CN103135140B - A kind of central loop TEM full phase true resistivity computing method of non-flanged effect - Google Patents

Abstract

The invention discloses a method for calculating the full-period true resistivity of a central loop TEM without edge effects. Starting from the electric field formula of a circular loop at a microelement at a current-carrying point, according to the relationship between the electric field, magnetic field, and induced electromotive force, Solved the problem of difficult analysis and solution of the central point and outer field points; according to the relative concept in resistivity exploration, the asymptotic formula of a large number of Bessel functions was used to solve the calculation problem of Bessel function integrals. The present invention comprises the following steps: the step of obtaining the analytical expression of the induced electromotive force of any field point; obtaining the analytical expression of the induced electromotive force of the single Bessel function of the arbitrary field point The steps; the step of substituting the analytical formula of the induced electromotive force of the single Bessel function at any field point into the inversion program to obtain the true resistivity of the central loop TEM without edge effects. This method fundamentally eliminates the influence of the edge effect, improves the correct judgment rate of the underground geological structure, and can be applied to the processing and interpretation of the central loop TEM data to improve the interpretation accuracy.

Description

A Calculation Method of Central Loop TEM Whole-phase True Resistivity Without Edge Effect

technical field

The invention belongs to the field of geophysical prospecting, and in particular relates to an interpretation method for electric and electromagnetic prospecting data. .

Background technique

In order to improve the construction efficiency of the central loop TEM (Transient Electro-Magnetic, TEM), in the field exploration, the observation point was expanded from the central point to the central 1/3 area, as shown in Figure 1. However, the inhomogeneity of the field in the central area forms the edge effect shown in Figure 2. Due to the adoption of the apparent resistivity defined by the center point formula, the edge effect forms a rhythmic change related to the emission loop but not related to the geological structure on the apparent resistivity-depth profile, which leads to misjudgment of the underground geological structure. In order to solve this problem, the existing technology unifies the theoretical formulas of the large fixed source loop and the center loop ^[1-2] , and the obtained apparent resistivity is still obtained, and the theoretical formula of the large fixed source loop is derived from the dipole The distance from the field point of the center loop to the source derived from the submicron is far from the dipole assumption, and the error is still large; for the calculation of true resistivity, the existing technology uses the correction method of measuring point homing to eliminate Edge effect ^[3] , but the edge effect is the essential performance of the loop source field, this method not only cannot eliminate the edge effect, but also introduces new errors. Misjudgment of subsurface geological structures still exists.

Compare documents and references

[1] Li Jianping, Li Tonglin, Zhao Xuefeng, Liang Taimu. Calculation of the full-area apparent resistivity of arbitrarily shaped loop source transient electromagnetic in layered media

Research. Advances in Geophysics, 2007,22(6):1777-1780

[2] Shi Xianxin, Yan Shu, Fu Junmei, Chen Mingsheng. Improvement of Data Interpretation Method for Transient Electromagnetic Method Central Loop Device. Earth Objects

Acta Science, 2009, 52(7):1931-1936

[3] http://www.phoenix-geophysics.com/

[4]KnightJH, RaicheAP.transientelectromagneticcalculationsusingtheGaver-StehfestinverseLaplacetransformmethod.Geophysics,1982,47(1):47-50

[5] AndersonWL.NumericalintegrationofrelatedHankeltransformsoforder0and1byadaptivedigitalfiltering.Geophysics,1979,44(7):1287-1305.

[6] Koefoed O, Ghoch DP, Polmen GJ. Computation of type curves for electromagnetic depth sounding with horizontal transient coil by means of digital linear filter. Geophysical Prospecting, 1972, 20: 406-420.

[7] VermaRK, Koefoed O. Anote on the linear filter method of computing electronics sounding curves. Geophysical Prospecting, 1973, 21:70-76.

[8] Chen Mingsheng, Chen Leshou, Wang Tiansheng, Bai Gaixian. Interpretation of magnetotelluric sounding and electric sounding data with improved generalized inverse matrix method. Acta Geophysics, 1983, 26(4): 390-400.

Contents of the invention

In order to overcome the defects of the edge effect elimination method in the prior art, the present invention provides a center loop TEM full-period true resistivity calculation method without edge effect, which eliminates the misjudgment of the underground geological structure caused by the edge effect.

The key to obtain the true resistivity of the central loop TEM without edge effects: First, obtain the analytical expression of the induced electromotive force V(t) at any point in the loop. However, due to the inhomogeneity of the field distribution, the induced electromotive force other than the central point cannot be obtained by integrating the electric field E _θ around the receiving coil; second, the double Bessel in different forms in the central loop TEM theoretical formula The problem of numerical integration of functions.

In order to solve the above technical problems, the technical solution adopted by the present invention is as follows.

A calculation method of full-period true resistivity of central loop TEM without edge effect comprises the following steps:

Step 1: Obtain the analytical expression of the vertical magnetic field at any field point in the central loop TEM

In the cylindrical coordinate system, when the midpoint of the loop coincides with the coordinate origin, the frequency domain expression of the TEM electric field E _θ of the central loop on the earth surface is

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; j\&omega;\&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; a</span>}\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, r is the distance from a point on the ground to the coordinate origin; ω=2πf is the circular frequency, where f is the frequency; μ ₀ =4π×10 ^-7 H/m is the magnetic permeability of the non-magnetic earth; I is the emission current, a is Radius of the launch loop; J ₁ is the first-order Bessel function, R _n is the total reflection coefficient on the layered earth surface; λ is the integral variable of Hankel transformation;

Using the Maxwell curl equation

▽×E＝-jωμ ₀ H(2)

Where E is the electric field strength and H is the magnetic field strength. Since the electric field has only the θ component and is only a function of r, the magnetic field H _z with the following vertical component

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}\frac{<span\; class="notranslate">\; \&part;</span>}{<span\; class="notranslate">\; \&part;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; E</span>}}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&lambda;J</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

J ₀ in formula (3) is the 0th order Bessel function. The analytical formula (3) contains double Bessel functions, and it needs to be further transformed into a single Bessel function, so that the value of the integral can be obtained by applying existing algorithms such as filter coefficients.

Step 2. Obtain the analytical expression of the induced electromotive force of the single Bessel function at any field point

For the widely used large transmission loop of a=600m～800m, the progressive formula of Bessel function is used

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Substitute formula (4) into formula (3)

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; \&ap;</span>\frac{\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; a</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}\mathrm{<span\; class="notranslate">\; a</span>}}}\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&lambda;J</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; r</span>}}{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Perform inverse Laplace transform on formula (5) to get the time domain form

The relationship between the measured induced electromotive force V(t) and h _z (t) is

$\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; \&part;</span>}{<span\; class="notranslate">\; \&part;</span>\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

After substituting formula (6) into formula (7), the analytical expression of the induced electromotive force of a single Bessel function at any field point is

Step 3: Substituting formula (8) into the inversion program, that is, to obtain the full-period true resistivity of the central loop TEM without edge effects.

The above formula (8) is evaluated using Laplace's differential property, G-S algorithm, and filter coefficient algorithm.

The described filter coefficient algorithm is the 47 filter coefficients provided by Koefoed etc. in the document [6] to calculate the 1st order Bessel function, and the 51 filter coefficients provided by Verma in the document [7] to calculate the 0th order Bessel function; or use the document [5] The 441 filter coefficients provided by Anderson in ] calculate the 1st order and 0th order Bessel functions.

The invention has beneficial effects. The method for solving the full-period true resistivity of the central loop TEM without edge effect disclosed by the invention starts from the electric field formula of the circular loop at the current-carrying point micro-element, and overcomes the inherent error of the dipole micro-element. According to the relationship between electric field, magnetic field and induced electromotive force, the problem of difficult analysis and solution of the center point and outer field point is solved; according to the relative concept in resistivity exploration, the asymptotic formula of a large number of Bessel functions is used to solve the problem of Bessel function integrals Calculation problems fundamentally eliminate the edge effect; by substituting the induced electromotive force formula (8) of the single Bessel function at any field point of the present invention into the inversion program, the full-period true resistivity and thickness of the layered earth can be obtained. The accuracy of central loop TEM detection of underground geological structure is improved. The full-term true resistivity can better reflect the underground geological structure; it provides a theoretical formula in analytical form for the study of TEM response at any point in the loop.

Description of drawings

Figure 1 is a schematic diagram of the distribution of measuring points in the actual exploration of the central loop TEM. The rectangular box in the figure is the emission loop, and the cross mark is the measuring point.

Fig. 2 is the track map of the measured data with edge effect. The observation time is 30 ms, and the time track is 20. The last 4 channels have a lot of interference, and only the first 16 tracks are taken. The emission loop is 600m×600m, and the central measurement area is 200m×200m.

Fig. 3 is a comparative diagram of the TEM resistivity-depth profile of the central loop line without edge effect and corrected edge effect, where (a) is the resistivity calculated by the standard software of the V8 instrument of the Canadian Phoenix company, which still has the influence of the edge effect after correction- Depth profile, (b) is the full-period central loop TEM true resistivity-depth profile without edge effects of the present invention.

Detailed ways

The specific embodiments of the present invention will be described in further detail below in conjunction with the accompanying drawings.

Taking the measured data obtained in coalfield hydrogeological exploration as an example, the launch loop is 600m×600m, and the observation is carried out in the central area of 200m×200m. Figure 3 (a) is the resistivity-depth profile calculated by the standard correction edge effect software of the V8 instrument of the Canadian phoenix company. It can be seen that the correction of the measuring point homing does not eliminate the influence of the edge effect. For the same measured data, the full-period true resistivity method without edge effects is calculated as follows:

During exploration and construction, it is necessary to record the ownership relationship between each measuring point and the launch loop, and the position to the midpoint of the launch loop. Considering that the launch loop is generally square in actual construction, the launch radius in formula (8) is converted by the following formula

$\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; L</span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In the formula, L is the side length of the square launch loop. The value range of the midpoint r in formula (8) is within the range of one-third of the middle of the launch loop, as shown in FIG. 1 .

Apply Laplace's differential properties, GS algorithm ^[4] ; the filter coefficient algorithm uses the 441 filter coefficients ^[5] provided by Anderson in the literature [5] to program the above formula (8), and then compare it with the measured data shown in Figure 2 Together, they are substituted into the improved generalized inverse matrix ^[8] inversion program for inversion calculation, and the full-period true resistivity and formation thickness are obtained, and the resistivity-depth profile shown in (b) in Fig. 3 is generated by drawing software such as Surfer. There are many ways to set the initial parameters of the inversion. In this embodiment, a uniform half-space geoelectric model is adopted. _The earth resistivity ρ1 is estimated by the early or late apparent resistivity formula. Compared with the true resistivity-depth profile ^[3] shown in (a) in Fig. 3, which still has the influence of the edge effect after correction, the present invention eliminates the influence of the edge effect.

Claims (3)

1. the central loop TEM of non-flanged effect full phase true resistivity computing method, is characterized in that comprising the following steps:

Step one, obtains any field of central loop TEM point vertical magnetic field analytical expression

In cylindrical-coordinate system, when loop line mid point overlaps with true origin, central loop TEM electric field E on Earth Surface _θfrequency field expression formula be

$E_{\mathrm{\&theta;}}(r,\mathrm{\&omega;})=-{\mathrm{j\&omega;\&mu;}}_{0}I\left(\mathrm{\&omega;}\right)a\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}{R}_n(\mathrm{\&lambda;},\mathrm{\&omega;})J_1\left(\mathrm{\&lambda;}a\right)J_1\left(\mathrm{\&lambda;}r\right)d\mathrm{\&lambda;}---\left(1\right)$

In formula, r is a bit to true origin distance on ground; ω=2 π f is circular frequency, and wherein f is frequency; μ ₀=4 π × 10 ^-7h/m is non magnetic the earth magnetic permeability; I is transmitter current, and a is transmitting loop radius; J ₁be 1 rank Bessel function, R _ntotal reflectance on multi-layered earth surface; λ is the integration variable of Hankel conversion;

Utilize Maxwell vorticity equation

▽×E＝-jωμ ₀H(2)

Obtain the magnetic field H of vertical component _z

$H_z=\frac{1}{r}\frac{\&part;}{\&part;r}\left({\mathrm{rE}}_{\mathrm{\&theta;}}\right)=\frac{I\left(\mathrm{\&omega;}\right)a}{r}\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}{R}_n(\mathrm{\&lambda;},\mathrm{\&omega;})J_1\left(\mathrm{\&lambda;}a\right)\&lsqb;{\mathrm{\&lambda;J}}_0\left(\mathrm{\&lambda;}r\right)-\frac{1}{r}{J}_1\left(\mathrm{\&lambda;}r\right)\&rsqb;d\mathrm{\&lambda;}---\left(3\right)$

In formula (2), E is electric field intensity, and H is magnetic field intensity;

J in formula (3) ₀it is 0 rank Bessel function;

Step 2, obtains the induced electromotive force analytical expression of any field single point Bessel function

For the large transmitter loop of the a=600m ~ 800m generally applied, utilize the gradual of Bessel function

$\begin{array}{cc}{J}_1\left(x\right)\&ap;\sqrt{\frac{2}{\mathrm{\&pi;}x}}cos\left(x-\frac{3\mathrm{\&pi;}}{4}\right)& (x\&RightArrow;\mathrm{\&infin;})\end{array}---\left(4\right)$

Formula (4) is substituted into formula (3)

$H_z\&ap;\frac{I\left(\mathrm{\&omega;}\right)a}{r}\sqrt{\frac{2}{\mathrm{\&pi;}a}}\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}{R}_n(\mathrm{\&lambda;},\mathrm{\&omega;})\sqrt{\frac{1}{\mathrm{\&lambda;}}}cos\left(\mathrm{\&lambda;}a-\frac{3\mathrm{\&pi;}}{4}\right)\&lsqb;{\mathrm{\&lambda;J}}_0\left(\mathrm{\&lambda;}r\right)-\frac{1}{r}{J}_1\left(\mathrm{\&lambda;}r\right)\&rsqb;d\mathrm{\&lambda;}---\left(5\right)$

Inverse Laplace conversion is done to formula (5), obtains time domain form

Actual measurement induced electromotive force V (t) and h _zt the pass of () is

$V\left(t\right)=\frac{\&part;}{\&part;t}{h}_z\left(t\right)---\left(7\right)$

The induced electromotive force analytical expression of field single point Bessel function is arbitrarily obtained after formula (6) being substituted into formula (7)

Step 3, substitutes into formula (8) in inversion program, namely obtains the full phase true resistivity of the central loop TEM of non-flanged effect.

2. central loop TEM full phase true resistivity computing method for non-flanged effect as claimed in claim 1, is characterized in that in described step 2, and the evaluation of formula (8) utilizes the Differential Properties of Laplace, G-S algorithm, filter factor algorithm.

3. the central loop TEM full phase true resistivity computing method of a non-flanged effect as claimed in claim 2, it is characterized in that, described filter factor algorithm calculates 1 rank Bessel function for 47 filter factors that Koefoed etc. provides, and 51 filter factors provided with Verma calculate 0 rank Bessel function.