Full Waveform Inversion by Iterative Depth Migration and Impedance Estimation Using Well Control

Abstract

We relate full waveform inversion (FWI) to processes familiar to practicing geophysicists. A key theoretical result behind FWI is that a linear update to a migration velocity model is proportional to a prestack reverse-time migration of the data residual (the difference between the actual data and data predicted by the model) where the proportionality factor must be estimated. We argue that in most real-world cases this factor will be frequency dependent, or in the time domain, it will be a convolutional wavelet. The estimation of the velocity update from the migrated section and the common process of impedance inversion are analogous, and we view FWI as a practical cycle of data modeling, migration of the data residual, and "calibration" of this migration to deduce the velocity update. The calibration step can be accomplished like a conventional impedance inversion where the migrated data residual is tied to the velocity residual (the difference between actual velocity and migration velocity) at a well. As there are a great many established algorithms for impedance inversion, so there are a plethora of possibilities for calibration. We present an extended example using the Marmousi model in which we use wave-equation migration (e.g. depth stepping) of the data residual and a simple least-squares amplitude scaling and constant phase rotation, determined at a simulated well, to calibrate the migration. We find that our approach produces a much improved velocity model in only a few iterations.

Full-Waveform Inversion in Time Domain by Increased Frequency Iteratively

“…Research on the FWI method with synthetic data has long been carried out by several universities in the world since 2000. However, this method was first introduced in 1983 by Lailly, then continued by Tarantola in 1984, and in 1986, Mora introduced the method too [5] In 2010, Magrave et al reviewed developments and proposed the FWI is an iterative cycle that can involve forward modeling, impedance inversion, velocity model updates, and pre-stack migration [3].…”

Reconciling seismic AVO and precritical reflection FWI - Analysis of the inverse Hessian

“…A fully realized methodology for precritical reflection data has not as yet been achieved, in part because of longstanding issues such as missing wavelengths (Kelly et al, 2013). Acquisition is one potential route to addressing these issues, for instance via incorporation of well-control (Margrave et al, 2012b), and via access to data with increasingly low temporal frequencies (Margrave et al, 2012a;Plessix et al, 2012). We will proceed in this paper assuming pre-critical reflection modes have a significant role to play in practical FWI.…”