Using artificial field source to measure AMT has the advantages of strong signal, easy observation and high production efficiency, but it also introduces a series of problems related to artificial field source. First of all, the use of high-power artificial sources makes the equipment of CSAMT method very heavy and the production cost is high. Secondly, due to the limited transmission power, in order to maintain a strong enough observation signal, the transmitting and receiving distance R is always limited. In this way, when the relative skin depth δ= 2ρ/ρμ of R is not very large at middle and low frequencies, the electromagnetic field enters the "near zone" (r/δ? 1) or "transition zone" (r/δ approaches 1). However, Cania's apparent resistivity formula is aimed at the far region (or wave region, r/δ? 1). In the transition region or near region, the apparent resistivity ρs of Cania will be distorted. Even under the condition of uniform earth, the calculated ρs obviously deviates from the real resistivity of the earth, which is called waveless field effect or near field effect. Phoenix Company of Canada proposed a near-field correction method-transition triangle method, which can correct ρs of near-field and transition zone to be close to the true resistivity of the earth under the condition of uniform earth, but there is still a relative error of 10% ~ 20%. Chinese scholars have established a new near-field correction method by iterative method and numerical approximation method, and the correction effect is good. Under the condition of uniform earth, the corrected equivalent resistivity or full frequency domain apparent resistivity is very close to the real earth resistivity. The latter near-field correction method is now introduced.

As mentioned above, when the transmitting-receiving distance r is small or the working frequency f is low, the observed electromagnetic field belongs to near field or transition field, so it is necessary to correct the non-wave field or near field. It is a good near-field correction method to calculate the full frequency domain apparent resistivity ρs from the measured Kaniya apparent resistivity.

(1) Algorithm principle for calculating near-field correction of apparent resistivity in full frequency domain.

The algorithm of full frequency domain apparent resistivity ρs is based on non-magnetic, uniform earth conditions and electromagnetic field characteristics of ground electric dipole source. Under this assumption, according to the observation and coordinate system shown in Figure 4-2-2, the expression of Kaniya apparent resistivity can be written as:

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Figure 4-2-2 Coordinate System for Calculating Observation Parameters of CSAMT Method with Coupled Sources

Where I0, I 1, K0 and K 1 are Bessel functions with first and second imaginary independent variables, respectively, and their independent variables are (-ikr/2); (r, θ) is the coordinate of the observation point (see Figure 4-2-2); μ0 and ρ are the permeability and resistivity of non-magnetic uniform earth, respectively; The expression of angular wave number (propagation coefficient) k=:

Iωμ0/ρ, the product of it and the distance r:

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Among them, the induction number

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δ is the skin depth.

The normalized apparent resistivity formula can be written by formula (4-2-3), where the independent variables of I0, I 1, K0, K 1 are.

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The calculation results of equation (4-2-6) show that it is a monotonic decreasing function of p, so that the value of p can be determined in turn in a single value through actual measurement; In addition, the earth resistivity can be calculated from P according to the evolution formula of (4-2-5):

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Under the condition of non-uniform earth, the parameter calculated from P by the above method with the help of formula (4-2-7) is defined as apparent resistivity ρ s. Since this apparent resistivity is equal to the true resistivity of the earth under the condition of uniform earth, no matter what the working frequency f = Ω/2π is (that is, whether in the far area, transition area or near area), it is called full frequency domain apparent resistivity. It is well understood that it is different from Kaniya apparent resistivity, but the apparent resistivity is uniformly corrected in the near field.

The difficulty of calculating apparent resistivity ρ in full frequency domain according to the above definition is how to further calculate P from measured data. This is because (4-2-6) is a complex function with formula p, and it is difficult to get the analytical expression of its inverse function p = ψ. In order to overcome this difficulty, imitating Hasegawa's practice, p = ψ is expressed as a power exponential polynomial by numerical approximation:

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For different azimuth angles θ of measuring points (see Figure 4-2-2), the reasonable subsection interval is studied, and the corresponding values of power exponent (α 1, α2, α3) and coefficient (a 1, a2, a3) are calculated. For example, for θ = 0, it is divided into five segments:

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See table 4-2- 1 for the power exponent sum coefficient values of each paragraph.

In this way, given the transmitting and receiving distance r and azimuth θ of the measuring point, when the Kaniya apparent resistivity of each frequency f is measured, the near-field correction can be carried out according to the following steps: calculating the apparent resistivity ρs of the whole frequency domain.

(1) Normalized apparent resistivity calculated according to actual measurement:

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(2) According to the sum of θ, select the power exponent polynomial of the corresponding section and calculate the induction number:

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(3) According to the calculated P value, calculate the near-field corrected apparent resistivity (full frequency domain):

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Where the angular frequency ω = 2π f; Free space permeability μ 0 = 4 π× 10-7 h/m

Table 4-2- 1 is the exponent and coefficient value (θ = 0) in the formula (4-2-8) for calculating p.

(2) Correction example

In order to test the validity of the near-field correction method, the correction effect is illustrated by taking the uniform earth as an example. For comparison, the theoretical curves of Kaniya apparent resistivity frequency sounding of CSAMT and MT are drawn, and the correction results of "transition triangle method" (referred to as the old method) and "full frequency domain apparent resistivity method" (referred to as the new method) are also drawn.

Figure 4-2-3 shows a set of results of uniform earth. It can be seen that the frequency measurement curve of CSAMT deviates from the real earth resistivity value ρ at low frequency (transition zone and near zone), and increases with the decrease of frequency f, which cannot vividly reflect the uniform earth electrical structure. In sharp contrast, the frequency measurement curve of MT is a horizontal straight line in the whole frequency band, = ρ. After the near-field correction by the new method, the curves of ρs and MT are very close, except that some points ρs have a deviation of about 4.4% from the true resistivity ρ of the earth, and the deviations of other points are all within 65438 0%. In contrast, the correction result of the old method is poor, the deviation is generally more than 5%, and a considerable part of it is 10% ~ 12% (the maximum deviation is more than 20% under other conditions). The above situation shows that it is necessary to correct CSAMT data in the near field. The new method introduced here can be considered that the correction effect is very good under the condition of uniform earth.

Figure 4-2-3 Theoretical Sounding Curve and Near-field Correction Results of Coupled Sources CSAMT and MT on Uniform Earth