﻿ 组合薄板状导体的地-井瞬变电磁异常理论计算
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 地质与资源 2022, Vol. 31 Issue (5): 653-659, 706 0

NIU Zheng, QIN Chang-chun, HAN Yao-ji, LUO Jing. MODELING STUDY ON MULTIPLE THIN-PLATE CONDUCTORS BASED ON SURFACE-HOLE TRANSIENT ELECTROMAGNETIC ANOMALY RESPONSES[J]. Geology and Resources, 2022, 31(5): 653-659, 706.

MODELING STUDY ON MULTIPLE THIN-PLATE CONDUCTORS BASED ON SURFACE-HOLE TRANSIENT ELECTROMAGNETIC ANOMALY RESPONSES
NIU Zheng , QIN Chang-chun , HAN Yao-ji , LUO Jing
No. 2 Comprehensive Geophysical Exploration Brigade of Shaanxi Geology and Mining Group Co., Ltd., Xi'an 710016, China
Abstract: The surface-hole transient electromagnetic method (SHTEM) is used to explore deep mineral resources by which field source is excited on surface and transient responses are observed through receiving coil in borehole. The mutual inductance coefficient and induced voltage between equivalent eddy current ring and Rx are calculated based on the principle of equivalent eddy current ring method. By establishing a mathematic model of multiple thin-plate conductors, the response superimposed field is calculated and simulated under the condition that there are combinations of multiple thin conductive plates underground to study the surface-hole transient electromagnetic anomaly responses of multiple conductors and analyze their characteristics and rules. It is considered that multiple combinations of thin plate orebodies can be distinguished through SHTEM when they are close to the borehole.
Key words: SHTEM    multiple conductor    conductive plate    equivalent eddy current

0 引言

1 等效涡流环计算方法

 \begin{align} & M=\frac{{{\mu }_{0}}}{4\pi }\int\limits_{0}^{{{l}_{1}}}{\int\limits_{0}^{{{l}_{2}}}{\frac{\text{d}{{l}_{1}}\cdot \text{d}{{l}_{2}}}{{{R}_{12}}}}} \\ & =\frac{{{\mu }_{0}}}{4\pi }\int\limits_{{{x}_{1}}}^{{{x}_{2}}}{\int\limits_{{{x}^{\prime }}_{1}}^{{{x}^{\prime }}{{2}_{2}}}{\frac{\text{d}{{l}_{1}}\cdot \text{d}{{l}_{2}}}{\sqrt{{{\left( {{l}_{1}}+{{l}_{2}} \right)}^{2}}+\Delta {{Y}^{2}}+\Delta {{Z}^{2}}}}}} \\ \end{align} (1)

R12为dl1与dl2间距; l1两端的横坐标为x1x2, l2两端的横坐标为x1x2; ΔYΔZ分别为dl1与dl2纵向和垂向的距离, 因该式为两条同样走向平行线, 故ΔYΔZ的值固定; μ0为磁导率, 地层中一般取1. 256×10-6 H/m. 式(1)进一步推导[12-13]可得:

 \begin{aligned} M=& \frac{\mu_0}{4 \pi}\left[\left(x_2-x_1^{\prime}\right) \ln \left(x_2-x_1^{\prime}+\sqrt{\left(x_2-x_1^{\prime}\right)^2+\Delta Y^2+\Delta Z^2}\right)\right.\\ &\left.-\sqrt{\left(x_2-x_1^{\prime}\right)^2+\Delta Y^2+\Delta Z^2}\right] \\ &-\frac{\mu_0}{4 \pi}\left[\left(x_2-x_2^{\prime}\right) \ln \left(x_2-x_2^{\prime}+\sqrt{\left(x_2-x_2^{\prime}\right)^2+\Delta Y^2+\Delta Z^2}\right)\right.\\ &\left.-\sqrt{\left(x_2-x_2^{\prime}\right)^2+\Delta Y^2+\Delta Z^2}\right] \\ &+\frac{\mu_0}{4 \pi}\left[\left(x_1-x_2^{\prime}\right) \ln \left(x_1-x_2^{\prime}+\sqrt{\left(x_1-x_2^{\prime}\right)^2+\Delta Y^2+\Delta Z^2}\right)\right.\\ &\left.-\sqrt{\left(x_1-x_2^{\prime}\right)^2+\Delta Y^2+\Delta Z^2}\right] \\ &-\frac{\mu_0}{4 \pi}\left[\left(x_1-x_1^{\prime}\right) \ln \left(x_1-x_1^{\prime}+\sqrt{\left(x_1-x_1^{\prime}\right)^2+\Delta Y^2+\Delta Z^2}\right)\right.\\ &\left.-\sqrt{\left(x_1-x_1^{\prime}\right)^2+\Delta Y^2+\Delta Z^2}\right] \end{aligned} (2)

 $\mathit{\Phi}_1=I \cdot M_1$ (3)
 $\mathit{\Phi}_2=i_0 \cdot \mathrm{e}^{-t / \tau} \cdot M_2$ (4)

Φ1为导体内产生的磁通量; Φ2为Rx接收二次场产生的磁通量; I为Tx所通电流; i0·e-t/τ为感应等效涡流. 式中感应电流的初始值以及时间常数的经验表达式分别为[2-3]:

 $i_0=0.6 H_{1 \mathrm{n}} \cdot a \cdot f_1(b / a)$ (5)
 $\tau=\mu_0 \cdot S \cdot a \cdot f_2(b / a) / 10$ (6)

H1n(即H1·cosθ)[3]为作用于薄板体的一次场法向分量; H1为一次场; θ为薄板导体与Tx所在平面(一般即水平面)的夹角; S为纵向电导.

Rx产生的感应电压为[1-2]:

 $V(t)=-\frac{\partial \mathit{\Phi}_2}{\partial t}$ (7)

2 多个薄板状导体的地-井TEM响应特征

2.1 单板体地-井TEM的一般响应特征

 图 1 不同钻孔接收水平单板体异常响应曲线 Fig.1 Surface-hole TEM response curves for single horizontal conductive plate in different boreholes 1—测道1响应时间, t1=0. 108 ms (response time of track No. 1); 2—测道2响应时间, t2=0. 170 ms (response time of track No. 2); 3—测道3响应时间, t3=0. 280 ms (response time of track No. 3); 4—测道4响应时间, t4=0. 440 ms (response time of track No. 4)

 图 2 不同钻孔接收倾斜单板体异常响应曲线 Fig.2 Surface-hole TEM response curves for single tilt conductive plate in different boreholes 1—测道1响应时间, t1=0. 108 ms (response time of track No. 1); 2—测道2响应时间, t2=0. 170 ms (response time of track No. 2); 3—测道3响应时间, t3=0. 280 ms (response time of track No. 3); 4—测道4响应时间, t4=0. 440 ms (response time of track No. 4)
2.2 多板体地-井TEM的一般响应特征及分析

 图 3 不同钻孔接收水平多板体纵向组合异常曲线 Fig.3 Surface-hole TEM response curves for vertical combination of multiple horizontal conductive plates in different boreholes 1—组合板响应(response for multiple conductive plates); 2—薄板1响应(response for No. 1 conductive plate); 3—薄板2响应(response for No. 2 conductive plate); 4—薄板3响应(response for No. 3 conductive plate); 5—薄板4响应(response for No. 4 conductive plate); 6—组合板响应幅值(response amplitude for multiple conductive plates)

 图 4 不同钻孔接收倾斜多板体纵向组合异常曲线 Fig.4 Surface-hole TEM response curves for vertical combination of multiple tilt conductive plates in different boreholes 1—组合板响应(response for multiple conductive plates); 2—薄板1响应(response for No. 1 conductive plate); 3—薄板2响应(response for No. 2 conductive plate); 4—薄板3响应(response for No. 3 conductive plate); 5—薄板4响应(response for No. 4 conductive plate); 6—组合板响应幅值(response amplitude for multiple conductive plates)

3 通过组合体地-井TEM异常响应分辨各单板体

 图 5 由不同钻孔观测水平板组合异常响应分辨单个板体 Fig.5 Distinction of single plates by responses of multiple horizontal conductive plates in different boreholes 1—组合板响应(response for multiple conductive plates); 2—薄板2响应(response for No. 2 conductive plate); 3—薄板1响应(response for No. 1 conductive plate)

 图 6 由固定钻孔观测水平板组合异常响应分辨单个板体 Fig.6 Distinction of single plates by responses of multiple horizontal conductive plates in the same borehole 1—组合板响应(response for multiple conductive plates); 2—薄板2响应(response for No. 2 conductive plate); 3—薄板1响应(response for No. 1 conductive plate)

4 结语

1) 总结了纵向排布下多板体组合在不同位置钻孔观测得到异常响应的特征规律, 并结合单板体的响应特征进行了分析, 重点分析了多个板体异号响应叠加抵消产生的幅值减小情况;

2) 通过多板体响应叠加形成总异常响应, 分析其特征规律, 认识到地-井TEM在对组合体的观测中, 除异常响应曲线以外, 不考虑正负号的响应幅值曲线也可以提供组合体相关信息, 作为对组合体进行推断的依据;

3) 对比地面大定回线源TEM剖面法对板体组合中单体进行分辨的条件, 分析了在某些条件下, 通过多个平行板体纵向组合产生的地-井TEM总异常响应对其中单个组成部分进行分辨的情况.

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