跨孔雷达全波形反演成像方法的研究

Study of cross-hole radar tomography using full-waveform inversion

跨孔雷达全波形反演是一种使用全波形信息反演两钻孔之间地下信息的层析成像技术.常规的层析成像反演大部分采用射线追踪方法,其中基于初至时的射线追踪方法可以反演出速度剖面(介电常数剖面),基于最大振幅的层析成像可以反演出衰减剖面(电导率剖面).常规射线追踪方法有许多不足,究其原因是该方法仅使用了小部分的信号信息.为了进一步提高成像分辨率,本文全面推导了全波形跨孔雷达层析成像反演方法,该方法利用雷达波全幅度相位信息能够反演出地下高分辨率的介电常数和电导率图像.本文通过基于局域网的分布式并行算法,有效地解决了巨量数据正演计算问题.文中首先建立了基于单轴各向异性介质完全匹配层的时间域有限差分二维正演算法,进而通过应用包括时间维度在内的全波场信息与残场逆向传播的全波场信息乘积来计算梯度方向,通过求取以步长为自变量的目标函数的极值确定步长公式,并提出以第一次介电常数反演作为同步反演的初始模型,能够有效提高收敛速度.本文对多组模型进行成像实验,取得了较好的反演效果.

Full waveform inversion of cross-hole radar is a kind of tomographic imaging technique. It uses full-waveform information to obtain the electric parameters of the underground media between the boreholes. Most conventional tomographic inversions use ray tracing method, the velocity profile （permittivity image） can be obtained by first-arrival wave, and attenuation profile （conductivity image） can be obtained from maximum amplitude. There are many shortcomings of conventional method. The main reason is that it just uses a small portion of the signal information. In this paper, we derive the algorithm of cross-hole radar full-wave inversion. The parallel algorithm based on distributed computers effectively solves the problem of massive data computation. First of all, we establish a 2D-TE mode finite-difference time-domain method （FDTD） with uniaxial perfectly matched layers （UPML） as forward modeling algorithm. What＇s more, image good i we derive the gradient and step formulas. And we propose the first permittivity inversion as the initial model of simultaneous inversion. Finally we test several models and achieve nversion results.