Full Seismic Waveform Modelling and Inversion

Abstract

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, BerlinPrinted on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To my family and Carolin ForewordOur planet is permanently vibrating, excited by oceans, atmosphere, earthquakes, or man-made sources. Luckily, Earth's physical properties are such that these vibrations -elastic waves to be more specific -often propagate to large distances carrying information on the medium they encounter along the way. The problem of making an educated guess at the subsurface structure from observations of ground motions is as old as instrumental seismology itself (so not that old, maybe a century or so). Let us call the problem seismic tomography akin to CT scanning in medicine, a field seismologists have always envied. Because of limitations in illuminating the Earth with sufficient coverage we have never obtained the sharp and detailed internal structures so familiar from medical imaging.Up to now we have mostly cut corners in the way we model and fit our seismic data. We typically reduce long, wiggly seismograms to a few bytes of information (e.g. travel times, phase velocities) and try to explain these data with approximate theories. This has been for a good reason. Our computers were simply not fast and big enough to allow the calculation of complete wave fields through 3D Earth structures. Frequently the data just do not warrant the use of sophisticated physics.The situation regarding computational power in connection with 3D wave propagation has dramatically changed in the past few years. Even on a global scale the calculation of wave fields across the complete observed frequency range is in sight. On smaller scales (continents, basins, volcanoes, reservoirs) we are already witnessing the emergence of 3D wave propagation as the tool for data modelling, inversion and parameter studies.This was Albert Tarantola's (and others) dream 25 years ago: just simulate the physics correctly and let the data (i.e. the misfit to a theoretical seismogram) decide whether the Earth model is good or not. In his world (the probabilistic approach) this should be done using a Monte Carlo-type approach: calculate zillions of models and use all the results to estimate parameters and uncertainties. Unfortunately, we are not there yet. We still need to resort to linearisations around (hopefully good) starting models and employ adjoint-type techniques to update our Earth models. Fortunately, in many situations, good starting models can be found, making iterative waveform inversion the preferred tool to improve our Earth models using most or all of the observed data. vii viii ForewordThe book in your hands is the first to provide a broad overview on how to solve the forward problem to calculate accurate seismograms in 3D Earth m...

Pre-stack full waveform inversion of ultra-high-frequency marine seismic reflection data

“…The inversion of pre-stack marine seismic data is often addressed within the acoustic approximation to obtain a detailed pressure wave velocity model (Fichtner, 2011;Virieux & Operto, 2009;Tarantola, 1984). Although this approach is widely employed in both industry and academia as an effective tool to improve the quality of the seismic imaging , acoustic waveform inversion fails to reproduce an accurate model of the subsurface when shear properties vary in the subsurface, or density is not correlated to P-impedance variations, creating significant amplitude and phase versus offset effects (Mallick & Adhikari, 2015;Silverton et al, 2015).…”

“…FWI is a non-linear and ill-posed parameter estimation technique, which iteratively updates the earth model m by minimising a weighted measure of the difference between the computed and recorded seismic data δd(m) (Tarantola, 1984;Virieux & Operto, 2009;Fichtner, 2011). The objective or misfit functional accounts for the amplitude and phase characteristics of the wavefield, either as in the full seismogram, or extracted as pre-stack attributes (Fichtner, 2011;JimenezTejero et al, 2015) and it is regularised in order to penalise physically non-meaningful solutions (Menke, 1989;Asnaashari et al, 2012).…”

“…Although such properties can be retrieved through the inversion of the reflections' AVO, a full waveform approach has the advantage to account for all the wave phenomena (Tarantola, 1984(Tarantola, , 1986Fichtner, 2011), within the required resolution and modelling approximation. By exploiting the information contained in the complete waveform, FWI outperforms AVO inversion in most realistic reservoir geophysics application (Mallick & Adhikari, 2015), especially when complicated layer interference and velocity gradients are present (Xu et al, 1993;Igel et al, 1996), which is likely to be a factor in UHF near-surface seismic data.…”

A local adaptive method for the numerical approximation in seismic wave modelling

“…This problem is known as Full Waveform Inversion (FWI) (see, e.g., [2,7]). Many local or global different optimization strategies have been studied in recent years.…”

“…Here we assume only P-wave propagation and heterogeneous density data that are small if compared to pressure and source term variations. In this case [3,7], the seismic wave propagation can be approximated by the following equation:…”