基于单能窄束伽马射线算法计算高分辨率屏蔽自然伽马探测器的三维测井响应

本文应用单能窄束伽马射线理论建立高分辨率屏蔽自然伽马探测器三维测井响应的数值模拟算法.首先利用单能窄束原理，用稳态扩散方程描述伽马光子密度的空间分布，根据扩散方程基本解、放射源空间分布、探测器位置和屏蔽情况，将屏蔽探测器上的总伽马通量表示成放射性地层中的有效探测区域上的体积分和晶体表面上有效接收面的面积分形式.并根据伽马射线传播路径和探测器屏蔽情况，给出有效探测区域的解析表达式，通过数值积分法计算任意复杂情况下探测器上的自然伽马通量，获得伽马测井响应的3D数值模拟算法.并通过数值模拟结果与模型井数据的对比验证了该算法的有效性.最后通过3D数值模拟算法系统研究考察晶体形状（圆柱形晶体、方形晶体）、晶体长度、仪器在井轴中的位置（居中屏蔽探测器、贴井壁屏蔽探测器）、以及测速等不同情况下自然伽马测井响应，设计出新型高分辨率自然伽马测井仪器.

Simulation of 3D responses of high-resolution natural gamma ray detector with shielding in inhomogeneous formation based on the theory of single energy narrow-beam gamma-ray

Based on the method of single energy narrow-beam, we establish the 3D numerical algorithm for simulation of the responses of high-resolution natural Gamma ray detector with shielding. First, according to the principle of single energy narrow-beam, the stationary-state diffusion equation of gamma photon density is used to describe the spatial distribution of natural Gamma ray in radioactive formation. Then, by using the basic solution of the stationary-state diffusion equation, the spatial distributions of radioactive sources in the formation, the tool location and shielding conditions of natural Gamma ray detector, we express the total Gamma photon flux entering the surface of the detector as the form of both the 3D volume integral in the effective exploring domain in the formation and 2D surface integral on the effective detector surface. We analytically describe the effective exploring domain according to the propagation path of Gamma ray in formation and both shielding condition and location of the detector so that the flux in any complex conditions is efficiently computed by 3D numerical method. The 3D numerical tests are applied to investigate the influence of changes in the size of the detector, the shape of the detector, the location of detector at borehole axis or on borehole wall, and logging velocity on the vertical resolution of logging tool so that a high resolution Gamma ray tool is finally designed and developed.