摘要
本文使用最小二乘线性迭代反演方法对跨孔雷达直达波初至时数据进行反演,每次迭代过程中,用有限差分法求解走时程函方程,并用高精度快速推进方法(HAFMM)进行波前扩展,通过追踪波前避免了进行射线追踪.为了验证该方案,我们对三组合成数据进行了测试,分析了单位矩阵算子、一阶差分算子和拉普拉斯算子等三种不同模型参数加权算子对模型的约束和平滑效果;讨论了FMM和HAFMM对反演精度的影响;测试了LSQR,GMRES和BICGSTAB等三种矩阵反演算法的反演效果.此外,我们还对一组野外实测数据进行了反演,对比了基于本方案以及基于平直射线追踪和弯曲射线追踪的走时层析成像反演效果.对比分析结果表明,使用拉普拉斯算子和HAFMM进行反演能较好地进行目标体重建,而三种矩阵反演方法对反演效果的影响差别不大;并且通过对波前等时线图的分析可以定性地判断异常体的性质和位置;而在对实测数据目标体的重建上,本方案能达到甚至优于弯曲射线算法的重建效果.
We perform a least square iteratively linearized inversion method for the crosshole radar traveltime tomography by using the observed first arrival data. In each iteration process, traveltimes are calculated by solving the traveltimes eikonal equation using the finite difference method and wavefront expansion is achieved by using the High Accuracy Fast Marching Method （HAFMM）, in other words, traveltimes are achieved by tracing wavefronts instead of rays. We test the suggested method on three assumed physical models with abnormal velocity areas. In model 1, three types of model parameter weighting matrix are introduced. In model 2, both FMM （Fast Marching Method） and HAFMM are considered to improve the accuracy of the inversion. In model 3, we also analyze three types of matrix inversion method, respectively. We also test our algorithm on a field data set from the Xiuyan giant jade, and we compared our scheme for the field data with the one obtained by a straight ray-tracing-based algorithm and the one obtained by a curve ray-tracing-based algorithm, respectively. The comparison results indicated that the reconstruction using the Laplace operator and HAFMM at the same time can get the best result, and there is almost no difference for the inversion result by using each one of the three types of matrix inversion method. And the wavefront traveltimes contour line of the synthetic data model implied the features and positions of the anomalous bodies. By comparison with the straight ray-tracing-based algorithm and curve ray-tracing-based algorithm, our scheme is able to generate a solution better than the one resulting from a curve ray-based scheme.
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2013年第11期3896-3907,共12页
Chinese Journal of Geophysics
基金
国家自然科学基金(40874043
41074076)
国家高技术研究发展计划(863计划)(2013AA064603)
中国石油集团东方地球物理公司中青年科技创新基金项目(11-06-2013)资助
关键词
跨孔雷达
迭代线性反演
程函方程
有限差分
HAFMM
层析成像
Crosshole radar, Iteratively linearized inversion, Eikonal equation, Finite difference, HAFMM, Tomography
