The full-time apparent resistivity definition of the multi-channel transient electromagnetic method

摘要

Apparent resistivity is a critical parameter for providing information about underground structures. Since the fields of the transient electromagnetic method (TEM) are an implicit function of resistivity, full-time apparent resistivity definition has always been one of the difficult issues. Besides, the definition of TEM apparent resistivity was always based on the magnetic field. However, the multi-channel transient electromagnetic method (MTEM) mainly collects electric fields, of which the apparent resistivity definition is much more difficult. In this paper, the definition of the MTEM full-time apparent resistivity is mainly investigated. First, we briefly introduces the MTEM principles. Subsequently, a detailed study on the definition of MTEM full-time apparent resistivity is carried out. The analysis of theoretical expression of the impulse response in uniform half-space shows that the electric field is a non-monotonic function of the resistivity. Although the apparent resistivity can be obtained by dividing the calculation interval into two monotonic intervals, there will be a false anomaly in the apparent resistivity curve. In searching for a better definition, we obtain the step-off response by integrating the impulse response. The step-off response is still a non-monotonic function, and there is also distortion in the apparent resistivity curve. However, the expression of step-on response is a monotonic function, and there is no false anomaly in the apparent resistivity curve. It is well known that the sum of the step-off response and the stepon response is constant at any time, and apparent resistivity of the early time is equal to the first layer resistivity. Through the above relationship, we can obtain the step-on response using the impulse response, and then calculate the apparent resistivity. The algorithm is verified through numerical simulation and field tests.