The MRS Response of 3D Model in Uniformity Medium

MRS forward calculation of 3D water-contained medium involves two difficulties. First is to calculate expression of exciting field, which is an integration including two Bessel functions' product. The integration is divided into two integral intervals. In the first interval, Hankel expression of Bessel functions and the latter asymptotic properties of large volume are used, the double Bessel integration is converted into Fourier sine(cosine) transformations and fast calculation to the transformations is adopted to finish the integration in this interval. Traditional calculation method can achieve high accuracy in the second interval. The second difficulty is the space discretization of the 3D water-contained medium. Discretization methods in both cylindrical and rectangular coordinates system are introduced. The cubic grids in rectangular coordinates system can construct 3D water-contained bodies of any shape. Based on what mentioned above, forward calculations are done for several common 3D water-contained bodies. By analyzing the magnitude responses, the following disciplines were found:(1) All the magnitude response curves were similar to responses of horizontal layered medium;(2) The pulse moment corresponding to the maximum of the magnitude increased as the model depth increased;(3) For bodies containing the same quantity of water, the bigger the scale was, the larger the maximum of the magnitude was;(4) If the scale of the model is too small, it cannot be detected by current instruments;(5) The 3D pattern of the water-contained body cannot be defined if the signal is received by the same loop that excites the field.