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A nonlinear method for imaging with acoustic waves via reduced order model backprojection

机译:一种非线性的声波成像降阶方法   模型反投影

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摘要

We introduce a novel nonlinear imaging method for the acoustic wave equationbased on data-driven model order reduction. The objective is to image thediscontinuities of the acoustic velocity, a coefficient of the scalar waveequation from the discretely sampled time domain data measured at an array oftransducers that can act as both sources and receivers. We treat the waveequation along with transducer functionals as a dynamical system. A reducedorder model (ROM) for the propagator of such system can be computed so that itinterpolates exactly the measured time domain data. The resulting ROM is anorthogonal projection of the propagator on the subspace of the snapshots ofsolutions of the acoustic wave equation. While the wavefield snapshots areunknown, the projection ROM can be computed entirely from the measured data,thus we refer to such ROM as data-driven. The image is obtained bybackprojecting the ROM. Since the basis functions for the projection subspaceare not known, we replace them with the ones computed for a known smoothkinematic velocity model. A crucial step of ROM construction is an implicitorthogonalization of solution snapshots. It is a nonlinear procedure thatdifferentiates our approach from the conventional linear imaging methods(Kirchhoff migration and reverse time migration - RTM). It resolves alldynamical behavior captured by the data, so the error from the imperfectknowledge of the velocity model is purely kinematic. This allows for almostcomplete removal of multiple reflection artifacts, while simultaneouslyimproving the resolution in the range direction compared to conventional RTM.
机译:我们介绍了一种基于数据驱动的模型阶数约简的声波方程非线性成像新方法。目的是成像声速的不连续性,该声速是从在既可以用作源又可以用作接收器的换能器阵列处测量的离散采样时域数据中得到的标量波方程的系数。我们将波方程与换能器功能视为一个动力系统。可以计算此类系统的传播者的降阶模型(ROM),以便它精确地内插测得的时域数据。最终的ROM是传播器在声波方程解快照的子空间上的正交投影。虽然不知道波场快照,但可以完全根据测量数据计算投影ROM,因此我们将此类ROM称为数据驱动的。通过反投影ROM获得图像。由于投影子空间的基函数未知,因此我们将其替换为针对已知的平滑运动速度模型计算的基函数。 ROM构建的关键步骤是解决方案快照的隐式正交化。这是一个非线性程序,使我们的方法与传统的线性成像方法(基尔霍夫偏移和逆时偏移-RTM)有所不同。它解决了由数据捕获的所有动力学行为,因此速度模型的不完全知识所带来的误差纯粹是运动学上的。与传统的RTM相比,这几乎可以完全消除多个反射伪影,同时提高了范围方向上的分辨率。

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