基于L-BFGS算法的时间域全波形反演

全波形反演是大规模参数、强烈非线性的最小值问题, 在数学上利用无约束的非线性最优化方法求解。本文基于标量波动方程, 利用最小二乘法建立了无约束的目标函数, 推导了时间域目标函数的梯度算子表达式; 在迭代求解问题上利用有限内存L-BFGS算法, 结合最优化一维线搜索方法, 求解全波形反演的强非线性问题。通过复杂断块模型的理论测试验证了反演算法的稳定性和适应性, 实际资料的初步测试验证了反演算法的有效性。

Full waveform inversion in time domain based on limited-memory BFGS algorithm

Full waveform inversion (FWI) is a multi-parameter, strong nonlinear global minimum problem. Non-constrained iterative local optimization methods are usually used to solve this problem. In this paper, we propose a FWI method based on scalar wave equation. First we establish object functions using the least square, and then deduce gradient equations. For the iteration, we apply the limited-memory BFGS (L-BFGS) method and line search to the time domain FWI, which will migrate the inversion illness. A numeric test on a complex velocity model shows that the proposed method has higher inversion precision than the conventional gradient method, and can accelerate the convergence of the object function. On real data test, similar encouraging results are obtained.