Modeling the TDEM response for a lateral change in conductivity

Abstract

The solution of the transient response of a layered earth excited by a vertical magnetic dipole is well known and used. Expansion of the solution for a 2D or 3D earth, where the conductivity changes in not just the z-direction, is extremely difficult and has only been done by way of numerical schemes, which are laborious even on powerful computers. In this study a current filament is used to generate magnetic fields and its derivative. This current filament diffuses like a smoke ring, downwards and outwards through the earth in time, and is defined by the following parameters: a current amplitude, a horizontal expansion velocity and a vertical or downward velocity. The influence of the conductivity and layer thickness are investigated and it is found that the parameters of the moving current filament is an integrated function of the total resistivity distribution of the layered earth model. For this study a current ring in different environments is used and the results compared. This process indicates that the current filament can be used to model differences in apparent conductivity without considering the thicknesses of layers. The parameters of the current filament are changed one at a time, keeping the other constant, to investigate the influences of each. This technique is then applied to a 2D case, where transient sounding data is generated in the centre of the transmitter loop. The 2D model consists of a vertical geo-electrical boundary which is infinite in strike. The resistivity ratio between the two regions is low and it is assumed that only a primary field is present, as is the case with a layered earth. A qualitative approach is used to determine if and when there are significant changes in the measured temporal field. The apparent resistivity is calculated using the derivative of the magnetic field as defined m Kaufman and Keller, 1983. This has also been applied to the magnetic field and it has been found that there is no difference for this qualitative model between the two approaches. It has been found that the distortion of the current filament is dependent on the locality of the transmitter loop, with a larger distortion when the transmitter loop is located on the more conductive side of the discontinuity. Lastly, this study proven has the feasibility of using the concept of a moving current filament to formulate forward models for 2D and 3D models, if the proper velocity functions are known.