Transfer function measured by electromagnetic sounding with an accurately controlled signal

Abstract

We present the fundamentals of an electromagnetic sounding with an accurately controlled source signal. In this method, the tensor transfer function between transmitted and received vector electromagnetic fields is measured. We formulated the transfer function by introducing a ray model that describes the propagation of the general electromagnetic field in the whole frequency region. The transfer function includes information of the underground structure: electromagnetic parameters, propagation distance, and boundary planes. The information of the electromagnetic parameters and the propagation distance is commonly described in all the tensor elements. It is in a form of complex functions of frequency. The information concerning the boundary planes is described as real coefficients of the complex functions. The coefficients are different for each of the tensor elements. When we use an accurately controlled signal, we can estimate the information as a linear inversion problem. A profile of the transfer function varies with the frequency region: it decays rapidly in the low-frequency region and oscillates in the high-frequency region. Such a profile can be explained by the approximate form of the transfer function: a sum of complex exponential functions in a narrow frequency band. The approximate form also provides a good model for data decomposition.