number apparent resistivity can also effectively reflect the deep resistivity information, and the apparent resistivity curve distortion does not exist. However, the low-frequency asymptote of the apparent resistivity of the wave number in a near region is not equal to the resistivity of a bottom layer, which indicates that the receiving and transmitting distance cannot be far smaller than the detection depth, and the distance value is determined according to experiments and experiences, and the invention is defined by a minimum receiving and transmitting distance; it should be understood that any transmit-receive range is suitable for use with the aspects of the present invention, except for this requirement. In addition, the apparent resistivity and the phase of the wave number based on the electric dipole source have better reflection effects on the sensitivity of the low-resistance layer and the high-resistance layer.
In conclusion, the apparent resistivity obtained by the method can be suitable for calculating the apparent resistivity of the electric dipole source under various receiving and transmitting distances, the transmitter power is expected to be reduced due to the fact that the electromagnetic field energy is strong when the receiving and transmitting distances are short, instrument lightening is achieved, the apparent resistivity and the phase are sensitive to a high-resistance target, and a detection scheme for detecting the high-resistance target is provided.
It should be emphasized that the examples described herein are illustrative and not restrictive, and thus the invention is not to be limited to the examples described herein, but rather to other embodiments that may be devised by those skilled in the art based on the teachings herein, and that various modifications, alterations, and substitutions are possible without departing from the spirit and scope of the present invention.
Claims (7)
1. A wave number apparent resistivity measuring method based on a horizontal electric dipole source is characterized by comprising the following steps: the method comprises the following steps:
step 1: laying a grounded horizontal electric dipole source on the ground surface and supplying current; and laying measuring points on the surface of the earth, recording the transmitting-receiving distance r of the measuring points, and measuring the tangential electric field E φ And a vertical magnetic field H z ；
Wherein, in the layered medium, assuming N layers of medium, each layer has a conductivity of sigma j Layer thickness of h j The tangential electric field and the vertical magnetic field at the surface measuring point are obtained by the following formula:
in the above equation phi represents the phase,
the reflection coefficient of electromagnetic wave in TE polarization mode at the earth surface measuring point, the emitting electric dipole moment Ids is the product of current and the length ds of the emitting wire, Y 0 Which represents the intrinsic admittance of the air layer,
the comprehensive admittance of all resistance layers below j layers is represented by the expression
Wherein the content of the first and second substances,
is the intrinsic conductance of the j-th layerNano;
can be calculated from the conductivity of each layer, since the conductivity in air is zero, u 0 μ is the vacuum permeability, λ is the intermediate parameter, ω is the angular frequency;
the reflection coefficient of the TM polarization mode is shown,
the surface resistance of the j-th layer is shown,
the intrinsic impedance of the j-th layer is shown, where,
represents the admittance ratio of the j-th layer,
J 1 (λr),J 0 (lambdar) is a first-order and zero-order Bessel function, and the integral parameter lambdar is integrated from zero to an infinite interval, so that the electromagnetic field response of the earth surface of the layered medium can be obtained;
and 2, step: the receiving and transmitting distance r and the tangential electric field E are measured φ And a vertical magnetic field H z Substituting a unitary quartic equation analytic parameter x;
ax 4 +(3a+b)x 3 +(3a+b+2)x 2 +3x+3＝0
wherein the content of the first and second substances,
x = ikr, a, b are coefficients of a univariate polynomial,
respectively represent the normalized tangential electric field E φ And a vertical magnetic field H z K is the wave number of the electromagnetic wave, i represents the unit of imaginary number;
the unary quartic equation is based on the tangential electric field E of a horizontal electric dipole source φ And a vertical magnetic field H z Two component formulas of (a);
and step 3: and calculating the wave number apparent resistivity based on the parameter x, wherein the parameter x with the phase between 0 and 90 is selected to calculate the wave number apparent resistivity.
2. The method of claim 1, wherein: the tangential electric field E φ And a vertical magnetic field H z The normalization formula of (a) is as follows:
wherein y is the coordinate of the measuring point, ω is the angular frequency, μ is the vacuum permeability, I is the intensity of the current supplied, and ds is the length of the horizontally long wire of the horizontal electric dipole source.
3. The method of claim 1, wherein: the calculation formula of the apparent resistivity of the wave number is as follows:
in the formula, ρ a And expressing apparent resistivity corresponding to a certain frequency at the measuring point, Z is expressed as a complex intermediate parameter, phi represents a phase, im (Z) represents an imaginary part of the intermediate parameter Z, re (Z) represents a real part of the intermediate parameter Z, omega is an angular frequency, and mu is vacuum permeability.
4. The method of claim 1, wherein: further comprising: and (3) sequentially changing the frequency, calculating the wave number apparent resistivity under each frequency on the corresponding measuring point according to the mode of the step (2-3), and drawing a frequency-wave number apparent resistivity curve.
5. The method of claim 4, wherein: further comprising: and moving the measuring points in sequence, changing the frequency of each measuring point in sequence, and calculating the apparent resistivity of the wave number at each frequency of the corresponding measuring point according to the mode of the step 2-3, thereby obtaining the frequency-wave number apparent resistivity curve of all the measuring points.
6. An apparatus based on the method of any one of claims 1-5, characterized in that: the method comprises the following steps: a horizontal electric dipole source, a transmitter, a receiver and a processor;
wherein the horizontal electric dipole source is laid on the ground surface and connected with the transmitter, and the transmitter supplies current to the horizontal electric dipole source;
the receiver is arranged on the measuring point and records measuring data, and at least comprises a tangential electric field measuring module and a vertical magnetic field measuring module, wherein the tangential electric field measuring module is used for measuring a tangential electric field E φ The vertical magnetic field measurement module is used for measuring a vertical magnetic field H z ；
The processor is connected with the receiver and used for acquiring measurement data and transmitting and receiving distance r and tangential electric field E in the measurement data φ And a vertical magnetic field H z Substituting a unitary quartic equation analysis parameter x; and calculating the apparent resistivity of the wave number based on the parameter x.
7. A readable storage medium, characterized by: a computer program is stored, which is called by a processor to implement the method of any of claims 1-5.
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