CN101706586A - Computing method for time-domain apparent resistivity - Google Patents

Abstract

The invention discloses a computing method for time-domain apparent resistivity, which makes uses of the induced electromotive force data of two components of x and z to compute apparent resistivity in a united way. Because any induced electromotive force data of a single component is a double valued function of the apparent resistivity, the apparent resistivity value is difficult to determine; therefore, the invention defines an amplitude ratio computing method of sampled data in two fixed intervals of the induced electromotive force of the two components x and z, wherein the theoretical amplitude ratio data obtained according to the definition and observed ratio data are in a relationship of a single valued function so that apparent resistivity of induced electromotive force data is determined accurately. Simultaneously, in order to improve a computing speed to meet the requirement on the explanation of aeronautical transient electromagnetic data, the invention adopts the computing method of data query and local transect interpolation, and thus, the method has extremely fast computing speed, accurate result, and stability and reliability.

Description

A kind of computing method of time-domain apparent resistivity

Technical field

The present invention relates to a kind of computing method of time-domain apparent resistivity, belong to time domain aviation electromagnetic data processing method category.

Background technology

The aviation electromagnetic method is a kind of geophysical exploration method fast and efficiently, is bringing into play important effect in investigation of reconnaissance geological survey, mineral resources and the aspects such as regional prospecting that can't carry out the ground investigation and prospecting.Because the time domain aviation electromagnetic method has the advantage that efficient is higher, resolution is higher with respect to frequency field aviation electromagnetic method, therefore time domain aviation transient electromagnetic method obtains paying attention to day by day in recent years, and the research of aviation transient electromagnetic DATA PROCESSING interpretation procedure also becomes focus.China's up to the present also not free territory airborne electromagnetic system, the research of handling interpretation procedure also is blank, no matter is that technical method or fundamental research all fell behind world level at least 30 years.Thankfully China has been listed the aviation transient electromagnetic among " 863 " major project in Eleventh Five-Year Plan, and relevant research also launches rapidly, therefore presses for new theoretical method and technological innovation.

At present, aeroelectromagnetic explanation is still with dimension solutions and is interpreted as the master, adopts the distribution of conductivity of the underground section of the survey line of inversion imaging technical interpretation flight fast correspondence more.Most inversion imaging methods need be calculated the apparent resistivity data, specifically are that measured data is converted to the apparent resistivity data, by the inversion imaging method apparent resistivity data interpretation are become the resistivity profile data of geoelectric cross section, thus the interpretation process of finishing.Good apparent resistivity computing method can make inversion interpretation become easily, and inversion result is also more accurate, therefore need the computing method of a kind of effective apparent resistivity of research.With respect to ground transient electromagnetic method, the aviation electromagnetic method has characteristics such as the measurement data amount is big, data quality is lower, theoretical defects is more outstanding makes that its difficulty of inversion interpretation is bigger, needs special interpretation procedure.Aviation transient electromagnetic method is had relatively high expectations to processing speed, and the measurement data of magnanimity needs processing speed faster, is difficult to be competent at by ground transient electromagnetic disposal route.On the other hand, relative ground transient electromagnetic method, the difficulty in computation of the apparent resistivity of aviation transient electromagnetic increases greatly, as in the loop line transient electromagnetic method of center, ground, the induced electromotive force response of homogeneous half space model all can be provided by analytic formula, thereby the calculating of apparent resistivity can obtain by dual mode: first kind is to obtain early according to analytic formula, the field in late period concern with the explicit function of ground electrical quantity and obtain respectively in early days and late period apparent resistivity analytical expression (Kafman A.A.and Keller G.V., 1983), or more further early, be similar to synthetic approximate omnidistance apparent resistivity late period; Or carry out deep derivation by the analytical expression of transient electromagnetic field in the homogeneous half space, obtain the transient response curve and have the translation expansion performance with underground conductivity, the transmitting loop length of side and observation time, and a kind of method (Wang Huajun, 2008) of new direct calculating APPARENT RESISTIVITY proposed in view of the above; Second method is according to analytical expression numerical evaluation apparent resistivity (WardS.H.and Hohmann G.W., 1987), and numerical evaluation can adopt Series Expansion Method (Spies B.R.and Raiche A.P., 1980; Piao Huarong, 1990) or iterative algorithm (Raiche A.P., 1981; ).After this, utilize alternative manner match observed reading and theoretical value method to calculate apparent resistivity and be widely used (Yang Sheng, 1986; Chiristensen N.B., 1995); Bai Denghai etc. (2003) combine the advantage of two kinds of methods, determined early stage turning point according to analytic formula and with the method for iteration to apparent resistivity exact value in late period, yet thereby obtain a complete omnidistance apparent resistivity curve. for aviation transient electromagnetic method, because the Hankel infinite integral formula in the induced electromotive force computing formula can not be resolved the Integral Solution that obtains it, thereby it is not early stage yet, the field in late period and the explicit function relational expression of location parameters, so can't calculate apparent resistivity value with first kind method, also make numerical method calculate apparent resistivity and become very complicated, computing velocity is very slow, do not meet the actual requirement of aviation transient electromagnetic, so relevant aviation transient electromagnetic apparent resistivity definition method is very limited, Huang Haoping (1983) supposition induced electromotive force response attenuation curve under log-log coordinate is a straight line, with least-squares linear regression method iterative optimization method, the theoretical response curve of measured data and certain homogeneous half space model is carried out match, yet the homogeneous half space resistivity value that obtains is as apparent resistivity., aviation electromagnetic is measured the induced electromotive force data has two to separate the response of satisfying the field usually, and obviously result of calculation can not guarantee to provide correct value.

Summary of the invention

The object of the present invention is to provide that a kind of computing velocity is fast, precision is high, and the computing method of having only the time-domain apparent resistivity of unique solution, this method is applicable to the time domain aviation electromagnetic one dimension, intend two dimension, intend that three-dimensional apparent resistivity is directly explained and inversion interpretation in the calculating of apparent resistivity, can make that inversion interpretation becomes easier, inversion result is more accurate.

For achieving the above object, the method that the present invention adopts may further comprise the steps:

(1) calculates two component amplitude ratio observation datas

Two induced electromotive force component data Vx, Vz by actual measurement calculate corresponding each explanation T constantly _k=(t _k+ t _K+nkThe amplitude ratio data of)/2:

Described k=1,2 ..., n-nk, n are the sampling time number;

(2) calculate two component amplitude ratio data question blanks

Given m discretize inquiry resistivity data ρ _i ⁰, it respectively as the resistivity value of homogeneous half space, is calculated its two component aviation Transient electromagnetic response V earlier _x ⁰, V _z ⁰, calculate the theoretical data query body of two component ratios again

Described i=1,2 ..., m; K=1,2 ..., n-nk, n are the sampling time number;

(3) calculate apparent resistivity value

Explain T constantly with each _kTwo corresponding component amplitude ratio data A ⁰(ρ _i, T _k) as the single-valued function relation of resistivity, calculate actual measurement two component amplitude ratio data A (T with the method for local spline interpolation _k) corresponding resistivity value, be k the apparent resistivity value of being asked of explaining the moment, calculate n-nk one by one and explain T constantly _kApparent resistivity value, promptly finished the calculating of the apparent resistivity of aviation transient electromagnetic, described i=1,2 ..., m; K=1,2 ..., n-nk, n are the sampling time number.

The present invention utilizes amplitude ratio of induced electromotive force response data definition of homogeneous half space x, z component, it is the principle of the single-valued function of homogeneous half space resistivity, with observation data as variable, the method of the homogeneous half space resistivity by the interpolation calculation correspondence obtains aeroelectromagnetic apparent resistivity.

Principle of the present invention is as follows:

As the evenly overhead greatly airborne electromagnetic system of Fig. 1, the emission vertical magnetic dipole is ht apart from being M apart from floor level, and the receiving coil height is hr, and the level transmitting-receiving is apart from being r, and the receiving coil useful area is Sr, and n sampling time is respectively t _k, k=1,2 ..., n.

The homogeneous half space resistivity of supposing discretize is ρ _i ⁰, i=1,2 ..., m, then the x of the homogeneous half space model of each resistivity value correspondence, the response of z component aviation transition induced electromotive force are:

$V_x({\mathrm{\&rho;}}_{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="H2009102165281E0000012.png"\; state="\{\{state\}\}">i</figure-callout>}}^0,t_k)=-{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="4"\; label="S\; r\; M"\; filenames="H2009102165281E0000012.png"\; state="\{\{state\}\}">S</figure-callout>}}_r\frac{M}{}\frac{}{4\mathrm{\&pi;}}{L}^{-1}\left\{{\&Integral;}_0^{\&infin;}\right[e^{-\mathrm{\&lambda;}(\mathrm{ht}-\mathrm{hr})}-\frac{\mathrm{\&lambda;}-u}{\mathrm{\&lambda;}+u}{e}^{-\mathrm{\&lambda;}(\mathrm{ht}+\mathrm{hr})}\left]{\mathrm{\&lambda;}}^2{J}_1\left(\mathrm{\&lambda;r}\right)\mathrm{d\&lambda;}\right\}---\left(1\right)$

$V_z({\mathrm{\&rho;}}_{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="H2009102165281E0000012.png"\; state="\{\{state\}\}">i</figure-callout>}}^0,t_k)=-{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="4"\; label="S\; r\; M"\; filenames="H2009102165281E0000012.png"\; state="\{\{state\}\}">S</figure-callout>}}_r\frac{M}{}\frac{}{4\mathrm{\&pi;}}{L}^{-1}\left\{{\&Integral;}_0^{\&infin;}\right[e^{-\mathrm{\&lambda;}(\mathrm{ht}-\mathrm{hr})}-\frac{\mathrm{\&lambda;}-u}{\mathrm{\&lambda;}+u}{e}^{-\mathrm{\&lambda;}(\mathrm{ht}+\mathrm{hr})}\left]{\mathrm{\&lambda;}}^2{J}_0\left(\mathrm{\&lambda;r}\right)\mathrm{d\&lambda;}\right\}---\left(2\right)$

Wherein, μ ₀Be permeability of vacuum,

κ is a wave number, satisfies

L ^-1Be inverse laplace transform, J ₀And J ₁Be respectively the first kind 0 rank and 1 rank Bessel's function.In the computation process, adopt numerical filter algorithm (Guptasarm, 1997) calculating Hankel conversion wherein; Inverse laplace transform is wherein calculated by Gaver-Stehfest probability transformation algorithm (being called for short the G-S converter technique, Knight, 1982).

Given aeroelectromagnetic x, z two weight sense motional electromotive force response time sequence ε _x, ε _zAfter, T is constantly explained in definition _k=(t _k+ t _K+nk)/2, (k=1,2 ..., two component amplitude in the time of n-nk) are than value function, and it is resistivity and T _kFunction:

$F_A(\mathrm{\&rho;},T_k)=\frac{\sqrt{{\mathrm{\&epsiv;}}_x^2(\mathrm{\&rho;},t_k)+{\mathrm{\&epsiv;}}_x^2(\mathrm{\&rho;},t_{k+\mathrm{nk}})}}{\sqrt{{\mathrm{\&epsiv;}}_z^2(\mathrm{\&rho;},t_k)+{\mathrm{\&epsiv;}}_z^2(\mathrm{\&rho;},t_{k+\mathrm{nk}})}}---\left(3\right)$

Press the definition of following formula, calculate each by two weight sense motional electromotive force observation data Vx, Vz and explain T constantly _kThe time two component amplitude ratio observation datas:

(k＝1，2，…，n-nk)，(4)

With the observation data of A when calculating apparent resistivity.Know that by (1), (2) and (4) ratio calculation causes apparent resistivity value that the present invention obtains and emission magnetic moment, receiving coil area irrelevant, this method with the obvious advantage.

Equally, calculate two component amplitude, be used for the apparent resistivity data computing than theoretical data query.It is calculated by (3) formula by aviation transition x, the z component response data of the homogeneous half space of different resistivity.Resistivity value wherein is chosen in the general ground resistivity value scope, and adopts that logarithm is equally spaced discrete to be m value, calculates two weight sense motional electromotive force V of this m resistivity correspondence successively _x ⁰, V _z ⁰, and calculate n-nk and explain that two component amplitude in the moment are than theoretical data query:

(i＝1，2，…，m；k＝1，2，…，n-nk) (5)

A0 is kept in the two-dimensional array, can repeatedly uses it and ask apparent resistivity.

Now consider single induced electromotive force data V respectively _x ⁰, V _z ⁰With with two components associatings data A ⁰, study the funtcional relationship of they and resistivity value.Suppose that underground medium is three layers of medium, resistivity is respectively 50 ohm meters, 30 ohm meters and 50 ohm meters, and last two layers of thickness is 50 meters, and the aircraft flight height is 120 meters, and emission is the step pulse signal down, and the emission magnetic moment is 300,000 Am ², the receiving coil useful area is 100 square metres, and height off the ground is 70 meters, and the dispatch coil level is apart from being 100 meters, and time-delay 0.01ms begins sampling, and in totally 28 sampling times, the time interval number nk that adopts when calculating apparent resistivity is taken as 3.Fig. 2 explains induced electromotive force data constantly and the function curve between the resistivity with each, and wherein figure (a), figure (b) and figure (c) are respectively each and explain V constantly _x ⁰, V _z ⁰And A ⁰With the function relation curve collection of resistivity, as seen, single induced electromotive force data V _x ⁰, V _z ⁰And between the resistivity two-valued function relation, and A ⁰And between the resistivity single-valued function relation.So, be monodrome with two weight sense motional electromotive force amplitude ratio data separating of carrying out that apparent resistivity inquiry obtains, thus can according to the observation data monodrome obtain apparent resistivity value.

According to above-mentioned thinking, by two component amplitude ratio observation data A and theoretical lookup table data A ⁰, each is explained corresponding constantly data, inquire about, search for each apparent resistivity value successively.The traversal queries A of elder generation ⁰Two component amplitude ratio theoretical values of each resistivity value correspondence of tables of data correspondence, compare with the two component amplitude ratio observed readings of corresponding explanation during the moment among the data A, if both equate, just the resistivity value of correspondence is explained apparent resistivity value constantly as this, if do not equate, then search is near the pairing resistivity value ρ of the theoretical data query of observation data _p ⁰, use ρ _p ⁰And the theoretical data query sequence formation of the two component amplitude ratios discrete function corresponding relation of near several inquiry resistivity value sequences and their correspondences, carry out the local spline search, obtain the apparent resistivity value ρ of two component amplitude ratio observation value correspondences _p ^sFormulate is as follows with calculating:

To p=1 arbitrarily, 2 ..., m, (6)

Wherein, ρ _p ^sBe according to the local funtcional relationship between the theoretical data query of inquiry resistivity value when explaining Ti constantly, obtain the apparent resistivity value of observation data correspondence with spline interpolation, with inquiring about ρ in the resistivity sequence _P0 ⁰Front and back are nn=k2-k1+1 inquiry resistivity value (ρ altogether _K1 ⁰, ρ _K1+1 ⁰..., ρ _P0 ⁰..., ρ _K2 ⁰) as the theoretical Query Value (A of two corresponding with it component ratios _K1 ⁰, A _K1+1 ⁰..., A _K2 ⁰) funtcional relationship and the resistivity value that obtains with spline interpolation, and

Np is given parameter, and the resistivity value sequence that the local spline interpolation is calculated in expression is positioned at the inquiry electricalresistivity _P0 ⁰Number before and after the value, it is excessive that it can not select, otherwise can cause calculated amount to increase, also meaningless to result of calculation, all is taken as 9 in the example calculation that the present invention uses.

Fig. 3 is for calculating apparent resistivity curve by the response data of a three layer model as stated above.

As seen from the figure, early stage reflection ground floor resistivity of media 50 ohm meters, subsequently, being subjected to second layer resistivity is the influence of the low resistivity zone of 30 ohm meters, apparent resistivity diminishes, reach minimum 36.8 ohm meters after, be subjected to the influence of the basalis of 50 ohm meters again, apparent resistivity value increases again gradually, meets truth.In order to investigate the apparent resistivity result of calculation of more complex layered medium, Fig. 4 provides the apparent resistivity curve comparison diagram of the RESPONSE CALCULATION of 7 kinds of three layer models, be denoted as the layer resistivity of three layer model among the figure, the preceding two layers of thickness of model is 50 meters, and other parameter is with the corresponding parameter of Fig. 3.The fluctuations of each apparent resistivity curve is all consistent with true model resistivity layer Changing Pattern, all near the true resistance rate, wherein, resistivity is that 50/150/150 ohm meter and 50/10/10 ohm meter are actually two layer medium, the initial stage apparent resistivity value is ground floor resistivity of media 50 ohm meters, along with the time increases, apparent resistivity is respectively near layer dielectric resistivity---150 ohm meters or 10 ohm meters, and when three layers of resistivity of media are 50 ohm meters, also be the homogeneous half space model, its apparent resistivity is a true resistance rate value, meets general resistivity definition requirement.Fig. 5 is the apparent resistivity curve of the RESPONSE CALCULATION of more complicated multi-layered media, has represented the layer resistivity value among the figure, and each layer thickness is 50 meters, and the result has also all shown the vertical situation of change of resistivity on stratum with higher resolution capability ground.Obvious, the apparent resistivity that the two component amplitude ratio query methods that propose with the present invention calculate does not have multi-solution, the resolution capability height, and computing velocity is fast.

Core of the present invention is: (1) uses the induced electromotive force of x, two components of z to calculate apparent resistivity; (2) calculate apparent resistivity with the observation data that is the time road of nk indirectly; (3) ratio by the amplitude of two time road response datas of two components defines two component amplitude ratios, calculates two component amplitude than observation data with by the two component amplitude ratios theory data query of a series of resistivity data query correspondences by observation data respectively according to this definition; (4) explain corresponding constantly theoretical data query and the relation of the single-valued function between the resistivity, each explains corresponding constantly apparent resistivity value with the local spline interpolation calculation according to each. based on These characteristics, the present invention has following advantage:

(1) owing to made full use of the aviation electromagnetic metrical information of two components, therefore the underground medium information that obtains than any one independent induced electromotive force component is more abundant, thereby makes that the apparent resistivity value that finally calculates is more accurate;

(2) owing to adopt at interval the induced electromotive force amplitude ratio data in two time roads of nk to calculate apparent resistivity, therefore than directly with the easier stable data noise of induced electromotive force data computation apparent resistivity of a moment point;

(3) any simple component induced electromotive force data are the two-valued function of resistivity, and the apparent resistivity that obtains has two values in theory, when two resistivity values near the time, be difficult to determine which be selected; And be the single-valued function of resistivity with two component amplitude of uniting definition of two weight sense motional electromotive force data than value function, can overcome above-mentioned defective, make the calculating of apparent resistivity become easier;

(4) owing to adopt data query, local data's interpolation method to calculate apparent resistivity, so computing velocity is fast, and can obtain global optimum, meets the requirement of aviation transient electromagnetic, makes the in-flight possibility that is treated as in real time of aviation electromagnetic;

(5) can be used for various aviation transition system, it is more obvious especially the apparent resistivity of complex dielectrics to be calculated effect.

Description of drawings

Fig. 1 is evenly overhead greatly airborne electromagnetic system synoptic diagram.

Fig. 2 inscribes Vx, Vz and two component amplitude ratio A and the relation curve of inquiring about resistivity for each when explaining.Wherein figure (a) represents x sense of direction motional electromotive force component and the relation curve of inquiring about resistivity; Figure (b) expression z sense of direction motional electromotive force component and the relation curve of inquiring about resistivity; Figure (c) expression is by the two component amplitude ratios of x, z sense of direction motional electromotive force component combined calculation and the relation curve of inquiry resistivity.

Fig. 3 is for being the apparent resistivity curve of theoretical response data computation that 50-30-50 ohm meter, preceding two layers of thickness are the three layer model that is 50 meters by resistivity.

Fig. 4 is 7 kinds of differently apparent resistivity curve comparison diagrams of the theoretical response data computation of the three layer model of electrical quantity, has indicated each layer resistivity of media value among the figure, and the preceding two layers of thickness of three layer model is 50 meters.

Fig. 5 is the apparent resistivity curve experiment with computing result of the multi-layered media of complexity, has indicated each layer resistivity of media value among the figure, and each layer thickness of model is 50 meters.

Embodiment

The present invention is based on a kind of amplitude ratio of two weight sense motional electromotive force data and the single-valued function relation of resistivity, calculate the apparent resistivity curve of aviation transient electromagnetic data with the method for local spline interpolation by the method for observation data inquiry, local spline interpolation, specifically comprise the steps:

(1) input calculating parameter.Inquiry resistivity number m, the equally spaced inquiry resistivity of logarithm sequence ρ _i ⁰, i=1,2 ..., m, local spline interpolation parameter Np; The height hr of aviation transient electromagnetic systematic parameter: flying height ht, emission magnetic moment M, receiving coil useful area Sr, receiving coil, the level of dispatch coil be apart from r, the time-delay number of samples n of received signal and sampling time sequence t _i(i=1,2 ..., n); Calculate the time interval number n k of two sampled datas that two component amplitude ratios use; Receive x, z weight sense motional electromotive force signal data Vx, Vz;

(2) calculate two component amplitude ratio observation datas.Explain T constantly to n-nk _k=(t _k+ t _K+nkCirculating in)/2, calculates the two component amplitude ratio observation datas of each explanation during the moment:

(k＝1，2，…，n-nk)；

(3) calculate the theoretical data query table of two component amplitude ratios, calculation procedure is as follows:

(a) to inquiry resistivity sequence ρ _i ⁰(i=1,2 ..., m) carry out cycle calculations, make i=1;

(b) the calculated resistance rate is ρ _i ⁰The theoretical aviation transient electromagnetic two weight sense motional electromotive force response sequences of homogeneous half space model

${\hat{V}}_x^0({\mathrm{\&rho;}}_{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="H2009102165281E0000012.png"\; state="\{\{state\}\}">i</figure-callout>}}^0,t_k)=-{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="4"\; label="S\; r\; M"\; filenames="H2009102165281E0000012.png"\; state="\{\{state\}\}">S</figure-callout>}}_r\frac{M}{}\frac{}{4\mathrm{\&pi;}}{L}^{-1}\left\{{\&Integral;}_0^{\&infin;}\right[e^{-\mathrm{\&lambda;}(\mathrm{ht}-\mathrm{hr})}-\frac{\mathrm{\&lambda;}-u}{\mathrm{\&lambda;}+u}{e}^{-\mathrm{\&lambda;}(\mathrm{ht}+\mathrm{hr})}\left]{\mathrm{\&lambda;}}^2{J}_1\left(\mathrm{\&lambda;r}\right)\mathrm{d\&lambda;}\right\}$

${\hat{V}}_z^0({\mathrm{\&rho;}}_{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="H2009102165281E0000012.png"\; state="\{\{state\}\}">i</figure-callout>}}^0,t_k)=-{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="4"\; label="S\; r\; M"\; filenames="H2009102165281E0000012.png"\; state="\{\{state\}\}">S</figure-callout>}}_r\frac{M}{}\frac{}{4\mathrm{\&pi;}}{L}^{-1}\left\{{\&Integral;}_0^{\&infin;}\right[e^{-\mathrm{\&lambda;}(\mathrm{ht}-\mathrm{hr})}-\frac{\mathrm{\&lambda;}-u}{\mathrm{\&lambda;}+u}{e}^{-\mathrm{\&lambda;}(\mathrm{ht}+\mathrm{hr})}\left]{\mathrm{\&lambda;}}^2{J}_0\left(\mathrm{\&lambda;r}\right)\mathrm{d\&lambda;}\right\}$

Wherein, μ ₀Be permeability of vacuum,

Calculate successively under n the sampling instant

With Response data, time cycle indicator k=1 wherein, 2 ..., n;

(c) calculated resistance rate value is ρ _i ⁰Corresponding each explanation is T constantly _k=(t _k+ t _K+nkThe theoretical Query Value of two component amplitude ratios of)/2 o'clock

Time cycle indicator k=1 wherein, 2 ..., n-nk;

(d) make i=i+1,, continue cycle calculations if i＜m then returns (a); If during i=m, two component amplitude ratio data A of whole m resistivity value correspondences ⁰(ρ _i ⁰, T _k), (i=1,2 ..., m; K=1,2 ..., n-nk) calculate and to finish, be kept in the two-dimensional array as the data query table, enter step (4);

(4) calculate each and explain apparent resistivity value ρ constantly _a(i) (i=1,2 ..., n-nk)

(a) make i=1,

J=1, nj=1;

(b) calculate

If d _j=0.0,

Forward (g) to; Otherwise,

If d＜dj, d=dj, nj=j forwards (c) to;

(c)j＝j+1；

(d) if j≤m returns (b); If j＞m forwards (e) to;

(e) structure interpolating function, if nj＞Np, k1=nj-Np, otherwise k1=1; If nj＜m-Np, k2=nj＜m-Np, otherwise, k2=m; Nn=k2-k1+1 the local electrical resistance rate sequence that then is used for interpolation is (ρ _K1 ⁰, ρ _K1+1 ⁰..., ρ _P0 ⁰..., ρ _K2 ⁰), corresponding theoretical data query is (A _K1 ⁰(ρ _K1 ⁰, T _i), A _K1+1 ⁰(ρ _K1+1 ⁰, T _i) ..., A _K2 ⁰(ρ _K2 ⁰, T _i));

(f) by resistivity sequence (ρ _K1 ⁰, ρ _K1+1 ⁰..., ρ _P0 ⁰..., ρ _K2 ⁰) and data query (A _K1 ⁰(ρ _K1 ⁰, T _i), A _K1+1 ⁰(ρ _K1+1 ⁰, T _i) ..., A _K2 ⁰(ρ _K2 ⁰, T _i)) corresponding funtcional relationship, adopt spline interpolation calculating observation data A (T _i) corresponding resistivity value ρ _c, promptly obtain i and explain apparent resistivity ρ constantly _a(i)=ρ _c

(g)i＝i+1；

(h) if i≤n-nk returns (a); Otherwise apparent resistivity calculates and finishes, and quits a program.

Claims (1)

1. the computing method of a time-domain apparent resistivity is characterized in that this method may further comprise the steps:

(1) calculates two component amplitude ratio observation datas

Two induced electromotive force component data Vx, Vz by actual measurement calculate corresponding each explanation T constantly _k=(t _k+ t _K+nkThe amplitude ratio data of)/2

Described k=1,2 ..., n-nk, n are the sampling time number;

(2) calculate two component amplitude ratio data question blanks

Given m discretize inquiry resistivity data ρ _i ⁰, it respectively as the resistivity value of homogeneous half space, is calculated its two component aviation Transient electromagnetic response V earlier _x ⁰, V _z ⁰, calculate the theoretical data query body of two component ratios again

Described i=1,2 ..., m; K=1,2 ..., n-nk, n are the sampling time number;

(3) calculate apparent resistivity value

Explain T constantly with each _kTwo corresponding component amplitude ratio data A ⁰(ρ _i, T _k) as the single-valued function relation of resistivity, calculate actual measurement two component amplitude ratio data A (T with the method for local spline interpolation _k) corresponding resistivity value, be k the apparent resistivity value of being asked of explaining the moment, calculate n-nk one by one and explain apparent resistivity value constantly, promptly finished the calculating of the apparent resistivity of aviation transient electromagnetic, described i=1,2 ..., m; K=1,2 ..., n-nk, n are the sampling time number.

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