Fast waveform inversion without source‐encoding. (10th July 2012)

• Record Type: Journal Article
• Authors: van Leeuwen, Tristan; Herrmann, Felix J.
• Is Part Of: Geophysical prospecting. Volume 61:(2013:Jun.)supplement s1
• Page Start: 10
• Page End: 19
• Publication Date: 2012-07-10
• Subjects: Full‐waveform inversion -- Source‐encoding -- Stochastic optimization; Prospecting -- Geophysical methods -- Periodicals; 622.15
• DOI: 10.1111/j.1365-2478.2012.01096.x
• Languages: English
• ISSNs: 0016-8025

Abstract

ABSTRACT: Randomized source‐encoding has recently been proposed as a way to dramatically reduce the costs of full waveform inversion. The main idea is to replace all sequential sources by a small number of simultaneous sources. This introduces random cross‐talk in model updates and special stochastic optimization strategies are required to deal with this. Two problems arise with this approach: i) source‐encoding can only be applied to fixed‐spread acquisition setups and ii) stochastic optimization methods tend to converge very slowly, relying on averaging to suppress the cross‐talk. Although the slow convergence is partly off‐set by a low iteration cost, we show that conventional optimization strategies are bound to outperform stochastic methods in the long run. In this paper we argue that we do not need randomized source‐encoding to reap the benefits of stochastic optimization and we review an optimization strategy that combines the benefits of both conventional and stochastic optimization. The method uses a gradually increasing batch of sources. Thus, iterations are initially very cheap and this allows the method to make fast progress in the beginning. As the batch‐size grows, the method behaves like conventional optimization, allowing for fast convergence. Stylized numerical examples suggest that the stochastic and hybrid methods perform equally well with and without source‐encoding and that the hybrid method outperforms both conventional and stochastic optimization. The method does not rely on source‐encoding techniques and can thus be applied to marine data. We illustrate this on a realistic synthetic model.