A Nonlinear Method for Imaging with Acoustic Waves Via Reduced Order Model Backprojection
A Nonlinear Method for Imaging with Acoustic Waves Via Reduced Order Model Backprojection
复制标题
通过降阶模型反投影进行声波成像的非线性方法
DOI：
10.1137/17m1133580
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
M. Zaslavsky
中科院分区：
文献类型：
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作者：
V. Druskin;A. Mamonov;M. Zaslavsky
提出了一种基于模型降阶的声波方程非线性成像新方法。我们的目标是成像的声速，标量波动方程的系数从离散采样的时域数据测量的换能器阵列，可以作为源和接收器的不连续性。我们把波动方程沿着与换能器泛函作为一个动力系统。可以计算这种系统的传播子的降阶模型（ROM），使得它精确地内插测量的时域数据。所得到的ROM是声波方程的解的快照的子空间上的传播算子的正交投影。虽然波场快照是未知的，但投影ROM可以完全从测量数据计算。图像是通过反投影ROM。由于投影子空间的基函数是未知的，我们将它们替换为一个已知的光滑运动学速度模型计算。ROM构造的关键步骤是解快照的隐式正交化。这是一个非线性的过程，区别于传统的线性成像方法（克希霍夫偏移和逆时偏移- RTM），我们的方法。它解决了数据捕获的所有动力学行为，因此来自速度模型的不完善知识的误差纯粹是运动学的。这允许几乎完全去除多次反射伪影，同时与常规RTM相比提高了距离方向上的分辨率。
We introduce a novel nonlinear imaging method for the acoustic wave equation based on model order reduction. The objective is to image the discontinuities of the acoustic velocity, a coefficient of the scalar wave equation from the discretely sampled time domain data measured at an array of transducers that can act as both sources and receivers. We treat the wave equation along with transducer functionals as a dynamical system. A reduced order model (ROM) for the propagator of such system can be computed so that it interpolates exactly the measured time domain data. The resulting ROM is an orthogonal projection of the propagator on the subspace of the snapshots of solutions of the acoustic wave equation. While the wavefield snapshots are unknown, the projection ROM can be computed entirely from the measured data. The image is obtained by backprojecting the ROM. Since the basis functions for the projection subspace are not known, we replace them with the ones computed for a known smooth kinematic velocity model. A crucial step of ROM construction is an implicit orthogonalization of solution snapshots. It is a nonlinear procedure that differentiates our approach from the conventional linear imaging methods (Kirchhoff migration and reverse time migration - RTM). It resolves all the dynamical behavior captured by the data, so the error from the imperfect knowledge of the velocity model is purely kinematic. This allows for almost complete removal of multiple reflection artifacts, while simultaneously improving the resolution in the range direction compared to conventional RTM.