CN112925029B - Transient electromagnetic passive source exploration method - Google Patents
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Abstract
The invention belongs to the technical field of ground exploration, and particularly relates to a transient electromagnetic passive source exploration method which comprises the steps of selecting a reference point, enabling each signal receiving unit of a signal receiving array to explore and receive transient electromagnetic random signals of the reference point, arranging measuring points on the signal receiving array, enabling translation paths of the measuring points to form measuring lines, exploring and receiving the transient electromagnetic random signals along the measuring lines, then constructing a speed dispersion curve, a conductivity dispersion curve and a depth-conductivity curve, representing the variation curves of the conductivity of all positions of the measuring lines along with the depth by colors, drawing together to form a profile of the conductivity along with the depth, and obtaining the longitudinal distribution condition of the formation conductivity. The method can realize the fine detection of the near-surface area according to the stratum conductivity information, is convenient and reliable to operate, does not damage the original environment, and is a measuring method for measuring the stratum physical parameters and evaluating the lithology in the ground engineering exploration construction.
Description
Technical Field
The invention belongs to the technical field of ground exploration, and particularly relates to a transient electromagnetic passive source exploration method.
Background
In the process of ground exploration and underground space development, the spatial distribution of the transverse wave velocity of the stratum can be effectively obtained by measuring the random signals of the vibration excited by the passive source, and the method can be applied to stratum detection in many fields.
After the transient electromagnetic field is excited, the transient electromagnetic field propagates and diffuses in the conductive stratum in two modes of displacement current and conduction current respectively. Different from electromagnetic waves, the transient electromagnetic field has amplitude attenuation in the diffusion process, the attenuation amplitude is different when different frequencies are diffused, the low-frequency attenuation is small, the diffusion area is large, the high-frequency attenuation is large, and the diffusion area is small. Thus, the transient electromagnetic field received at a distance is attenuated and phase shifted in response, and is already significantly different from the waveform of the excitation source.
Meanwhile, the inventor finds that the existing exploration method is low in measurement accuracy, easy to damage the environment, incapable of extracting a section of the conductivity changing along with the depth from the measured transient electromagnetic random waveform and incapable of knowing the longitudinal distribution condition of the conductivity of the stratum. Therefore, a new exploration method is needed to solve the above problems.
Disclosure of Invention
The invention aims to: aiming at the defects of the prior art, the transient electromagnetic passive source exploration method is provided, the fine detection of a near-surface region can be realized, the operation is convenient and reliable, the original environment cannot be damaged, in addition, the section of the conductivity changing along with the depth can be extracted from the measured transient electromagnetic random waveform, and therefore the longitudinal distribution condition of the stratum conductivity can be obtained.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method of transient electromagnetic passive source surveying, comprising:
s1, selecting a reference point, arranging a signal receiving array, wherein a plurality of signal receiving units are uniformly distributed in the signal receiving array, each signal receiving unit is used for exploring and receiving transient electromagnetic random signals of the reference point, measuring points are arranged on the signal receiving array, the signal receiving array and the measuring points are moved according to a preset translation distance, a translation path of each measuring point forms a measuring line, and the transient electromagnetic random signals are explored and received along the measuring line;
s2, constructing a speed dispersion curve and a conductivity dispersion curve, and converting the conductivity dispersion curve into a depth-conductivity curve;
and S3, representing the change curves of the conductivity at all positions of the measuring line along with the depth by colors, and drawing the change curves together to form a section of the conductivity along with the depth to obtain the longitudinal distribution condition of the conductivity of the stratum.
Further, the process of constructing the velocity dispersion curve in S2 includes: and constructing a spatial correlation coefficient of the transient electromagnetic random signal in a spatial spectrum mode, and compensating the spatial correlation coefficient by adopting an exponential function, so that the compensated spatial correlation coefficient and the phase of the Bessel function are fitted to construct speed dispersion curves with different frequencies.
Further, the process of constructing the conductivity dispersion curve in S2 includes: and converting the velocity dispersion curve into a conductivity dispersion curve by utilizing the relation between the velocity of the conductive medium and the conductivity of the stratum.
Further, the process of obtaining the depth-conductivity curve in S2 includes: and converting the conductivity dispersion curve into a depth-conductivity curve by taking the quotient of frequency and velocity as a wavenumber k.
Further, the signal receiving array in S1 is a regular polygon, the center and each vertex of the regular polygon are provided with the signal receiving unit, and the regular polygon includes but is not limited to a regular triangle, a regular hexagon, and a regular dodecagon.
Further, the signal receiving unit is an electrode or a coil.
Further, the measurement point in S1 is set at the center of the regular polygon.
Further, the reference point in S1 is a reference electrode.
The invention has the beneficial effects that: according to the invention, transient electromagnetic random signals of the array are effectively processed according to equivalent propagation characteristics of phase shift change of a transient electromagnetic field, a change curve of the conductivity along with the depth can be extracted from a measured transient electromagnetic random waveform, and a section of the conductivity along with the depth can be further obtained, so that the ground exploration near the earth surface is effectively carried out by using the electromagnetic excitation source in the earth and the underground, the manufacturing cost of an artificial source and the cost of used electric power and oil are effectively saved, and the environment-friendly exploration is realized; meanwhile, the random source has rich excitation frequency, the detection depth covers high-frequency and low-frequency regions, the resolution ratio is high, the detection depth is deep, and the longitudinal distribution condition of the stratum conductivity can be obtained through transient electromagnetic signals excited by the passive source.
Drawings
FIG. 1 is a flow chart of a method of exploration of the present invention.
Fig. 2 is a diagram of the arrangement of the stages in embodiment 1 of the present invention.
Fig. 3 is a flowchart of constructing a velocity dispersion curve according to embodiment 1 of the present invention.
Fig. 4 is a depth-conductivity profile plotting flow chart of example 1 of the present invention.
Fig. 5 is a diagram of the arrangement of the stages in embodiment 2 of the present invention.
Detailed Description
As used in this specification and the appended claims, certain terms are used to refer to particular components, and it will be appreciated by those skilled in the art that a manufacturer may refer to a component by different names. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. "substantially" means within an acceptable error range, and a person skilled in the art can solve the technical problem within a certain error range to substantially achieve the technical effect.
In the description of the present invention, it is to be understood that the terms "upper", "lower", "front", "rear", "left", "right", horizontal ", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience in describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention.
In the present invention, unless otherwise explicitly stated or limited, the terms "mounted," "connected," "fixed," and the like are to be construed broadly and may, for example, be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
The present invention will be described in further detail with reference to the accompanying drawings 1 to 5 and specific examples, but the present invention is not limited thereto.
Example 1
A transient electromagnetic passive source exploration method is shown in figures 1-4 and comprises the following steps:
s1, selecting a reference point, wherein the reference point can be a reference electrode, arranging a signal receiving station array, uniformly distributing a plurality of signal receiving units in the signal receiving station array, and each signal receiving unit surveys and receives transient electromagnetic random signals of the reference point, wherein the signal receiving station array is a regular hexagon, the center and each vertex of the regular hexagon are provided with signal receiving units, each signal receiving unit is the same electrode, so that the signal receiving station array is provided with 7 same electrodes, the signal receiving unit positioned at the center of the signal receiving station array is used as a measuring point S1, the signal receiving station array and the measuring point S1 are moved according to a preset translation distance, the translated measuring points are sequentially marked as S2, S3, S4, …, S1, S2, S3 and S4 which are connected to be a translation path of a measuring point S1, the translation path forms a measuring line, and the transient electromagnetic random signals are surveyed and received along the measuring line, because the position of 2 electrodes in the signal receiving array is unchanged, and the other 4 electrodes can move together, the difficulty of arrangement is reduced, and the construction efficiency is improved.
S2, processing the signal data, constructing a velocity dispersion curve and a conductivity dispersion curve, and converting the conductivity dispersion curve into a depth-conductivity curve through a wave number k, wherein the S2 comprises the following steps:
s2-1, constructing a speed dispersion curve, constructing a spatial correlation coefficient of the transient electromagnetic random signal in a spatial spectrum mode, compensating the spatial correlation coefficient by adopting an exponential function, and fitting the compensated spatial correlation coefficient and the phase of a Bessel function to construct the speed dispersion curve with different frequencies, wherein the method comprises the following steps:
(a) and constructing a functional expression of the transient electromagnetic random signal.
The transient electromagnetic field excited by natural phenomena is a random signal, with respect to time t and position function
So that, in a conducting medium, the propagation of a transient electromagnetic field is characterized by both attenuation and phase shift, and therefore, over a period of time in a region, the transient electromagnetic random signal at a point can be expressed as:
in the formula (1), ckn＝ωn＝2πfnWhere c is the equivalent propagation velocity, θmFourier coefficient of white noise for incidence (projection) direction of m component wave
And spatial spectral density G(A)(kn,θm)、G(B)(kn,θm) Can express Anm、Bnm。
Wherein:
according to the nature of white noise:
substituting equation (4) into equations (2) and (3) yields:
wherein, | G(A)(kn,θm)|2Is the spatial spectral density of the initial shift, and | G(B)(kn,θm)|2Are the spatial spectral densities of the initial velocity, which are independent of each other and independent of time, only related to the initial velocity and the initial position, and therefore it can be assumed that:
(b) representing spatial correlation coefficients of a transient electromagnetic random signal in the form of a spatial spectrum and compensating the spatial correlation coefficients, comprising the steps of:
defining the spatial correlation function of the transient electromagnetic random signal as:
the summation in the formula (8) is converted into integral, and further simplified to obtain:
wherein the above equation (9) indicates that the spatial correlation coefficient of the transient electromagnetic signal is time-independent.
At the same time, with an exponential function e(kξcosθ+kηsinθ)The spatial correlation coefficient is compensated to obtain a compensated spatial correlation function as follows:
and carrying out Fourier transform on the compensated spatial correlation function to obtain:
|G(k,θ)|2＝∫∫ψ(ξ,η)e(-ikξcosθ-ikξsinθ)dξdη (11)
(c) calculating the relation between the time spectrum and the space spectrum of the transient electromagnetic random signal, and providing the relation between the compensated space correlation function and the time spectrum, wherein the method comprises the following steps:
the temporal spectral density of transient electromagnetism can be written as:
wherein, U herec(ωn) Is the coefficient of the cosine function of the Fourier expansion of the transient electromagnetic random signal U (x, y, t) at the position (x, y) with respect to time t, and similarly to Us(ωn) Are coefficients of a sine function.
Because:
substituting equations (5), (6) and (13) into equation (12) yields a time spectrum density of:
the above equation (14) shows that the temporal spectrum of the transient electromagnetic random signal is the integral of the spatial spectrum in all directions.
Substituting equation (11) into equation (14) can yield:
replacing (ξ, η) with a polar coordinate system (r, Φ): ξ ═ rcos Φ, η ═ rcos Φ; constructing a relational expression:
obtained from the formula (15):
and carrying out azimuth averaging on the compensated spatial correlation function:
the relationship of the compensated average spatial correlation function to the temporal spectrum can be written as:
and performing a hankel transform on equation (18) to obtain:
the above equation (19) expresses the relationship between the compensated average spatial autocorrelation function and the spectral density in the time domain.
(d) Calculating the spatial correlation coefficient of the transient electromagnetism, comprising the following steps:
transient electromagnetic fields disperse waves as they propagate through the earth, taking into account the relationship between the time domain spectrum and the spatial autocorrelation function for dispersive conditions.
When the wave is dispersive, we take Δ k for any nnIs a constant. Note that at this time, Δ ωnIs no longer a fixed value but varies with n, while the speed c is a function of ω:
the time spectrum obtained from equation (14) is:
substituting equations (11) and (17) into equation (20) can yield:
the expression (21) is subjected to a hankel transformation to obtain:
in actual measurement, the measured wave passes through a center frequency of omega0The filtered transient electromagnetic spectrum density is:
φ(ω)＝P(ω0)δ(ω-ω0) ω>0 (22)
δ (ω) is a dirac function, the spatial correlation function of equation (21) is:
defining spatial autocorrelation coefficients:
substituting (23) into (24) can obtain the spatial correlation coefficient as:
(e) the method comprises the following steps of solving a spatial correlation coefficient through a transient electromagnetic signal of a frequency domain, fitting the spatial correlation coefficient with a first-class zero-order Bessel function to obtain the phase velocity of the transient electromagnetic, and solving a frequency dispersion curve, wherein the method comprises the following steps:
because:
(26) in the formula
Is in a position X1And X2The cross-power spectrum of the transient electromagnetic random signal between the two stations,
and
are each X1And X2And (3) processing the self-power spectrum of the station transient electromagnetic random signal. The spatial correlation coefficient obtained by the equation (26) needs to be fitted with a zero-order Bessel function to obtain a dispersion curve of the transient electromagnetic random signal.
There are two variables: the frequency f and radius r, one of the variables is usually fixed and then fitted. In a related method, a fixed station radius r0And obtaining the change relation of the autocorrelation coefficient along with the frequency, and fitting the autocorrelation coefficient with the Bessel function.
Order to
Obtained from the formula (25):
when the radius r is fixed and different frequencies f are taken, the radius r corresponds to a rho value, the rho value is fitted with a first class zeroth-order Bessel function through a least square method, when the variance is minimum, the independent variable part X of the Bessel function is solved, and then the X is 2 pi fr0(f) the phase velocity c of the transient electromagnetic wave is obtained, while the corresponding frequency f is also known. Thus, a velocity dispersion curve v-f of the transient electromagnetic wave is obtained.
S2-2, converting the velocity dispersion curve into a conductivity dispersion curve by using the relation between the velocity of the conductive medium and the conductivity of the stratum, and comprising the following steps:
the basic equation from the transient electromagnetic field is:
in the formula (27), the compound represented by the formula (I),
is the strength of the magnetic field,
μ is magnetic induction, and μ is magnetic permeability. The stratum in the application range of the invention is all non-ferromagnetic medium, and the relative magnetic permeability is close to 1.
By
Substituting equation (27) can obtain:
assuming that the physical quantities of all transient electromagnetic fields follow a sinusoidal law e with time-iωtChange, i.e.
Considering the case of a passive field (no current source to excite the transient electromagnetic field), the degree of rotation is calculated across equation (27) and will be
Substituting and arranging to obtain:
using formulas
And (3) the charge distribution q in the medium is not equal to 0, so that a transient electromagnetic field equation of a three-dimensional space is obtained:
taking the electric field intensity E in the x directionxAs a study object, (30) formula becomes:
this is a second order constant coefficient differential equation with respect to the coordinate z.
Let lambda2＝-jμσω+μεω2 (32)
The solution to the equation is: ex＝C1ejλz+C2e-jλz (33)
Wherein, C1And C2Is a coefficient, and e-jωtTaken together, it can be seen that: c1ejλz -jωtDescribing the transient electromagnetic field propagating (diffusing) in the positive z direction, C1e-jλz -jωtTransient electromagnetic fields propagating (diffusing) in the opposite direction of z are described.
For the excitation spectrum and its response starting from 0Hz, σ > ε ω, the second term in the (32) equation is much smaller than the first term and can be neglected. At this time, λ2Is given by-j μ σ ω, k
If only transient electromagnetic fields propagating in the positive z-direction are consideredThen (33) can be written as:
(34) attenuation coefficient in the formula
Exactly the wavenumber k, it can be seen that the essential feature of the propagation of the transient electromagnetic field in the formation is both attenuation and phase shift, and the coefficients of attenuation are exactly the wavenumber.
From wave number
The phase velocity of the transient electromagnetic field can be found:
(35) formula for displaying the change of phase velocity of transient electromagnetic field with frequency and the velocity of electromagnetic wave
The constants are different, the higher the frequency, the faster the speed and the shorter the delay; the lower the frequency, the slower the speed, and the greater the delay. The attenuation coefficient also changes along with the frequency, the higher the frequency is, the larger the attenuation is, and the shorter the diffusion distance is; the lower the frequency, the smaller the attenuation and the longer the distance of diffusion. This is a major feature of transient electromagnetic responses.
And (3) substituting the relation between the velocity of the transient electromagnetic field and the formation conductivity obtained by the formula (35) into the velocity dispersion curve of the transient electromagnetic field obtained in the previous step to obtain a conductivity dispersion curve sigma-f.
S2-3, because the wavenumber k is the quotient of frequency and velocity, the wavelength of the reciprocal of wavenumber k, corresponds to the skin depth H in the conductive medium, and thus the conductivity dispersion curve σ -f can be further converted into the skin depth-conductivity curve σ -H.
And S3, representing the change curves of the conductivity at all positions of the measuring line along with the depth by colors, summarizing depth-conductivity data acquired at each measuring point on the measuring line, drawing the measuring line as a horizontal coordinate and the depth as a vertical coordinate together to form a profile of the conductivity along with the change of the depth, and acquiring the longitudinal distribution condition of the formation conductivity.
And step S1 further includes connecting all the electrodes to an acquisition system through cables, the acquisition system transmitting the acquired data to an upper computer through a USB cable, the data acquisition time is in the daytime or at night, which does not affect the accuracy of data recording, but preferably avoids areas with large human interference, otherwise the data is disturbed stably and randomly. Wherein, the collection time of each measuring point on the measuring line is generally 20 minutes, the data sampling rate is 1K, the continuous collection is carried out, and the measuring line is moved to the next point after one point is measured. In addition, the acquisition mode of the transient electromagnetic random signal can also be acquired through a multi-channel data acquisition box.
The spatial correlation coefficient in step S2 can be obtained by calculating the self-power spectrum and the cross-power spectrum between the electrodes, respectively. The self-power spectrum can be obtained by Fourier transform of the autocorrelation function, so that the autocorrelation function of the transient electromagnetic random signal is solved first, and then FFT is carried out to obtain the self-power spectrum of the signal. In the spectrum analysis, the window function can reduce the spectrum leakage and correct the non-periodicity of the signal. Therefore, a window function is added when calculating the cross-power spectrum, and the cross-power spectrum of two transient electromagnetic random signals at different positions can be obtained by Fourier transform through a cross-correlation function. Substituting the self-power spectrum and the cross-power spectrum of the center electrode and any electrode of the regular hexagon into the formula (26) to obtain the spatial correlation coefficient between the pair of electrodes. And calculating the space correlation coefficients of the center electrode and the rest electrodes on the circumference of the circumscribed circle of the regular hexagon, and finally averaging to obtain the average space correlation coefficient between the electrodes with the distance R.
And the radius of a circumscribed circle of the regular hexagon is R, when the array is used for observing transient electromagnetic random signals, after obtaining a spatial correlation coefficient, a value corresponding to the spatial correlation coefficient when different frequencies f are taken, the value is fitted with a first class of zero-order Bessel function through a least square method, and when the variance is minimum, the independent variable part of the Bessel function is obtainedX, further from X2 π fr0(f) the phase velocity c of the transient electromagnetic wave is obtained, while the corresponding frequency f is also known. Therefore, the velocity dispersion curve of the transient electromagnetic random signal can be obtained.
Example 2
This embodiment is different from embodiment 1 in that, as shown in fig. 5, the electrodes of the signal receiving array in the step S1 are arranged in a nested triangle, the center and each vertex of the triangle are provided with signal receiving units, and each signal receiving unit is the same electrode.
Other steps in this embodiment are the same as those in embodiment 1, and are not described herein again.
Obviously, the exploration method can receive natural transient electromagnetic signals, then process the acquired transient electromagnetic signals to obtain a speed dispersion curve and further obtain a conductivity-depth curve, draw the conductivity-depth curves on a measuring line together to obtain a profile of conductivity changing along with depth, and realize fine detection of a near-surface area according to stratum conductivity information.
Variations and modifications to the above-described embodiments may also occur to those skilled in the art, which fall within the scope of the invention as disclosed and taught herein. Therefore, the present invention is not limited to the above-mentioned embodiments, and any obvious improvement, replacement or modification made by those skilled in the art based on the present invention is within the protection scope of the present invention. Furthermore, although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.
Claims (6)
1. A method of transient electromagnetic passive source exploration, comprising:
s1, selecting a reference point, arranging a signal receiving array, wherein a plurality of signal receiving units are uniformly distributed in the signal receiving array, each signal receiving unit is used for exploring and receiving transient electromagnetic random signals of the reference point, a measuring point is arranged on the signal receiving array, the signal receiving array and the measuring point are moved according to a preset translation distance, a translation path of the measuring point forms a measuring line, and the transient electromagnetic random signals are explored and received along the measuring line;
s2, constructing a speed dispersion curve and a conductivity dispersion curve, converting the speed dispersion curve into a conductivity dispersion curve by utilizing the relation between the speed of a conductive medium and the conductivity of the stratum, and converting the conductivity dispersion curve into a depth-conductivity curve through a wavenumber k by taking the quotient of the frequency and the speed as the wavenumber k, wherein the specific process is as follows: due to wave number
f is frequency, sigma is conductivity, mu is permeability, and omega is angular velocity, the phase velocity of the transient electromagnetic field is obtained by calculation:
substituting the obtained relation between the velocity of the transient electromagnetic field and the stratum conductivity into the obtained velocity dispersion curve of the transient electromagnetic field to obtain a conductivity dispersion curve sigma-f, wherein the wave number k is the quotient of the frequency and the velocity, and the wavelength of the reciprocal of the wave number k corresponds to the skin depth H in the conductive medium, so that the conductivity dispersion curve sigma-f can be further converted into the skin depth-conductivity curve sigma-H;
and S3, representing the change curves of the conductivity at all positions of the measuring line along with the depth by colors, and drawing the change curves together to form a section of the conductivity along with the depth to obtain the longitudinal distribution condition of the conductivity of the stratum.
2. The transient electromagnetic passive source surveying method as claimed in claim 1, wherein the process of constructing the velocity dispersion curve in S2 comprises:
constructing spatial correlation coefficients of the transient electromagnetic random signal in a spatial spectrum form;
compensating the spatial correlation coefficient by adopting an exponential function;
and fitting the compensated spatial correlation coefficient and the phase of the Bessel function to construct speed dispersion curves of different frequencies.
3. The transient electromagnetic passive source survey method of claim 1, wherein: the signal receiving array in S1 is a regular polygon, and the signal receiving units are disposed at the center and each vertex of the regular polygon.
4. The transient electromagnetic passive source surveying method of claim 3, wherein: the signal receiving unit is an electrode or a coil.
5. The transient electromagnetic passive source surveying method of claim 3, wherein: the measurement point in S1 is set at the center of the regular polygon.
6. The transient electromagnetic passive source survey method of claim 1, wherein: the reference point in S1 is a reference electrode.
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