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

Abstract 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 basic 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 step-on 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.