CN104777516A - Apparent resistivity calculating method on basis of non-linear equation solution modular form - Google Patents

Abstract

The invention discloses an apparent resistivity calculating method on the basis of a non-linear equation solution modular form. Firstly, a non-linear equation based on a secondary center vertical magnetic field response expression under a transient electromagnetic center loop device is constructed, a sample training function is selected, a function of the non-linear equation is used as an input, a variable of the non-linear equation is used as an output and primary calculation is carried out by an actual measured value; then a solution function is constructed; a neural network structure in a non-linear equation mode is constructed; then according to different measurement characteristics, a calculation result is led into the trained neural network structure to carry out simulation so as to obtain actually measured data; according to set parameters, a calculated value is taken in to obtain an apparent resistivity value corresponding to the actually measured data. The apparent resistivity calculating method simplifies the core step of calculating the apparent resistivity, is easy to program, solves the problem of multiple values or a false value of the apparent resistivity, avoids fuzzy reflection on electrical parameters, can rapidly realize processing on the transient electromagnetic actually-measured data and provides the good apparent resistivity calculation basis for transient electromagnetic rapid imaging.

Description

Based on the computation of apparent resistivity method of Solving Nonlinear Equation modular form

Technical field

The present invention relates to the computation of apparent resistivity method, particularly a kind of computation of apparent resistivity method based on nonlinear equation modular form of transient electromagnetic method under Genter loop device.

Background technology

Transient electromagnetic method detects, send periodically with the pulsed electromagnetic signal turned off fast by transmitter, and gather by receiving trap the secondary field response signal that detected target body responds to, and be containing the magnetic induction of geological information parameter to time rate of change, namely induction electromotive force.To secondary field response signal Integral Processing, obtain secondary central vertical magnetic field, then utilize fast imaging instrument to solve to obtain the apparent resistivity value of the Electrical distribution information of different depth.Apparent resistivity is not real resistivity, the approximate substitution just to true resistance rate, and the electric characteristic abnormality in approximate representation true resistance rate reflection objective body and perimeter detection region and difference, use symbol ρ _srepresent, the same resistivity of unit is Ω m.In transient electromagnetic method, apparent resistivity is used to the electrical parameter reflecting detected target body, carries out apparent resistivity solve difference and the change that intuitively can reflect electric conductivity to whole search coverage.Because the Electrical distribution of search coverage is uneven, under same transient Electro-magnetic Launcher System and measurement mechanism, the resistivity that the response produced at synchronization is identical with the transient field response measurement value of homogeneous conductive half space is called apparent resistivity value.

The calculating of transient electromagnetic apparent resistivity mostly adopts defined formula in early stage or late period, easy, but mid-term, computation of apparent resistivity error was too large; The second is that utilize numerical method to ask for the inverse function of homogeneous half space transient response, solved by numerical radius or inversion iterates, common method has relative method, bisection method and Newton method etc. with step response iterative computation apparent resistivity.

In numerical computation method, it is compare effective method that FORWARD AND INVERSE PROBLEMS calculates, its process is: carry out forward modelling secondary field response by setting different-thickness different resistivity value, parameter is constantly revised in the basis of just drilling, constantly just drill iteration, until compare with the data that reality receives, final error meets the error range set, and just can jump out the circulation of iteration.The deficiency of this method is, first worker will have abundant geology detecting experience, can provide comparatively reasonably initially layer parameter in conjunction with image data, otherwise the calculated amount in later stage will be very large, and whole computation process can consume the plenty of time.This method be not fast imaging be satisfied with solution, object fast can not be reached.

The complicacy that FORWARD AND INVERSE PROBLEMS calculates has influence on the efficiency of later stage calculating, and scholars, by the response expression formula of homogeneous half space under calculating different device, derive and calculate apparent resistivity, save computing time, can obtain geologic anomaly distribution fast by measured value; The method calculating apparent resistivity with step response iterative algorithm has relative method, bisection method, Newton method etc., reach the object of saving computing time, but still do not have the tangible problem improving counting yield, data can not be received by actual measurement and obtain apparent resistivity value real-time.

The counterpropagation network computing method of apparent resistivity: build the definition of rate of change expression formula Kernel Function in time of secondary magnetic field under Genter loop device and apparent resistivity solved function, with kernel function value be input, the anti-coaching method that exports of transient parameters calculates apparent resistivity.The kernel function of secondary magnetic field in time in rate of change expression formula is two-valued function, and occurs without separating phenomenon in some codomain, solves apparent resistivity value and also there is demarcation interval or without the situation of separating, solve apparent resistivity complication like this.

Summary of the invention

Object of the present invention is just to provide a kind of computation of apparent resistivity method based on nonlinear equation modular form, adopt and build nonlinear equation and neural network structure, bring measured data again into calculate, solve the method obtaining apparent resistivity corresponding to given time, simplify the core procedure calculating apparent resistivity, be easy to programming, save computing time, efficiency is high, solve the many-valued or falsity problem of apparent resistivity, avoid the fuzzy reflection to electrical parameter, and the process of transient electromagnetic measured data can be realized fast, good computation of apparent resistivity basis is provided to transient electromagnetic fast imaging.

The object of the invention is by such technical scheme realize, it includes following concrete steps:

1) build the nonlinear equation under transient electromagnetic Genter loop device based on secondary central vertical magnetic responsiveness expression formula, carry out primary Calculation by measured data;

2) according to built nonlinear equation, the function solving the corresponding apparent resistivity of measured data is built;

3) under the nonlinear equation pattern set up, neural network structure is built;

4) bringing in the neural network structure built by solving the functional value obtained, after emulating, obtaining the variate-value that measured data is corresponding;

5) according to the emitter parameter arranged and receiving trap parameter, bring the variate-value of trying to achieve into, obtain the apparent resistivity value that measured data is corresponding.

Further, step 1) described in the detailed process of the nonlinear equation of structure under transient electromagnetic Genter loop device based on secondary central vertical magnetic responsiveness expression formula as follows:

1-1) by following formula by measured data induced voltage V _zt () converts secondary central vertical magnetic field B to _z(t):

$B_z\left(t\right)=-\frac{1}{\mathrm{Sn}}{\∫}_t^{t_N}{V}_Z\left(t\right)\mathrm{dt}---\left(1\right)$

Wherein, S represents the useful area receiving wire frame, and n represents coil turn, t _nrepresent the last sampling time, t represents the die-away time of secondary field;

1-2) the secondary central magnetic field after conversion is write as the expression formula of nonlinear equation pattern, under Genter loop device, secondary magnetic field vertical direction component B _znonlinear equation expression formula is:

$B_Z\left(t\right)=\frac{\mathrm{I\μ}}{2a}[\frac{3}{\sqrt{\mathrm{\π}}Z}{e}^{{-Z}^2}+(1-\frac{3}{2Z^2})\mathrm{erf}\left(Z\right)]---\left(2\right)$

Wherein: $Z=a/2\sqrt{\mathrm{\μ}/\mathrm{\ρt}},\mathrm{erf}\left(Z\right)=\frac{2}{\sqrt{\mathrm{\π}}}{\∫}_0^Z{e}^{-t^2}\mathrm{dt}---\left(3\right)$

In above formula, B _zrepresent the magnetic induction density of vertical direction, I represents transmitter current value, and ρ represents apparent resistivity value, and a represents transmitting wire frame radius, and t represents the die-away time of secondary field, and erf (u) represents error function, μ ≈ 4 π × 10 ^-7h/m represents permeability of vacuum;

1-3) by magnetic induction density B _zexpression formula be rewritten into following nonlinear equation pattern, and by item on the right of expression formula

$\frac{1}{u^2}[\frac{3u}{\sqrt{\mathrm{\π}}}{e}^{-u^2}+(u^2-\frac{3}{2})\mathrm{erf}\left(u\right)]---\left(4\right)$

Be defined as about independent variable u function Y (u), expression formula is as follows:

$\frac{B_{Z}2a}{\mathrm{I\μ}}=Y\left(u\right)=\frac{1}{u^2}[\frac{3u}{\sqrt{\mathrm{\π}}}{e}^{{-u}^2}+(u^2-\frac{3}{2})\mathrm{erf}\left(u\right)]---\left(5\right)$

Measured data is brought into and carries out primary Calculation, about the nonlinear equation of variable u when obtaining t die-away time.

Further, based on constructed nonlinear equation, the pad value of the secondary vertical magnetic field of given attenuation initiation t, the functional procedure solving this moment apparent resistivity ρ value of structure is:

First constructing nonlinear equation is:

$f\left(u\right)=\frac{1}{u^2}[\frac{3u}{\sqrt{\mathrm{\π}}}{e}^{{-u}^2}+(u^2-\frac{3}{2})\mathrm{erf}\left(u\right)]-\frac{B_{Z}2a}{\mathrm{I\μ}}=Y\left(u\right)-\frac{B_{Z}2a}{\mathrm{I\μ}}---\left(6\right)$

Bring measured data into calculate because Y (u) is only containing variable u, then equally only contains variable u in f (u), make f (u)=0, variable u value can be solved, then in conjunction with following formula, calculate corresponding apparent resistivity ρ value:

$\mathrm{\ρ}\left(t\right)=\frac{a^2\mathrm{\μ}}{{4\mathrm{tu}}^2}---\left(7\right)$

Further, under the nonlinear equation pattern built, neural network structure is built:

3-1) select effective sample data, according to the device parameter of the electrical property feature electrical resistivity range of detected target thing and transmitting, receiving system, determine that variable u span is [10 ^-3, 200];

3-2) by determining that the variable u value of span brings nonlinear equation expression formula (6) into, obtain the value of function Y (u) corresponding to variable u value;

3-3) select three layers of BP network, wherein hidden layer unit number is 10, then selects training algorithm to train selected network.

Further, the value of tried to achieve function Y (u) is brought in the neural network structure built, after emulating, obtain the value of the unknown variable u corresponding to function Y (u).

Further, the described value solving variable u, is characterized in that, according to the device parameter of transmitting, receiving system, brings tried to achieve variable u value into in formula (7), calculates the value of the apparent resistivity ρ corresponding to measured data.

Further, a kind of described computation of apparent resistivity method based on Solving Nonlinear Equation modular form, it is characterized in that, described measured data value is as follows:

Transmitter current value is 1.224A; Launching wire frame radius is 1.6m; Receiving coil area is 6m ²; Receiving secondary field section die-away time is Non uniform sampling, and sample range is 0.205 μ s-1.517ms;

Selected colleges and universities bombproof is measured, obtain measurement data: at Z=-4m place, there is a block high resistant object, length is 4m, 4m, 2m, and transmitting coil is at Z=0 place, and radius is 0.302m, oblique band jumps current excitation, amplitude is 16A, and the turn-off time is 25 μ s, and sampling time interval is 10 μ s.

Owing to have employed technique scheme, the present invention has following advantage:

(1) construct secondary central magnetic field about the nonlinear equation solving variable u, make solution apparent resistivity become the root asking nonlinear equation, thus simplify computation process.

(2) secondary central magnetic field is single-valued function about the nonlinear equation solving variable u, overcomes the phenomenon occurring without separating in some codomain.

(3) train the network obtained to be single-input single-output, make whole training process simple and easy to control.

(4) replace numerical calculations with network after training, computation process is simplified, programming is easy to realize.

(5) the parallel organization processing feature that has of neural network, makes greatly shorten computing time.

Other advantages of the present invention, target and feature will be set forth to a certain extent in the following description, and to a certain extent, based on will be apparent to those skilled in the art to investigating hereafter, or can be instructed from the practice of the present invention.Target of the present invention and other advantages can be realized by instructions below and claims and be obtained.

Accompanying drawing explanation

Accompanying drawing of the present invention is described as follows.

Fig. 1 is structural representation of the present invention.

Fig. 2 is secondary field vertical direction component B _znonlinear equation in function about the change curve of variable u.In figure: Y ₁u () is secondary field vertical direction component B _znonlinear equation in function about the function of variable u; U is the variable in nonlinear equation.

When Fig. 3 is neural metwork training frequency of training and error reduce between graph of a relation.In figure: horizontal ordinate is frequency of training; Ordinate is the error in trained formula.

Fig. 4 is the enforcement illustration calculating single measuring point.In figure: the apparent resistivity value of depth corresponding to the time delays that horizontal ordinate responds for secondary field; The degree of depth is looked corresponding to the time delays that ordinate responds for secondary field.

Fig. 5 is the enforcement illustration that application neuron network simulation calculates total data.In figure: space level point position when horizontal ordinate is measurement; Ordinate is the apparent resistivity value of application neural computing.

Embodiment

Below in conjunction with drawings and Examples, the invention will be further described.

Technical scheme of the present invention is that step is carried out in the following order:

1, import the data received, the inductive voltage value under Genter loop device, calculate by actual measurement inductive voltage value the B that secondary responds to vertical magnetic field _z, application expression formula

2, vertical magnetic field B is responded to by the secondary calculated _zy (u) value that value is corresponding, comprises the device parameter of Genter loop: transmitting loop radius a, transmitter current I, substitutes into formula calculate;

3, training network is constructed;

(1) as shown in Figure 2, using the one-to-one relationship between Y (u) and u as training sample, effective sample data is selected; Be [10 according to the electrical property feature electrical resistivity range of institute's detecting objects ^-3~ 10 ³Ω m] and the device parameter transmitting coil radius of emitting-receiving system be 0.302m and sampling time interval 10 ^-6s, in conjunction with determine that u value scope is [10 ^-3, 200].

(2) value of function Y (u) corresponding to u value is obtained above the u value determined substitutes into about the nonlinear equation of independent variable u sum functions Y (u).To u value equal interval sampling, such as, sample 4000, getting wherein 3700 calculating Y (u) values is input, and corresponding u value, for output is as training sample, remains 300 and builds training network as test sample book neural metwork training.

(3) compare training error situation, with less error for standard determination hidden layer unit number, the implicit number of plies of change is trained respectively, and to determine hidden layer unit and to select corresponding training algorithm to train, little with error, training pace is standard less.

(4) select three layers of BP neural network, hidden layer unit number 10, select the civilian Burger-Ma quart training algorithm of row to train network.

4, by step 2 calculate in the neural network trained in steps for importing 3, emulation obtains the value of variable u.

5, obtaining variate-value u in step 4, to each sampling time point t, substitute into in, calculate apparent resistivity value ρ.

The Matlab function list selected during table 1 training network

The trial training that table 2 does when determining hidden layer unit number and convergence knot

Table 3 with the simulation result with similarity method to when parameter information slip

What finally illustrate is, above embodiment is only in order to illustrate technical scheme of the present invention and unrestricted, although with reference to preferred embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that, can modify to technical scheme of the present invention or equivalent replacement, and not departing from aim and the scope of the technical program, it all should be encompassed in the middle of right of the present invention.

Claims (7)

1., based on a computation of apparent resistivity method for Solving Nonlinear Equation modular form, it is characterized in that, concrete steps are as follows:

1) build the nonlinear equation under transient electromagnetic Genter loop device based on secondary central vertical magnetic responsiveness expression formula, carry out primary Calculation by measured data;

2) according to built nonlinear equation, the function solving the corresponding apparent resistivity of measured data is built;

3) under the nonlinear equation pattern set up, neural network structure is built;

4) bringing in the neural network structure built by solving the functional value obtained, after emulating, obtaining the variate-value that measured data is corresponding;

5) according to the emitter parameter arranged and receiving trap parameter, bring the variate-value of trying to achieve into, obtain the apparent resistivity value that measured data is corresponding.

2. a kind of computation of apparent resistivity method based on Solving Nonlinear Equation modular form as described in claim 1, it is characterized in that, step 1) described in the detailed process of the nonlinear equation of structure under transient electromagnetic Genter loop device based on secondary central vertical magnetic responsiveness expression formula as follows:

1-1) by following formula by measured data induced voltage V _zt () converts secondary central vertical magnetic field B to _z(t):

Wherein, S represents the useful area receiving wire frame, and n represents coil turn, t _nrepresent the last sampling time, t represents the die-away time of secondary field;

1-2) the secondary central magnetic field after conversion is write as the expression formula of nonlinear equation pattern, under Genter loop device, secondary magnetic field vertical direction component B _znonlinear equation expression formula is:

In above formula, B _zrepresent the magnetic induction density of vertical direction, I represents transmitter current value, and ρ represents apparent resistivity value, and a represents transmitting wire frame radius, and t represents the die-away time of secondary field, and erf (u) represents error function, μ ≈ 4 π × 10 ^-7h/m represents permeability of vacuum;

1-3) by magnetic induction density B _zexpression formula be rewritten into following nonlinear equation pattern, and by item on the right of expression formula

Be defined as about independent variable u function Y (u), expression formula is as follows:

Measured data is brought into and carries out primary Calculation, about the nonlinear equation of variable u when obtaining t die-away time.

3. build the nonlinear equation under transient electromagnetic Genter loop device based on secondary central vertical magnetic responsiveness expression formula as claimed in claim 2, it is characterized in that, based on constructed nonlinear equation, the pad value of the secondary vertical magnetic field of given attenuation initiation t, the functional procedure solving this moment apparent resistivity ρ value of structure is:

First constructing nonlinear equation is:

Bring measured data into calculate because Y (u) is only containing variable u, then equally only contains variable u in f (u), make f (u)=0, variable u value can be solved, then in conjunction with following formula, calculate corresponding apparent resistivity ρ value:

4. structure as claimed in claim 3 solves apparent resistivity function corresponding to attenuation initiation t, it is characterized in that, under the nonlinear equation pattern built, builds neural network structure:

3-1) select effective sample data, according to the device parameter of the electrical property feature electrical resistivity range of detected target thing and transmitting, receiving system, determine that variable u span is [10 ^-3, 200];

3-2) by determining that the variable u value of span brings nonlinear equation expression formula (6) into, obtain the value of function Y (u) corresponding to variable u value;

3-3) select three layers of BP network, wherein hidden layer unit number is 10, then selects training algorithm to train selected network.

5. the neural network structure under structure nonlinear equation pattern as claimed in claim 4, it is characterized in that, the value of tried to achieve function Y (u) is brought in the neural network structure built, after emulating, obtain the value of the unknown variable u corresponding to function Y (u).

6. solve the value of variable u as claimed in claim 5, it is characterized in that, according to the device parameter of transmitting, receiving system, bring tried to achieve variable u value into in formula (7), calculate the value of the apparent resistivity ρ corresponding to measured data.

7. a kind of computation of apparent resistivity method based on Solving Nonlinear Equation modular form as claimed in claim 1, it is characterized in that, described measured data value is as follows:

Transmitter current value is 1.224A; Launching wire frame radius is 1.6m; Receiving coil area is 6m ²; Receiving secondary field section die-away time is Non uniform sampling, and sample range is 0.205 μ s-1.517ms;

Selected colleges and universities bombproof is measured, obtain measurement data: at Z=-4m place, there is a block high resistant object, length is 4m, 4m, 2m, and transmitting coil is at Z=0 place, and radius is 0.302m, oblique band jumps current excitation, amplitude is 16A, and the turn-off time is 25 μ s, and sampling time interval is 10 μ s.