TY - JOUR
T1 - Linear Wavefield Optimization Using a Modified Source
AU - Alkhalifah , Tariq
JO - Communications in Computational Physics
VL - 1
SP - 276
EP - 296
PY - 2020
DA - 2020/05
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2018-0144
UR - https://global-sci.org/intro/article_detail/cicp/16837.html
KW - Inversion, optimization, scattering theory.
AB - <p style="text-align: justify;">Recorded seismic data are sensitive to the Earth&#39;s elastic properties, and
thus, they carry information of such properties in their waveforms. The sensitivity
of such waveforms to the properties is nonlinear causing all kinds of difficulties to the
inversion of such properties. Inverting directly for the components forming the wave
equation, which includes the wave equation operator (or its perturbation), and the
wavefield, as independent parameters enhances the convexity of the inverse problem.
The optimization in this case is provided by an objective function that maximizes the
data fitting and the wave equation fidelity, simultaneously. To enhance the practicality and efficiency of the optimization, I recast the velocity perturbations as secondary
sources in a modified source function, and invert for the wavefield and the modified
source function, as independent parameters. The optimization in this case corresponds
to a linear problem. The inverted functions can be used directly to extract the velocity
perturbation. Unlike gradient methods, this optimization problem is free of the Born
approximation limitations in the update, including single scattering and cross talk that
may arise for example in the case of multi sources. These specific features are shown
for a simple synthetic example, as well as the Marmousi model.</p>