A nonlinear approach of elastic reflection waveform inversion

Abstract

SUMMARYElastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P-and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P-and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.

Elastic reflection waveform inversion with variable density

“…With a least-square optimization to the predicted image, Wu and Alkhalifah (2015) proposed a new optimization problem where the background model and perturbations are inverted simultaneously. Subsequently, Guo and Alkhalifah (2016) brought the concept of RWI to elastic media and developed elastic reflection waveform inversion that aims to invert for the long wavelength components of P-and S-wave velocities. However, the variable density as a potential reflector, with little influence on the propagation of waves, can not be neglected as a perturbation parameter.…”

Elastic Wave-equation Reflection Traveltime Inversion Using Dynamic Warping and Wave Mode Decomposition

“…Xu et al (2012) suggested using a reflection waveform inversion (RWI) method, which aim to invert the long-wavelength components of the model by using the reflections predicted by migration/demigration process. Through minimizing misfit function of waveform, the RWI method are developed by several work (Wu and Alkhalifah, 2015;Zhou et al, 2015), and recently extended to elastic case by Guo and Alkhalifah (2016).…”