发射电流波形对瞬变电磁一维正反演的影响

doi:10.19657/j.geoscience.1000-8527.2022.059

摘要/Abstract

摘要：

本研究实现了考虑发射电流波形的瞬变电磁一维正反演算法。正演采用矩形回线源,通过Duhamel积分计算梯形波的感应电压;反演采用Occam反演方案,得到一个光滑的层状反演结果模型。理论模型合成算例的计算结果表明:上升沿时间、持续时间和下降沿时间不同程度地影响了垂直磁感应强度对时间的偏导数(dB/dt)响应以及电阻率反演结果。理论模型的正演结果显示,上升沿时间、持续时间和下降沿时间分别主要影响晚期、中晚期和早期的瞬变电磁响应,并且取值越大影响越大。理论模型合成数据的反演算例显示,不同上升沿时间对反演结果几乎没有影响,而下降沿时间和持续时间分别影响浅部和深部的反演结果。

关键词: 瞬变电磁, 发射波形, 一维正反演

Abstract:

We have developed a 1D modeling and inversion algorithm for transient electromagnetic method (TEM) data with transmitter waveform. The source is a horizontal rectangular loop for the implementation. Through the Duhamel integral, the step response was converted to the response generated by the trapezoidal waveform. In the inversion, the Occam strategy is adopted to obtain a smooth layered model. The synthetic examples show that the time derivatives of the vertical magnetic fields, dB/dt, and the inversion results are distorted to different extents by the turn-on, steady and turn-off times. The investigated model response shows that the turn-on, steady, and turn-off times mainly affect the TEM data at late, intermediate-late, and early gate times, respectively. Furthermore, the distortions become greater with increasing durations of the turn-on, steady and turn-off times. Inversion results of the synthetic data indicate that the turn-on times have only minor influence on the inversion results, whilst the turn-off and steady times affect the inversion results of the shallow and deep parts, respectively.

Key words: transient electromagnetic method, transmitter waveform, 1D forward modeling and inversion

中图分类号:

P631

王胜涛, 林昌洪, 王旭东. 发射电流波形对瞬变电磁一维正反演的影响[J]. 现代地质, 2023, 37(01): 99-106.

WANG Shengtao, LIN Changhong, WANG Xudong. Effect of Transmitter Waveform on 1D Modeling and Inversion of Transient Electromagnetic Method Data[J]. Geoscience, 2023, 37(01): 99-106.

图/表 11

图1 本文程序与AarhusInv程序计算结果的对比图 (a)层状模型;(b)波形;(c)响应;(d)相对误差

Fig.1 Comparison between the 1D solutions of the AarhusInv code and the responses calculated by the developed algorithm in this paper on a layered model

图2 本文程序与AarhusInv程序反演结果的对比

Fig.2 Comparison between the 1D inversion result of the AarhusInv code and that inverted by the algorithm in this paper

图3 研究模型 (a)均匀半空间;(b)三层模型;(c)五层模型

Fig.3 Investigated model in this study

表1 一些瞬变电磁仪器波形参数

Table 1 Some TEM system parameters

仪器名称	发射电流/A	上升沿时间t₁/ms	下降沿时间t₀/μs
TERRA TEM 24瞬变电磁仪	50	10~2000	22
JS06-MSD-1瞬变电磁仪	1~20	480	8
PROTEM 57-MK2瞬变电磁仪	28		20~115
PROTEM-TEM 47发射机	3		2.5
SkyTEM瞬变电磁仪	30		4
SkyTEM306 HP(高频)	9	0.8	1018
SkyTEM306 HP(低频)	220~250	5	15×10³
SkyTEM312 HP(高频)	220~250	5	15×10³
YCS 150矿井瞬变电磁仪	2.5		0.5×10³
SkyTEM312 HP(低频)	220~250	8	32×10³

图4 梯形波参数设置

Fig.4 Parameters of trapezoidal wave

图5 图3中的均匀半空间模型(a)、三层模型(b)和五层模型(c)在不同上升沿时间t1时的dB/dt响应以及与阶跃波(t1=1 fs)响应的相对误差((d)、(e)和(f))

Fig.5 The dB/dt responses on the uniform half-space (a), three-layered (b) and five-layered (c) models in Fig.3 with different turn-on time and the relative error ((d), (e) and (f)) with the response of step waveform (t1=1 fs)

图6 图3中的均匀半空间模型(a)、三层模型(b)和五层模型(c)在不同持续时间t2时的dB/dt响应以及与三角波(t2=1 μs)响应的相对误差((d)、(e)和(f))

Fig.6 The dB/dt responses on the uniform half-space (a), three-layered (b) and five-layered (c) models in Fig.3 with different steady time and the relative error ((d), (e) and (f)) with the response of triangular wave (t2=1 μs)

图7 图3中的均匀半空间模型(a)、三层模型(b)和五层模型(c)在不同下降沿时间t0时的dB/dt响应以及与阶跃波(t0=1 fs)响应的相对误差((d)、(e)和(f))

Fig.7 The dB/dt responses on the uniform half-space (a), three-layered (b) and five-layered (c) models in Fig.3 with different turn-off time and the relative error ((d), (e) and (f)) with the response of step wave (t0=1 fs)

图8 图3中三层模型(a)和五层模型(b)的不同上升沿时间合成数据的反演结果

Fig.8 Inversion results of synthetic data for three-layered model (a) and five-layered model (b) in Fig.3 with different turn-on time

图9 图3中三层模型(a)和五层模型(b)的不同持续时间合成数据的反演结果

Fig.9 Inversion results of synthetic data for three-layered model (a) and five-layered model (b) in Fig.3 with different steady time

图10 图3中三层模型(a)和五层模型(b)的不同下降沿时间合成数据的反演结果

Fig.10 Inversion results of synthetic data for three-layered model (a) and five-layered model (b) in Fig.3 with different turn-off time

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