Linear Wavefield Optimization Using a Modified Source (Communications in Computational Physics, 2020)
Recorded seismic data are sensitive to the Earth's elastic properties, andthus, they carry information of such properties in their waveforms. The sensitivityof such waveforms to the properties is nonlinear causing all kinds of difficulties to theinversion of such properties. Inverting directly for the components forming the waveequation, which includes the wave equation operator (or its perturbation), and thewavefield, as independent parameters enhances the convexity of the inverse problem.The optimization in this case is provided by an objective function that maximizes thedata fitting and the wave equation fidelity, simultaneously. To enhance the practicality and efficiency of the optimization, I recast the velocity perturbations as secondarysources in a modified source function, and invert for the wavefield and the modifiedsource function, as independent parameters. The optimization in this case correspondsto a linear problem. The inverted functions can be used directly to extract the velocityperturbation. Unlike gradient methods, this optimization problem is free of the Bornapproximation limitations in the update, including single scattering and cross talk thatmay arise for example in the case of multi sources. These specific features are shownfor a simple synthetic example, as well as the Marmousi model.