Application of an unbalanced optimal transport distance and a mixed L1/Wasserstein distance to full waveform inversion

被引:7
作者
Li, Da [1 ]
Lamoureux, Michael P. [1 ]
Liao, Wenyuan [1 ]
机构
[1] Univ Calgary, Dept Math & Stat, 2500 Univ Dr NW, Calgary, AB T2N 1N4, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Inverse theory; Waveform inversion; Computational seismology; Wave propagation; MASS-TRANSFER; MISFIT;
D O I
10.1093/gji/ggac119
中图分类号
P3 [地球物理学]; P59 [地球化学];
学科分类号
0708 ; 070902 ;
摘要
Full waveform inversion (FWI) is an important and popular technique in subsurface Earth property estimation. In this paper, several improvements to the FWI methodology are developed and demonstrated with numerical examples, including a simple two-layer seismic velocity model, a cross borehole Camembert model and a surface seismic Marmousi model. We introduce an unbalanced optimal transport (UOT) distance with Kullback-Leibler divergence to replace the L2 distance in the FWI problem. Also, a mixed L1/Wasserstein distance is constructed that preserves the convex properties with respect to shift, dilation, and amplitude change operation. An entropy regularization approach and convolutional scaling algorithms are used to compute the distance and the gradient efficiently. Two strategies of normalization methods that transform the seismic signals into non-negative functions are discussed. The numerical examples are then presented at the end of the paper.
引用
收藏
页码:1338 / 1357
页数:20
相关论文
共 45 条
[1]   Numerical resolution of an "unbalanced" mass transport problem [J].
Benamou, JD .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2003, 37 (05) :851-868
[2]   The Monge-Kantorovitch mass transfer and its computational fluid mechanics formulation [J].
Benamou, JD ;
Brenier, Y ;
Guittet, K .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2002, 40 (1-2) :21-30
[3]   Mixed L2-Wasserstein optimal mapping between prescribed density functions [J].
Benamou, JD ;
Brenier, Y .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2001, 111 (02) :255-271
[4]  
Benamou JD, 2000, NUMER MATH, V84, P375, DOI 10.1007/s002119900117
[5]   Numerical solution of the Optimal Transportation problem using the Monge-Ampere equation [J].
Benamou, Jean-David ;
Froese, Brittany D. ;
Oberman, Adam M. .
JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 260 :107-126
[6]  
Bogachev V, 2007, Measure Theory, V1
[7]  
Bonneel N., 2007, ACM T GRAPHIC, V35, P71
[8]   SCALING ALGORITHMS FOR UNBALANCED OPTIMAL TRANSPORT PROBLEMS [J].
Chizat, Lenaic ;
Peyre, Gabriel ;
Schmitzer, Bernhard ;
Vialard, Francois-Xavier .
MATHEMATICS OF COMPUTATION, 2018, 87 (314) :2563-2609
[9]   Unbalanced optimal transport: Dynamic and Kantorovich formulations [J].
Chizat, Lenaic ;
Peyre, Gabriel ;
Schmitzer, Bernhard ;
Vialard, Francois-Xavier .
JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 274 (11) :3090-3123
[10]  
Cuturi M, 2013, Advances in Neural Information Processing Systems (NeurIPS), P2292