Complex-Valued Imaging with Total Variation Regularization: An Application to Full-Waveform Inversion in Visco-acoustic Media

衰减 声波方程 频域 非线性系统 全变差去噪 反问题 慢度 数学 参数化(大气建模) 算法 数学分析 计算机科学 声学 物理 声波 光学 辐射传输 量子力学 降噪
作者
Hossein S. Aghamiry,Ali Gholami,S. Operto
出处
期刊:Siam Journal on Imaging Sciences [Society for Industrial and Applied Mathematics]
卷期号:14 (1): 58-91 被引量:1
标识
DOI:10.1137/20m1344780
摘要

Full-waveform inversion (FWI) is a nonlinear PDE constrained optimization problem which seeks to estimate the constitutive parameters of a medium by fitting waveforms. Among these parameters, attenuation needs to be taken into account in viscous media to exploit the full potential of FWI. Attenuation is easily implemented in the frequency domain by using complex-valued velocities in the time-harmonic wave equation. These complex velocities are frequency-dependent to guarantee causality and account for dispersion. Since estimating a complex frequency-dependent velocity at each grid point in space is not realistic, the optimization is generally performed in the real domain by processing the phase velocity (or slowness) at a reference frequency and attenuation (or quality factor) as separate real parameters. This real parametrization requires an a priori empirical relation (such as the nonlinear Kolsky--Futterman (KF) or standard linear solid (SLS) attenuation models) between the complex velocity and the two real quantities, which is prone to generate modeling errors if it does not represent accurately the attenuation behavior of the medium. Moreover, it leads to a multivariate inverse problem, which is ill-posed due to the cross-talk between the two classes of real parameters. To alleviate these issues, we solve directly the optimization problem in the complex domain by processing narrow bands of frequencies in sequence under the assumption of bandwise frequency dependence of the complex velocities. Moreover, we use a relaxation method to extend the FWI search space by processing the wave equation as a weak constraint with the alternating direction method of multipliers (ADMM) to mitigate the risk of spurious local minima. To mitigate the ill-posedness of the inversion, three total variation (TV) regularization schemes based upon ADMM and proximity algorithms are presented. In the first, regularization is applied directly on the complex velocities. In the other two, separate TV regularizations are tailored to different attributes of the complex velocities (real and imaginary parts, magnitude and phase). The real phase velocity and attenuation factor are then reconstructed a posteriori at each spatial position from the estimated complex velocity using arbitrary empirical relation. The numerical results first show that the regularization of the amplitude and phase provides the most reliable results. Moreover, they show that the band-by-band design of the inversion limits the sensitivity of the recovered phase velocity and attenuation factor to the attenuation model used for their a posteriori extraction.
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
Tourist完成签到 ,获得积分10
1秒前
王路飞发布了新的文献求助10
1秒前
4秒前
5秒前
6秒前
西南楚留香完成签到,获得积分10
9秒前
Newky发布了新的文献求助10
10秒前
12秒前
12秒前
王路飞完成签到,获得积分10
13秒前
16秒前
mmm发布了新的文献求助10
17秒前
boltos发布了新的文献求助10
19秒前
ASA完成签到,获得积分10
19秒前
abin发布了新的文献求助10
20秒前
Newky完成签到,获得积分10
20秒前
卿君完成签到,获得积分10
24秒前
24秒前
Jasper应助乔佳怡采纳,获得10
26秒前
Akim应助hwezhu采纳,获得10
26秒前
27秒前
alpv完成签到,获得积分10
27秒前
28秒前
南冥发布了新的文献求助10
31秒前
31秒前
32秒前
迷路的绿藻头完成签到 ,获得积分10
32秒前
量子星尘发布了新的文献求助10
33秒前
哈哈完成签到,获得积分10
33秒前
A阿澍发布了新的文献求助10
34秒前
abin完成签到,获得积分10
34秒前
36秒前
36秒前
36秒前
hwezhu发布了新的文献求助10
37秒前
39秒前
jyy应助科研通管家采纳,获得10
41秒前
czh应助科研通管家采纳,获得20
41秒前
烟花应助科研通管家采纳,获得10
42秒前
充电宝应助科研通管家采纳,获得10
42秒前
高分求助中
A new approach to the extrapolation of accelerated life test data 1000
ACSM’s Guidelines for Exercise Testing and Prescription, 12th edition 500
‘Unruly’ Children: Historical Fieldnotes and Learning Morality in a Taiwan Village (New Departures in Anthropology) 400
Indomethacinのヒトにおける経皮吸収 400
Phylogenetic study of the order Polydesmida (Myriapoda: Diplopoda) 370
基于可调谐半导体激光吸收光谱技术泄漏气体检测系统的研究 350
Robot-supported joining of reinforcement textiles with one-sided sewing heads 320
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 3989263
求助须知:如何正确求助?哪些是违规求助? 3531418
关于积分的说明 11253814
捐赠科研通 3270066
什么是DOI,文献DOI怎么找? 1804884
邀请新用户注册赠送积分活动 882084
科研通“疑难数据库(出版商)”最低求助积分说明 809136