Sensitivity functions of transient electromagnetic methods

Abstract

Any geophysical measurement is a filter through which the distribution of a certain physical parameter in the subsurface is seen, and the sensitivity function is a characteristic of the method that reveals the nature of this filter. Insight into the structural pattern of the sensitivity function pertaining to a certain transmitter-receiver configuration provides the geophysicist with an image that allows an immediate qualitative understanding of the characteristics of the method. The assets and shortcomings of different measuring configurations can be discussed and understood, and the sensitivity function permits qualified predictions about resolution characteristics of new configurations and measuring strategies. I evaluated a rapid and accurate method for calculating 3D sensitivity functions of a homogeneous half-space model for a wide variety of transient electromagnetic configurations using the central loop and an airborne offset loop configuration as examples. Computations of 3D sensitivity functions were performed as convolutions in the time domain between the electric fields from the transmitter and the receiver, had it been used as a transmitter. The 2D and 1D sensitivity functions are found through numerical integration of the 3D functions. Beside offering insight into the resolution capability of the measuring configuration, the sensitivity functions lend themselves to rapid calculations of approximate responses and derivatives in various modeling and inversion strategies.