基于GPU并行的时间域全波形优化共轭梯度法快速GPR双参数反演

探地雷达（GPR）时间域全波形反演计算量巨大，内存要求高，在微机上计算难度大.本文中作者基于GPU并行加速的维度提升反演策略，采用优化的共轭梯度法，避免了Hessian矩阵的计算，在普通微机上实现了时间域全波形二维GPR双参数（介电常数和电导率）快速反演.论文首先推导了二维TM波的时域有限差分法（FDTD）的交错网格离散差分格式及波场更新策略.然后，基于Lagrange乘数法，将约束问题转化为无约束最小问题，构建了共轭梯度法反演目标函数，采用Fletcher-Reeves公式与非精确线搜索Wolfe准则，确保了梯度方向修正因子及迭代步长选取的合理性.而GPU并行计算及维度提升反演策略的应用，数倍地提升了反演速度.最后，开展了3个模型的合成数据的反演实验，分别从观测方式、梯度优化及天线频率等方面，分析了这些因素对雷达全波形反演的影响，说明双参数的反演较单一的介电常数反演，能提供更丰富的信息约束，有效提高模型重建的精度.

Fast Ground Penetrating Radar double-parameter inversion based on GPU-parallel by time-domain full waveform optimization conjugate gradient method

The time domain full waveform inversion (FWI) of ground penetrating radar (GPR) is difficult to calculate on personal computer due to its calculation and high memory requirements. In this paper, we use the optimized conjugate gradient method based on the GPU parallel acceleration with the dimensionality lifting scheme, and the calculation of Hessian matrix is avoided, realizing the fast inversion of the two-dimensional GPR double-parameter (dielectric constant and conductivity) in the time domain. Firstly, the staggered grid discrete difference scheme and wave field updating strategy of 2D TM wave finite difference time domain (FDTD) method are derived. Then, based on the Lagrange multiplier method, the constraint problem is transformed into the unconstrained minimum problem, and the conjugate gradient method is used to invert the objective function. The Fletcher-Reeves formula and the inexact line search Wolfe conditions are used to ensure the rationality of the selection of gradient direction correction factor and iteration. The introduction of GPU-based parallel computing and dimension to enhance the inversion strategy can improve the inversion speed several times. Finally, the inversion experiments of synthetic data of three models are carried out. The influence of these factors on the full waveform inversion is analyzed in detail from the aspects of observation mode, gradient optimization and antenna frequency, respectively. The results show that the inversion result of the two parameters can provide richer information constraints to a single dielectric constant inversion and improve the accuracy of model reconstruction, effectively.