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Full Seismic Waveform Modelling and Inversion
Springer Verlag, 2010
Wolfgang Sproessig and Andreas Fichtner
Eagle Publishing, 2005
I am Assistant Professor for Computational Seismology at the Swiss Federal Institute of Technology (ETH) in Zurich. In January 2010 I received my PhD from LMU Munich for my work on Full Seismic Waveform Inversion for Structural and Source Parameters. During my postdoc at Utrecht University , I worked on the development of resolution analysis and multiscale methods for seismic waveform inversion.
My principal research interests include the development and application of methods for full seismic waveform inversion, resolution analysis in tomography, seismic interferometry, and inverse theory. For my work I received the Keiiti Aki Award 2011 from AGU and the Early Career Scientist Award 2015 from IUGG.
Selection of recent work :
Generalised interferometry: We develop a general theory for interferometry by correlation that (i) properly accounts for heterogeneously distributed sources of continuous or transient nature, (ii) fully incorporates any type of linear and nonlinear processing, such as one-bit normalization, spectral whitening and phase-weighted stacking, (iii) operates for any type of medium, including 3-D elastic, heterogeneous and attenuating media, (iv) enables the exploitation of complete correlation waveforms, including seemingly unphysical arrivals, and (v) unifies the earthquake-based two-station method and ambient noise correlations. Our central theme is not to equate interferometry with Green function retrieval, and to extract information directly from processed interstation correlations, regardless of their relation to the Green function. We demonstrate that processing transforms the actual wavefield sources and actual wave propagation physics into effective sources and effective wave propagation. This transformation is uniquely determined by the processing applied to the observed data, and can be easily computed. The effective forward model, that links effective sources and propagation to synthetic interstation correlations, may not be perfect. A forward modelling error, induced by processing, describes the extent to which processed correlations can actually be interpreted as proper correlations, that is, as resulting from some effective source and some effective wave propagation. The magnitude of the forward modelling error is controlled by the processing scheme and the temporal variability of the sources. Applying adjoint techniques to the effective forward model, we derive finite-frequency Frechet kernels for the sources of the wavefield and Earth structure, that should be inverted jointly. The structure kernels depend on the sources of the wavefield and the processing scheme applied to the raw data. Therefore, both must be taken into account correctly in order to make accurate inferences on Earth structure. Not making any restrictive assumptions on the nature of the wavefield sources, our theory can be applied to earthquake and ambient noise data, either separately or combined. This allows us (i) to locate earthquakes using interstation correlations and without knowledge of the origin time, (ii) to unify the earthquake-based two-station method and noise correlations without the need to exclude either of the two data types, and (iii) to eliminate the requirement to remove earthquake signals from noise recordings prior to the computation of correlation functions. In addition to the basic theory for acoustic wavefields, we present numerical examples for 2-D media, an extension to the most general viscoelastic case, and a method for the design of optimal processing schemes that eliminate the forward modelling error completely. This work is intended to provide a comprehensive theoretical foundation of full-waveform interferometry by correlation, and to suggest improvements to current passive monitoring methods. read more
Resolution analysis by random probing: We develop and apply methods for resolution analysis in tomography, based on stochastic probing of the Hessian or resolution operators. Key properties of our methods are (i) low algorithmic complexity and easy implementation, (ii) applicability to any tomographic technique, including full-waveform inversion and linearized ray tomography, (iii) applicability in any spatial dimension and to inversions with a large number of model parameters, (iv) low computational costs that are mostly a fraction of those required for synthetic recovery tests, and (v) the ability to quantify both spatial resolution and inter-parameter trade-offs. Using synthetic full-waveform inversions as benchmarks, we demonstrate that auto-correlations of random-model applications to the Hessian yield various resolution measures, including direction- and position-dependent resolution lengths, and the strength of inter-parameter mappings. We observe that the required number of random test models is around 5 in one, two and three dimensions. This means that the proposed resolution analyses are not only more meaningful than recovery tests but also computationally less expensive. We demonstrate the applicability of our method in a 3D real-data full-waveform inversion for the western Mediterranean. In addition to tomographic problems, resolution analysis by random probing may be used in other inverse methods that constrain continuously distributed properties, including electromagnetic and potential-field inversions, as well as recently emerging geodynamic data assimilation. read more
The crust and upper mantle of the western Mediterranean: We present a full-waveform tomographic model of the western Mediterranean crust and mantle constructed from complete three-component recordings from permanent and temporary networks. The incorporation of body and multi-mode surface waves in the period range from 12-150 s allows us to jointly resolve crustal and mantle structures, including the Guadalquivir, Tajo and Ebro basins at shallow depth, as well as the western Mediterranean subduction system in the transition zone. No mantle plumes can be detected beneath the European Cenozoic rift system, including the Massif Central. In addition to the well-studied Alboran slab, a strong E-W trending high-velocity anomaly is present around 200-300 km depth beneath the Algerian coast. This previously undetected African slab is detached from the surface and broken into two segements. It may be interpreted as the slab that caused the opening of the Liguro-Provencal basin through successive roll-back between 35-15 Ma. read more
Source-structure trade-offs in ambient noise correlations: We analyse the physics and geometry of trade-offs between Earth structure and noise sources in inter-station noise correlations. Our approach is based on the computation of off-diagonal Hessian elements that describe the extent to which variations in noise sources can compensate for variations in Earth structure without changing the misfit beyond the measurement uncertainty. Despite the fact that all ambient noise inverse problems are special in terms of their receiver configuration and data, some general statements concerning source-structure trade-offs can be made: (i) While source-structure trade-offs may be reduced to some extent by clever measurement design, there are inherent trade-offs that can generally not be avoided. These inherent trade-offs may lead to a mispositioning of structural heterogeneities when the noise source distribution is unknown. (ii) When attenuation is weak, source-structure trade-offs in ambient noise correlations are a global phenomenon, meaning that there is no noise source perturbation that does not trade-off with some Earth structure, and vice versa. (iii) The most significant source-structure trade-offs occur within two elliptically shaped regions connecting a potential noise source perturbation to each one of the receivers. (iv) Far from these elliptical regions, only small-scale structure can trade off against changes in the noise source. (v) While source-structure trade-offs mostly decay with increasing attenuation, they are nearly unaffected by attenuation when the noise source perturbation is located near the receiver-receiver line. This work is intended to contribute to the development of joint source-structure inversions of ambient noise correlations, and in particular to an understanding of the extent to which source-structure trade-offs may be reduced. It furthermore establishes the foundation of future resolution analyses that properly quantify trade-offs between noise sources and Earth structure. read more