Full waveform inversion based on deep learning and optimal nearly analytic discrete method  

基于深度学习与优化近似解析离散方法的全波形反演

作　　者：Lu Fan Zhou Yan-Jie He Xi-Jun Ma Xiao Huang Xue-Yuan 卢凡;周艳杰;贺茜君;马啸;黄雪源(北京工商大学数学与统计学院数学系,北京100048;西北工业大学应用数学系,西安710072)

机构地区：[1]Department of Mathematics,School of Mathematics and Statistics,BTBU,Beijing 100048,China [2]Department of Applied Mathematics,Northwestern Polytechnical University,Xi’an 710072,China.

出　　处：《Applied Geophysics》2021年第4期483-498,593,共17页应用地球物理（英文版）

基　　金：supported by the National Key Research and Development Project of China (No. 2017YFC1500301);the Joint Earthquake Research Program of the National Natural Science Foundation and the China Earthquake Administration (No. U1839206);the National Natural Science Foundation of China (No. 41974114)

摘　　要：In this study,we implement forward modeling and inversion based on deep-learning strategies using an optimal nearly analytic discrete(ONAD)method.The forward-modeling method combines the ONAD method with recurrent neural network(RNN)for the fi rst time.RNN is a type of neural network that is suitable for sequential data,which uses information from both previous and current times to obtain output information.We express the ONAD method using an RNN framework to advance the time iteration of an acoustic equation.This process can simplify programming using RNN and convolution kernels.Next,we use deep learning based on the proposed forward-modeling method to study full waveform-inversion problems.Because the main purpose of inversion is to minimize the error between real and synthetic data,inversion is essentially an optimization problem.Many new optimizers are available in the framework of deep learning,such as the Adam and Nadam optimizers,which are used for optimizing velocity model in the inversion process.We perform six numerical experiments.The first two experiments demonstrate the forward-modeling results,which indicate that the forward-modeling method can effectively suppress numerical dispersion and improve computational effi ciency.The other four experiments demonstrate the inversion results,which show that the method proposed in this paper can eff ectively realize inversion imaging.We compare several optimizers used in deep learning and find that the Nadam optimizer has faster convergence and better effectiveness based on the ONAD method combined with RNN.本文通过采用一种有效的优化近似解析离散(ONAD)方法,实现了基于深度学习技术的正演与反演。本文的正演模拟方法首次将ONAD方法与循环神经网络(RNN)结合了起来。RNN是一种适用于序列数据的神经网络,它利用前一时刻和当前时刻的信息来获取输出信息。ONAD是一种有效的正演模拟方法,与RNN相似之处在于它利用历史时刻的波场来计算当前时刻的波场。基于此,我们可以利用RNN框架来表达ONAD方法。接下来,基于以上所提出的正演方法,我们利用深度学习技术来实现全波形反演。由于反演的主要目的是使实际数据与合成数据之间的误差最小化,因此反演本质上是一个优化问题。在深度学习的框架下有许多新的优化器,如Adam优化器和Nadam优化器,它们会被作为反演过程中的优化器来对速度模型进行优化。我们设计了六个数值实验,前两个给出了正演模拟结果,表明本文使用的正演模拟方法能有效地抑制数值频散,提高计算效率。另外四个实验给出了反演结果,表明本文的方法可以有效实现反演成像。我们比较了几种深度学习优化器,发现Nadam优化器的收敛速度更快,反演效果更好。总之,我们的数值实验表明,利用ONAD方法与深度学习技术来实现正演和反演是非常有效的。

关 键 词：Deep learning ONAD method RNN Nadam optimizer INVERSION 

分 类 号：P631[天文地球—地质矿产勘探]