Hierarchical approach of seismic full waveform inversion

Abstract

Full waveform inversion (FWI) of seismic traces recorded at the free surface allows the reconstruction of the physical parameters structure on the underlying medium. For such a reconstruction, an optimization problem is defined, where synthetic traces, obtained through numerical techniques as finite-difference or finite-element methods in a given model of the subsurface, should match the observed traces. The number of data samples is routinely around 1 billion for 2D problems and 1 trillion for 3D problems while the number of parameters ranges from 1 million to 10 million degrees of freedom. Moreover, if one defines the mismatch as the standard least-squares norm between values sampled in time/frequency and space, the misfit function has a significant number of secondary minima related to the ill-posedness and the nonlinearity of the inversion problem linked to the so-called cycle skipping. Taking into account the size of the problem, we consider a local linearized method where gradient is computed using the adjoint formulation of the seismic wave propagation problem. Starting for an initial model, we consider a quasi-Newtonian method, which allows us to formulate the reconstruction of various parameters such as P and S waves velocities or density or attenuation factors. A hierarchical strategy based on the incremental increase of the data complexity starting from low-frequency content to high-frequency content, from initial wavelets to later phases in the data space from narrow azimuths to wide azimuths and from simple observables to more complex ones. Different synthetic examples on realistic structures illustrate the efficiency of this strategy based on the data manipulation. This strategy related to the data space has to be inserted into a more global framework where we could improve significantly the probability to converge to the global minimum. When considering the model space, we may rely on the construction of the initial model or add constraints such as smoothness of the searched model and/or prior informations collected by other means. An alternative strategy concerns the building of the objective function and various possibilities must be considered, which may increase the linearity of the inversion procedure.

Multiscale reflection phase inversion with migration deconvolution

“…Bozdag et al (2011), Wu et al (2014) and Chen et al (2018) introduced a reflection multiscale envelope inversion method so that the signal's envelope carries ultra-low frequency information missing in the original signal. Furthermore, a set of methods have been developed to exclude the cycle-skipped events in different domains (Bunks et al, 1995;Asnaashari et al, 2012;Bi and Lin, 2014;AlTheyab and Schuster, 2015).…”

Vector acoustic full waveform inversion: taking advantage of de-aliasing and receiver ghosts

“…Multi-component data have been used in full waveform inversion in both the acoustic and elastic formulations in the time and frequency domain, including methods attempting to incorporate the advantages of both time and frequency domain formulations. Such inversion methods often incorporate nested hierarchical workflows (Choi et al, 2008;Brossier et al, 2009;Asnaashari et al, 2012;Plessix et al, 2013;Prieux et al, 2013;Yang et al, 2014, and others). The possibility of poro-elastic FWI has also been considered (Yang et al, 2018;Yang and Malcolm, 2019).…”

Inverting reflections using full-waveform inversion with inaccurate starting models

“…Cycle-skipped events are excluded by filtering in different transform domains (Bunks et al, 1995;Asnaashari et al, 2012), or by evaluating the phase lag between the observed and calculated data for each event and muting cycle-skipped events (Bi and Lin, 2014). In general, such methods apply FWI in multistages.…”