Simultaneous Inversion of the Background Velocity and the Perturbation in Full Waveform Inversion

Abstract

The gradient of standard full-waveform inversion (FWI) attempts to map the residuals in the data to perturbations in the model. Such perturbations may include smooth background updates from the transmission components and high wavenumber updates from the reflection components. However, if we fix the reflection components using imaging, the gradient of what is referred to as reflected-waveform inversion (RWI) admits mainly transmission background-type updates. The drawback of existing RWI methods is that they lack an optimal image capable of producing reflections within the convex region of the optimization. Because the influence of velocity on the data was given mainly by its background (propagator) and perturbed (reflectivity) components, we have optimized both components simultaneously using a modified objective function. Specifically, we used an objective function that combined the data generated from a source using the background velocity, and that by the perturbed velocity through Born modeling, to fit the observed data. When the initial velocity was smooth, the data modeled from the source using the background velocity will mainly be reflection free, and most of the reflections were obtained from the image (perturbed velocity). As the background velocity becomes more accurate and can produce reflections, the role of the image will slowly diminish, and the update will be dominated by the standard FWI gradient to obtain high resolution. Because the objective function was quadratic with respect to the image, the inversion for the image was fast. To update the background velocity smoothly, we have combined different components of the gradient linearly through solving a small optimization problem. Application to the Marmousi model found that this method converged starting with a linearly increasing velocity, and with data free of frequencies below 4 Hz. Application to the 2014 Chevron Gulf of Mexico imaging challenge data set demonstrated the potential of the proposed method.

Efficient full waveform inversion using the excitation representation of the source wavefield

“…To make this comparison more quantitative, we plot the correlation factor (C.F. ), defined as (Wu & Alkhalifah 2015b):…”

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

“…However, most of them admit S-wave artifacts in the resulting wavefield. These artifacts are reduced when the source is located in an isotropic layer (Alkhalifah 2000), but become unacceptable when the source is located in the anisotropic region or we have strong scattering acting as secondary sources (Wu & Alkhalifah 2015;.…”

Velocity Building by Reflection Waveform Inversion without Cycle-skipping

“…On the other hand, RWI produces relatively higher wavenumber wavepath updates as the matching criteria at the reference zero offset (and near offset) is weighted equally with the far offset, a feature not provided in DSO. However, RWI can include undesirable high wavenumber components (Wu and Alkhalifah, 2015) in real cases.…”