CN106842343A - A kind of grounded source transient electromagnetic electric field response imaging method - Google Patents
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Abstract
The invention discloses a kind of grounded source transient electromagnetic electric field response imaging method, belong to transient electromagnetic geophysical exploration method technical field.Purpose is to solve traditional transient electromagnetic fast imaging method and inversion method based on least square, the problem present invention that bottleneck is run into terms of the Explanation Accuracy of Transient electromagnetic response is further improved proposes a kind of new method being imaged to grounded source transient electromagnetic method electric field response, and method is specifically included：(1) the virtual wavelet analytic solutions of grounded source transient electromagnetic electric field response are derived；(2) virtual subnet ripple method of value solving；(3) the velocity analysis imaging of grounded source transient electromagnetic electric field response.Imaging method of the invention is based on the mathematic integral conversion between diffusion field and wave field, and amount of calculation is small, calculating speed is fast, is that the plan wave field Fine structural interpretation of transient electromagnetic field response is laid a good foundation.
Description
Technical field
Present invention relates particularly to a kind of grounded source transient electromagnetic electric field response imaging method, belong to transient electromagnetic geophysics
Exploitation method technical field.
Background technology
Transient electromagnetic method (Transient electromagnetic method, TEM) be widely used in coalfield flood,
It is a kind of important geophysical exploration method in mineral resources and subterranean resource detection.Grounded source transient electromagnetic method belongs to wink
Become a branch of electromagnetic method, it uses grounded source to inject electromagnetic field signal to underground, collection comes from underground during source turns off
The induced signal of geologic body is obtaining its distributed intelligence.
The treatment and explanation of transient electromagnetic field signal are one of key technologies of transient electromagnetic method.By the electricity of ground acquisition
Magnetic field signal, the Electrical distribution for analyzing underground medium is a typical Geophysical Inverse Problem.Generally, transient electromagnetic field response
By fast imaging methods such as apparent resistivity, " smoke ring " equivalent inverting and S invertings or the OCCAM based on least square,
Marquadt-Levenberg invertings obtain the resistivity distribution of underground medium.The imaging precision of fast imaging method is limited, and
Inversion algorithm based on least square by complexity that transient electromagnetic field response is calculated and it is computationally intensive limited, develop precision
Higher-dimension inverting difficulty higher is larger.Therefore, explore new transient electromagnetic interpretation technique having important practical significance.
The content of the invention
Therefore, it is to propose a kind of to be imaged grounded source transient electromagnetic method electric field response the present invention seeks to purpose
New method.
Specifically, the method for the present invention is comprised the following steps：
The derivation of the virtual wavelet analytic solutions of step A grounded source Transient electromagnetic responses；
Step A is specifically included：
Field value is carried out Laplace transform by step A1；
Step A2 carries out nonlinear transformation s=p2, obtain the equivalent expression between wave field and diffusion field；
Step A3 reverse drawing Laplace transforms；
The virtual wave field numerical solution of step B grounded source Transient electromagnetic responses；
The integral equation shown in formula one is carried out first discrete；
Wherein t is the time, and (x, y, z) is space coordinates, and q is referred to as virtual time, and its dimension is s1/2；
Obtain system of linear equations：D=Gm, formula two
Using the system of linear equations of the method solution formula two of regularization, two norms of the model vector of introducing are used as canonical
Change item, and optimal regularization factors are asked for using L-curve method；
The grounded source transient electromagnetic data that step C is based on virtual subnet crest value speed is imaged；
On the basis of step A and step B, grounded source transient electromagnetic field electric field response is imaged, analyzes virtual subnet
Crest value estimates the resistivity of underground medium with the spread speed of virtual time, by the peak value based on the virtual wavelet extracted
The spread speed at virtual moment is imaged.
Further, the derivation of the step A is specially：
Under homogeneous half space, the axial electric field response produced by unit dipole source excitation is：
Wherein, c2=ρ/μ, μ=4 π 10-7H/m, erf are error function.Order
Then formula three can be expressed as：
To F1T () carries out Laplace transform on time t, obtain
With F1T the Laplace transform of the virtual wave field corresponding to () is：
According to Laplace transform identity
Wherein H represents Heavi side functions, makes a=r/c, and inverse Laplace transform is carried out to formula nine, obtains
To the F in formula six2T () carries out Laplace transform, we obtain
With F2T the Laplace transform of the virtual wave field corresponding to () is：
Inverse Laplace transform is carried out to formula formula 13, can be obtained：
Formula 11 and formula 12 are combined, are obtained and axial electric field under the homogeneous half space represented by formula three
The analytical expression of the virtual wave field corresponding to analytic expression：
Abbreviation, obtains：
Further, discrete being specially is carried out in the step B to the integral equation shown in formula one：
Integrating range is expressed as [a, b], using mid-point formula, by its it is discrete be n integration subinterval, each subinterval
Midpoint is q1,q2,...,qn, then
Wherein,
Assuming that
Formula one can be with discrete：
Wherein,
Gi,j=G (ti,qj) Δ q formula 21
mj=m (qj) formula 22
Then we can obtain system of linear equations：
D=Gm formula two.
Further, in the step B, using singular value decomposition method, the regularization of Tikhonov zeroth orders, single order regularization,
Blocking SVD or damping SVD carries out the solution of regularization.
Further, in the step C, the acquisition methods of resistivity and spread speed are specially：
Homogeneous half space situation is considered first, and it is 200 Ω m, the homogeneous half space of 500 Ω m that resistivity is calculated respectively
Under, the virtual wavelet that the trailing edge step response produced by unit dipole source excitation is obtained through wave field transformation；
According to the wave equation that virtual wavelet is met, it is known that virtually the spread speed of wavelet isVirtual subnet
The peak value moment of ripple is equal to；
By calculating transformation relation of the peak value moment with offset distance, the spread speed of virtual wavelet is obtained, and then obtain ground
The resistivity of lower medium, by calculating the partial derivative of the peak value moment to the time of virtual wavelet, obtains the virtual subnet crest value moment
Spread speed.
The beneficial effects of the present invention are：This patent proposition is a kind of to be imaged to grounded source transient electromagnetic method electric field response
New method, solve traditional transient electromagnetic fast imaging method and inversion method based on least square, further carrying
The Explanation Accuracy aspect of Transient electromagnetic response high runs into the problem of bottleneck.The method is based on the mathematics between diffusion field and wave field
Integral transformation, amount of calculation is small, calculating speed is fast, is that the plan wave field Fine structural interpretation of transient electromagnetic field response is laid a good foundation.
Brief description of the drawings
Fig. 1 a to Fig. 1 d are the solving result as regularization term using the norm of model two, and wherein Fig. 1 a are zeroth order
Tikhonov Regularization Solutions；Fig. 1 b are solved for TSVD；Fig. 1 c are solved for DSVD；Fig. 1 d are the TSVD solutions of different point of cut-offs；
Fig. 2 a to Fig. 2 d are the solving result as regularization term using first order modeling roughness, and wherein Fig. 2 a are single order
Tikhonov Regularization Solutions；Fig. 2 b are solved for TSVD；Fig. 2 c are solved for DSVD；Fig. 2 d are the TSVD solutions of different point of cut-offs；
Fig. 3 a to Fig. 3 d are the solving result as regularization term using second-order model roughness, and wherein Fig. 3 a are second order
Tikhonov Regularization Solutions；Fig. 3 b are solved for TSVD；Fig. 3 c DSVD are solved；Fig. 3 d are the TSVD solutions of different point of cut-offs；
Fig. 4 a, Fig. 4 b are the virtual wavelet analytic solutions of different resistivity homogeneous half space, 200 Ohm-m in Fig. 4 a；Fig. 4 b
Middle 500Ohm-m；
Fig. 5 a, Fig. 5 b are the virtual subnet ripple numerical solution of different resistivity homogeneous half space, 200Ohm-m in Fig. 5 a；In Fig. 5 b
500Ohm-m；
Fig. 6 a, Fig. 6 b are Q pattern type virtual subnet ripple numerical solutions, ρ in Fig. 6 a1=50Ohm-m, ρ2=200Ohm-m；In Fig. 6 b
ρ1=200Ohm-m, ρ2=100Ohm-m；
Fig. 7 a, Fig. 7 b are three layer model virtual subnet ripple numerical solution, ρ in Fig. 7 a1=200Ohm-m, ρ2=50Ohm-m, ρ3=
200Ohm-m；ρ in Fig. 7 b1=50Ohm-m, ρ2=500Ohm-m, ρ3=50Ohm-m.
Specific embodiment
Specific embodiment of the invention is illustrated below in conjunction with the accompanying drawings：
It is one of probing direction of transient electromagnetic new interpretation technology that the plan wave field of transient electromagnetic field data is explained.Transient electromagnetic
Communication satisfaction maxwell equation group of the field in underground medium.Limited by the frequency band range of transient electromagnetic signal, it is with expansion
Scattered mode is propagated, and communication process Ke Yi Hai Muhuoci equations are characterized.Bragg (1968) and Filippi (1969) mathematically, from
Diffusion equation and wave equation set out, and have derived between the mathematical quantity for meeting the mathematical quantity of diffusion equation and meeting wave equation
Mathematic integral relational expression, if the formula to be applied to meet turning for the electromagnetic field E and the virtual wavelet U for meeting wave equation in diffusion field
Change, can obtain
Wherein t is the time, and (x, y, z) is space coordinates, and q is referred to as virtual time, and its dimension is s1/2.Lee (1993) is adopted
With the method for ray tracing, low frequency electromagnetic field response is imaged using formula (1), Lee (2006) utilizes frequency domain electromagnetic
Field data, obtains the imaging that virtual wavelet U realizes frequency domain electromagnetic response.At home, Lee mythical wild animal etc. (2006) will return
Line source transient electromagnetic field response is converted to virtual wavelet, and realizes Loop source transient electromagnetic sound using a gram western Hough offset method
The imaging answered.
The present invention proposes that a kind of new grounded source Transient electromagnetic response intends Seismic imaging method.The method is based on formula (1) institute
Integral Transformation between the diffusion field of derivation and wave field, can carry out accurately image to the resistivity information of underground medium.Specifically
Including：(1) derivation of the virtual wavelet analytic solutions of grounded source Transient electromagnetic response；(2) the virtual wave field of grounded source Transient electromagnetic response
Method of value solving；(3) the grounded source transient electromagnetic data imaging based on virtual subnet crest value speed.
(module 1)：The derivation of the virtual wavelet analytic solutions of grounded source Transient electromagnetic response
Integral transformation shown in formula (1) is Fredholm Linear Integral Equations of First Kind, it is impossible to directly carries out inverse transformation to it and asks for
The analytic solutions of virtual wavelet corresponding with electromagnetic field response under homogeneous half space.We are by following derivation step to grounded source wink
The virtual wavelet analytic solutions of Electromagnetic Field response are derived：
1) field value is carried out into Laplace transform；
2) nonlinear transformation s=p is carried out2, obtain the equivalent expression between wave field and diffusion field；
3) reverse drawing Laplace transform.
It is below specific derivation process：
In the measurement of grounded source transient electromagnetic method, if seeing the electric field component on the axial direction of source.It is single under homogeneous half space
Axial electric field produced by the dipole source excitation of position responds and is：
Wherein, c2=ρ/μ, μ=4 π 10-7H/m, erf are error function.Order
Then formula (2) can be expressed as：
To F1T () carries out Laplace transform on time t, obtain
Correspondingly, we obtain and F1T the Laplace transform of the virtual wave field corresponding to () is：
According to Laplace transform identity
Wherein H represents Heavi side functions, makes a=r/c, and inverse Laplace transform is carried out to formula (8), can obtain
Similarly, to the F in formula (5)2T () carries out Laplace transform, we obtain
Correspondingly, we obtain and F2T the Laplace transform of the virtual wave field corresponding to () is：
Inverse Laplace transform is carried out to formula (12), can be obtained：
Formula (10) and formula (11) are combined, you can obtain and axial electric field under the homogeneous half space represented by formula (2)
The analytical expression of the virtual wave field corresponding to analytic expression：
Abbreviation, obtains：
(module 2)：Grounded source Transient electromagnetic response virtual subnet ripple method of value solving
The virtual wavelet extraction of transient electromagnetic method of this module faces electrotropism source.Module 1 has derived the virtual wavelet of homogeneous half space
Analytic solutions.But under stratified model or two, threedimensional model, it is impossible to the analytic solutions of virtual wavelet are tried to achieve, it is necessary to using number
Value method is solved.This module gives the best practice of grounded source Transient electromagnetic response virtual subnet ripple numerical solution.First
Integral equation shown in formula (1) is carried out discrete.In example of calculation, integrating range is limited, is expressed as [a, b].
Using mid-point formula, by its it is discrete be n integration subinterval, the midpoint in each subinterval is q1,q2,...,qn, then
Wherein,
If assuming
Now, formula (1) can be with discrete：
Wherein,
Gi,j=G (ti,qj)Δq (20)
mj=m (qj) (21)
Then we can obtain system of linear equations：
D=Gm (22)
Therefore, the process that the Solve problems conversion of virtual wavelet is solved for system of linear equations shown in formula (23).Product
The pathosis of point expression formula (1) are such that the solution procedure of system of linear equations (23) has pathosis, it is necessary to using the side of regularization
Method is solved.Therefore, introduce model vector two norms as regularization term, and using L-curve method ask for optimal regularization because
Son.The solution procedure of regularization is carried out using singular value decomposition method (Singular value decomposition, SVD).Examine
Consider the regularization of Tikhonov zeroth orders, single order regularization, block SVD (truncated SVD, TSVD) and damping SVD (Damped
) etc. SVD method is solved.It is below solving result：
Fig. 1 a to Fig. 1 c sets forth the introducing norm of model two as regularization term, and Tikhonov canonicals are respectively adopted
Change, the solving result of TSVD and DSVD, ordinate represents amplitude in figure, and curve represents actual and virtual wavelet, and data point represents number
According to solving result.For Tikhonov regularizations and DSVD, regularization factors are obtained by L-curve；For TSVD, its point of cut-off
Position is obtained by L-curve, and regularization factors are designated with λ in figure.Zeroth order Tikhonov regularization solving results in Fig. 1 a
Late period stabilization, but early stage deviate actual value it is larger.DSVD solving results are early and late unstable in Fig. 1 c.Fig. 1 b
In the stability of TSVD solving results be better than other two methods, due to blocking for singular value, the solution of early stage it is unstable
Property suppressed, but solution late period occur in that slight vibration.Therefore, calculating the optimal regularization obtained by L-curve
TSVD solutions near parameter, are drawn in Fig. 1 b.With prolonging after point of cut-off, it is considered to singular value increase, it is resulting
The stability reduction of TSVD solution early stages.But, the amplitude of the virtual wavelet for being obtained closer to and actual value.On the contrary, with
Point of cut-off shifts to an earlier date, it is considered to singular value reduce, the TSVD solutions for obtaining in general stability increase.In general, using model
When two norms are as regularization term, the less stable of resulting Regularization Solution early stage.
Fig. 2 and Fig. 3 virtual wavelet that first order modeling roughness and second-order model roughness are obtained as regularization term respectively
Extract result., it is necessary to be solved using broad sense SVD (Generalized SVD) method when using high-order model roughness.
As seen from the figure, when using model roughness as regularization term, Tikhonov methods and the getable stabilization of TGSVD methods
Solution.But, the effect of the solution obtained using damping singular value decomposition is still undesirable.By contrast Tikhonov methods and
The solution that TGSVD methods are obtained, it is believed that TGSVD is more preferable to the peak value of virtual wavelet and the extraction effect of peak value moment.In addition, logical
The extraction result for crossing the TGSVD of comparison diagram 2d and Fig. 3 d understands, during using second-order model roughness as regularization term, is extracted
Virtual wavelet peak value and peak value moment it is more accurate.When using first order modeling roughness as regularization term, extracted
Virtual wavelet late period vibration it is weaker.
By above-mentioned analysis, the numerical solution of wave field transformation can not accurately recover virtual wavelet, and only be empty
Intend wavelet one is approximate.The difficult point for solving ill indirect problem be indirect problem in itself, rather than the regularization algorithm for being used.Cause
This, the understanding to ill indirect problem and the understanding to solving are often more even more important than trying to achieve the stable solution of indirect problem merely.This module
It is used as reference by using the Transient electromagnetic response and its corresponding virtual wavelet under homogeneous half space, gives different canonicals
The feature of the solution of change method.In follow-up imaging, it would however be of interest to the peak value moment of the virtual wavelet extracted, therefore
In these regularization methods, the characteristic of the solution obtained using second-order model roughness and using TGSVD more meets imaging needs.
(module 3)：The virtual Seismic imaging of grounded source transient electrical electromagnetic method
This module is imaged on the basis of module 1 and module 2 to grounded source transient electromagnetic field electric field response.In wink
During Electromagnetic Field data are explained, the purpose of imaging is the electrical resistivity property for obtaining underground medium.Under homogeneous half space, virtual wavelet
It is related with the spread speed of virtual time and the resistivity of underground medium.By analyzing biography of the virtual subnet crest value with virtual time
Broadcast the resistivity that speed can be evaluated whether underground medium.In order to use for reference the imaging technique in seismic data process, this module will be based on
The spread speed at the peak value virtual moment of the virtual wavelet extracted is imaged.
Homogeneous half space situation is considered first, and it is 200 Ω m, the homogeneous half space of 500 Ω m that resistivity is calculated respectively
Under, the virtual wavelet that the trailing edge step response produced by unit dipole source excitation is obtained through wave field transformation.Fig. 4 is offset distance
The analytic solutions of virtual wavelet in the range of 1000m to 7000m, Fig. 5 is corresponding numerical solution, and Fig. 4 middle conductors represent what is picked up
The peak value moment of virtual wavelet with offset distance change, the line segment in Fig. 5 in dotted line corresponding diagram 4.Due to it is contemplated herein that be empty
Intend the peak value moment of wavelet, therefore amplitude to the virtual wavelet of Fig. 4 and Fig. 5 has carried out normalized.According to virtual wavelet
The wave equation for being met, it is known that virtually the spread speed of wavelet isIn addition, under homogeneous half space, virtual wavelet
Analytical expression show that the peak value moment of virtual wavelet is equal to
It follows that by calculating transformation relation of the peak value moment with offset distance, you can obtain the propagation speed of virtual wavelet
Degree, and then obtain the resistivity of underground medium.By calculating the partial derivative of the peak value moment to the time of virtual wavelet shown in line segment,
Can obtain the spread speed at virtual subnet crest value moment.Table 1 gives virtual wavelet under the homogeneous half space of different resistivity
Spread speed and corresponding resistivity.
Table 1
As shown in Table 1, under different resistivity situations, the spread speed of the peak value moment by calculating virtual wavelet,
The resistivity of accurate underground medium can be obtained.In low-resistance medium, the spread speed of the peak value moment of virtual wavelet
Smaller, the spread speed at virtual subnet crest value moment is larger in high resistance medium, and this is fast in the diffusion of underground medium with electromagnetic field
The basic law of degree is consistent.
The numerical example
Grounded source transient electromagnetic electric field response imaging method and its application that this patent proposed are illustrated with the numerical example
Effect.Employ two-layer model and three layer model demonstrates the validity of the imaging method that this patent is proposed.
Two-layer model example.Fig. 6 gives the numerical solution of Q types and the virtual wavelet of D pattern types.Virtual wavelet shown in Fig. 6 a by
Parameter is ρ1=50 Ω m, h1=800m, ρ2The transient electromagnetic field response generation of the Q pattern types of=200 Ω m, shown in Fig. 6 b
Virtual wavelet is ρ by parameter1=200 Ω m, h1=800m, ρ2The transient electromagnetic field response life of the D pattern types of=100 Ω m
Into.Figure middle conductor represents the peak value moment of picked up virtual wavelet with the change of offset distance.It is different from homogeneous half space, Q patterns
The line segment picked up under type is divided into two sections.The spread speed for calculating two sections of peak value moments of virtual wavelet by Fig. 6 a is respectivelyWith Corresponding resistivity is calculated for 53.89 Ω m and 208.24 Ω m.By Fig. 6 a
Calculate two sections of peak value moments of virtual wavelet spread speed beWithCorresponding two-layer
The resistivity of model is 200.52 Ω m and 107.79 Ω m.The resistivity being calculated can be good at true with model
Resistivity is coincide.
Three layer model example.Fig. 7 a and Fig. 7 b sets forth the numerical solution of the virtual wavelet of H patterns type and K-type model.H
The parameter of pattern type is ρ1=200 Ω m, h1=800m, ρ2=50 Ω m, h2=200m, ρ3=200 Ω m, K-type model
Parameter is ρ1=50 Ω m, h1=800m, ρ2=500 Ω m, h2=200m, ρ3=50 Ω m.As shown in Figure 7, picked up
The peak value moment of virtual wavelet can be divided into three line segments, the peak of the corresponding virtual wavelet of H pattern types with the conversion of offset distance
The spread speed at value moment is respectivelyWithThe response being calculated
Resistivity be 204.86 Ω m, 53.72 Ω m and 195.52 Ω m.During the peak value of the corresponding virtual wavelet of K-type model
The spread speed at quarter is respectivelyWithThe resistivity being calculated point
Wei not 53.74 Ω m, 488.67 Ω m and 190.52 Ω m.H patterns type is obtained with the resistivity of each layer of K-type model
Preferably recover.It follows that imaging method proposed by the invention the resistivity of underground medium can be carried out more accurately into
Picture.
The above is the preferred embodiment of the present invention, it is noted that for those skilled in the art
For, on the premise of principle of the present invention is not departed from, some improvements and modifications can also be made, these improvements and modifications
Should be regarded as protection scope of the present invention.
Claims (5)
1. a kind of grounded source transient electromagnetic electric field response imaging method, it is characterised in that the described method comprises the following steps：
The derivation of the virtual wavelet analytic solutions of step A grounded source Transient electromagnetic responses；
Step A is specifically included：
Field value is carried out Laplace transform by step A1；
Step A2 carries out nonlinear transformation s=p2, obtain the equivalent expression between wave field and diffusion field；
Step A3 reverse drawing Laplace transforms；
The virtual wave field numerical solution of step B grounded source Transient electromagnetic responses；
The integral equation shown in formula one is carried out first discrete；
Wherein t is the time, and (x, y, z) is space coordinates, and q is referred to as virtual time, and its dimension is s1/2；
Obtain system of linear equations：D=Gm, formula two
Using the system of linear equations of the method solution formula two of regularization, two norms of the model vector of introducing are used as regularization
, and optimal regularization factors are asked for using L-curve method；
The grounded source transient electromagnetic data that step C is based on virtual subnet crest value speed is imaged；
On the basis of step A and step B, grounded source transient electromagnetic field electric field response is imaged, analyzes virtual subnet crest
It is worth the resistivity that underground medium is estimated with the spread speed of virtual time, the peak value based on the virtual wavelet extracted is virtual
The spread speed at moment is imaged.
2. grounded source transient electromagnetic electric field response imaging method as claimed in claim 1, it is characterised in that the step A's
Derivation is specially：
Under homogeneous half space, the axial electric field response produced by unit dipole source excitation is：
Wherein, c2=ρ/μ, μ=4 π 10-7H/m, erf are error function.Order
Then formula three can be expressed as：
To F1T () carries out Laplace transform on time t, obtain
With F1T the Laplace transform of the virtual wave field corresponding to () is：
According to Laplace transform identity
Wherein H represents Heaviside functions, makes a=r/c, and inverse Laplace transform is carried out to formula nine, obtains
To the F in formula six2T () carries out Laplace transform, we obtain
With F2T the Laplace transform of the virtual wave field corresponding to () is：
Inverse Laplace transform is carried out to formula formula 13, can be obtained：
Formula 11 and formula 12 are combined, obtain being parsed with axial electric field under the homogeneous half space represented by formula three
The analytical expression of the virtual wave field corresponding to formula：
Abbreviation, obtains：
3. grounded source transient electromagnetic electric field response imaging method as claimed in claim 1, it is characterised in that in the step B
Discrete being specially is carried out to the integral equation shown in formula one：
Integrating range is expressed as [a, b], using mid-point formula, by its it is discrete be n integration subinterval, the midpoint in each subinterval
It is q1,q2,...,qn, then
Wherein,
Assuming that
Formula one can be with discrete：
Wherein,
Gi,j=G (ti,qj) Δ q formula 21
mj=m (qj) formula 22
Then we can obtain system of linear equations：
D=Gm formula two.
4. grounded source transient electromagnetic electric field response imaging method as claimed in claim 1, it is characterised in that in the step B,
Using singular value decomposition method, the regularization of Tikhonov zeroth orders, single order regularization, block SVD or damping SVD carry out asking for regularization
Solution.
5. grounded source transient electromagnetic electric field response imaging method as claimed in claim 1, it is characterised in that in the step C,
The acquisition methods of resistivity and spread speed are specially：
Homogeneous half space situation is considered first, and it is 200 Ω m that resistivity is calculated respectively, it is single under the homogeneous half space of 500 Ω m
The virtual wavelet that trailing edge step response produced by the dipole source excitation of position is obtained through wave field transformation；
According to the wave equation that virtual wavelet is met, it is known that virtually the spread speed of wavelet isVirtual wavelet
Peak value moment is equal to；
By calculating transformation relation of the peak value moment with offset distance, the spread speed of virtual wavelet is obtained, and then obtain underground Jie
The resistivity of matter, by calculating the partial derivative of the peak value moment to the time of virtual wavelet, obtains the biography at virtual subnet crest value moment
Broadcast speed.
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| CN107422387A (en) * | 2017-06-27 | 2017-12-01 | 吉林大学 | A kind of transient electromagnetic emission source loading method of virtual Fdtd Method |
| CN107526109A (en) * | 2017-08-16 | 2017-12-29 | 桂林电子科技大学 | Transient electromagnetic modeling and inversion method based on virtual wave zone method |
| CN109828307A (en) * | 2019-03-01 | 2019-05-31 | 山东大学 | A kind of detection method of transient electromagnetic multi-frequency fusion and application |
| CN110346834A (en) * | 2019-07-22 | 2019-10-18 | 中国科学院地球化学研究所 | The forward modeling method of three-dimensional frequency domain controllable source electromagnetism, system |
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