Tutorial: the mechanics of waveform inversion

Abstract

Unresolved velocity anomalies lead to distortion in images: consequently, much effort has gone into developing model-building techniques to identify such anomalies. Historically, the industry has relied on ray-based tomography to achieve this, but ray methods are limited to detecting features that are typically larger than about five times the dominant wavelength of the recorded seismic data. More recently, model building based on wavefield tomography has been introduced (full waveform inversion). Waveform inversion methods are more costly than ray methods, but have the potential to resolve features smaller than the recorded seismic wavelengths. Using waveform inversion to update a parameter field comprises two main steps: firstly, determine the spatial location of where an observed error came from, and then, determine the magnitude of that error, so as to update the parameter model. The first step uses the same principles as reverse-time migration to construct an ‘image’ of the parameter error, and the second step employs gradient descent methods to estimate the magnitude of the required parameter update. In this tutorial, I will describe both steps of the waveform inversion procedure, and also discuss differing methods of characterizing the error in a given parameter model.