瞬变电磁勘探中采样率与地电结构重建的必要条件  

Sampling rate and necessary conditions for geoelectric structure reconstruction in transient electromagnetic exploration

作　　者：曹清华[1] 闫述[1] 邱卫忠 吴燕清 陈明生 Cao Qing-Hua;Yan Shu;Qiu Wei-Zhong;Wu Yan-Qing;Chen Ming-Sheng(School of Computer Science and Communication Engineering,Jiangsu University,Zhenjiang,212013,China;Shanxi Coal Geological 115 Exploration Institute,Datong,037003,China;School of Resources and Safety Engineering,Jiangsu University,Chongqing,400044,China;Xi’an Research Institute Co.Ltd.,China Coal Technology and Engineering Group,Xi’an 710077,China)

机构地区：[1]江苏大学计算机科学与通信工程学院,镇江212013 [2]山西省煤炭地质115勘查院,大同037003 [3]重庆大学资源与安全学院,重庆400044 [4]中煤科工集团西安研究院有限公司,西安710077

出　　处：《Applied Geophysics》2023年第4期556-571,672,673,共18页应用地球物理（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.41374129 and No.41474095);the Shanxi Science and Technology Program(No.20100321066)。

摘　　要：提高瞬变电磁法的探测精度,不仅需要加密测点还需要加密时窗。然主流瞬变电磁仪为保持各测量窗口的样本数基本不变,使采样率随发射频率的降低而降低,所增加的时窗数以减少参与统计平均的样本量为代价降低了原有的信噪比。论文以Phoenix Geophysics的V8仪器为例,分析了瞬变电磁仪信号检测的主要步骤,以Wiener-Khnchin大数定律为依据,提出了在增加时窗的同时,不减少参加每个时窗统计平均的样本数,形成固定高采样率接收机方案。从Nyquist采样定理出发,给出了以长度为量纲的探测精度的定义,根据重建地电结构的必要条件,确定了点线距和时窗间隔与地电信号频谱最小周期的关系式。以大同达子沟煤矿多层积水采空区的探测为例,展现了在地球物理前提存在的情况下,因欠采样造成的混叠和通过附加条件获得的精细地电剖面。地电结构重建的必要条件说明,满足Nyquist采样定理不一定能够重建地电结构,但不满足这个定理则一定不能完整地重建。To improve the detection precision of the transient electromagnetic method,dense observation points and windows are necessary.However,to keep the number of samples in every acquisition window unchanged,the sampling rate of principal transient electromagnetic instruments decreases with transmitter frequency,and the increased windows reduce the original signal-to-noise ratio at the cost of decreasing the number of samples participating in the statistical average.Taking the V8 receiver from Phoenix Geophysics as an example,this study analyzes the main steps in the signal detection of a transient electromagnetic instrument.Following the Wiener–Khinchin law of large numbers,herein,a fixed,high-sampling-rate receiver scheme,which does not decrease the number of samples participating in the statistical average while increasing the windows,is proposed.Starting from the Nyquist sampling theorem,we provide the defnition of detection precision with the dimension of length.Then,according to the necessary conditions for reconstructing a geoelectric structure,we determine the relationship between a survey grid space and a detection depth space corresponding to window interval as well as the minimum period in a geoelectric signal spectrum.The exploration of the multilayer,water-flled goaf of the Dazigou Coal Mine in Datong shows the aliasing caused by undersampling and the fne geoelectric section obtained using additional conditions under a geophysical premise.The necessary conditions for the reconstruction of the geoelectric structure indicate that satisfying the Nyquist sampling theorem may be insuffcient in reconstructing the geoelectric structure,but the structure must not be reconstructed completely without not satisfying this theorem.

关 键 词：采样率 大数定律 采样定理 地电结构 必要条件 

分 类 号：P631.325[天文地球—地质矿产勘探]