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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。
MRS method Three-dimensional water body NMR forward calculation involves two difficulties: ① excitation field expression of the fast calculation, the expression is the product of the double Bessel function integral, the expression is divided into two integral interval, the In an integral interval, the Hankel function expression of Bessel function and the asymptotic property of its bulk are applied to convert it into Fourier positive (residual) string transform, and the numerical calculation is realized by fast calculation method. The calculation of the other integral interval The application of general numerical integration algorithm that can obtain a higher accuracy. ② The three-dimensional water body is discretized in space to provide two kinds of discrete methods in column coordinate and rectangular coordinate, so as to construct any three-dimensional water body with arbitrary shape. On this basis, the corresponding forward program was developed, and several common MRS forward of three-dimensional water-bearing bodies were carried out, and their initial amplitude curves were summarized. The results show that the MRS amplitude response of three-dimensional aquifer is similar to the amplitude response of layered aquifer. It is difficult to distinguish the spatial shape of underground aquifer by using the co-circling mode.