均匀介质中MRS方法三维模型的核磁共振响应

MRS方法三维含水体的核磁共振正演计算涉及两个难点:①激发场表达式的快速计算,该表达式为包含双重Bessel函数乘积的积分式,将该表达式分为两个积分区间,第一积分区间应用贝塞尔函数的汉克尔函数表述式及其大宗量渐近特性,将其转化为Fourier正(余)弦变换,采用快速计算方法实现数值计算;另一积分区间的计算直接应用一般的数值积分算法即能获得较高的计算精度。②三维含水体的空间离散化,提供柱坐标和直角坐标中的两种离散方法,可对任意形状的三维含水体进行构建。在此基础上,开发出相应的正演程序,并进行几种常见的三维含水体的MRS正演,对其初始振幅曲线进行规律总结。结果表明,三维含水体的MRS振幅响应与层状含水层振幅响应类似,使用收发共圈的工作模式将难以辨别地下含水体的空间形态。

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.