Upcoming Virtual Tomography Sessions

• 6 April at 10 a.m. Pacific

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Full-Waveform Methods and Applications

6 April, 10 a.m.–12:40 Pacific

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Thank you to SmartSolo for sponsoring the Virtual
Tomography series!

smartsolo.com
smartsolo.com.cn

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Abstracts

“Adjoint Tomography of South America Based on 3D Spectral-Element Seismic Wave Simulations.” Caio Ciardelli, University of São Paulo

Advances in computational power during the last decade combined with the ever- growing seismographic coverage worldwide lead to better illumination of Earth’s interior and its dynamics. Full-waveform adjoint tomography has become a standard method in many seismic imaging studies, with the availability of computational facilities for large-scale simulations. We use 3D spectral-element continental-scale seismic wave simulations (Komatitsch & Tromp, 2002) and 112 earthquakes from the Harvard CMT catalog recorded by 1311 seismic stations to construct an adjoint tomography model of South America. We detect and remove noisy & problematic data using our multi-stage algorithm before the time-window selection, reducing the likelihood of discarding useful data or assimilating bad-quality waveforms in inversions. Our misfit function is a complex-exponentiated instantaneous phase, which optimizes the information extracted from each time series without the need for small-time windows, which is a requirement for cross-correlation measurements. Therefore we fine-tuned our window-selection algorithm to select long-time windows as much as the data quality permits. We use a preconditioner based on the pseudo-Hessian kernel and weight our misfit function to balance the source-receiver distribution for faster convergence. We have performed 23 iterations, gradually increasing the frequency content of the data to avoid local minima. Our final model (SAAM23) shows a significant decrease in the misfit. We further assessed the improvement by using cross-correlation measurements using 53 earthquakes that were not included in the adjoint inversion. In the long wavelengths, the model is compatible with previous studies, such as Feng et al. (2007), Celli et al. (2020), and Lei et al. (2020). SAAM23 agrees with many geological structures in the lithosphere, including the subduction along the Andes, the Amazonian craton, the São Francisco craton, and the Paranapanema block.

“A 3D Shear Wave Velocity Model of the Entire South American Subduction Margin.” Meng Liu, University of Massachusetts Amherst

The goal of this study is to image the seismic characteristics of the slab geometry along the entire South American subduction system, and to explore its spatial correlation with the distributions of volcanism and megathrust earthquakes. The collision between the Nazca plate and the South American continent has resulted in megathrust earthquakes and arc volcanoes, whose distribution patterns are significantly controlled by the geometry of the subducting plate. Previous studies revealed that subducting of the Nazca Ridge and the Juan Fernandez Ridge has contributed to the flat-slab segments in Peru and central Chile, respectively, where seismicity is absent. However, the lack of the lithospheric structures from trench to arc along the entire South American margin limits our understanding of the role of subduction dynamics on seismicity and volcanism. In this study, we construct a high-resolution shear velocity model of the crust and upper mantle within the entire South American subduction system by applying full-wave simulation and inversion method. We use 718 broadband seismic stations along the entire South American margin during 1994-2019. The vertical components of continuous seismic ambient noises between each station pair are cross-correlated and stacked in order to extract Rayleigh-wave empirical Green’s functions. The seismic velocity model is progressively improved by iteratively minimizing the phase delay measurements. Our tomographic results reveal four distinctive features, including (1) strong low-velocity anomalies (< 3.2 km/s) distributed extensively within the Andean continental crust, (2) two high-velocity flat slab segments located beneath southern Peru and central Chile, (3) complex slab geometry at flat-to-normal subduction transitions; and (4) low-velocity mantle wedge in correlation with surface volcanism. The scientific implications of our seismic observations in the South American subduction system will be further explored and discussed.

“Evolutionary Full-Waveform Inversion Applied to the African Plate.” Dirk-Philip van Herwaarden, ETH Zürich

We present a novel approach for the assimilation of new data in full-waveform inversion models. This evolutionary inversion is built on a form of stochastic L-BFGS that we refer to as dynamic mini-batch optimization. The motivation for this work is driven by the observation that seismic data volumes have been growing roughly exponentially. In theory, all this new data should enable us to improve our models. In practice, however, most Earth models are currently built from a static dataset, seeing little updates afterward.

In contrast to conventional waveform inversion, our approach uses dynamically changing mini-batches (subsets of data) that approximate the gradient of the larger dataset at each iteration. This has three major advantages, (1) We exploit redundancies within the dataset, which results in a reduced computational cost for model updates, (2) The size of the complete dataset does not directly impact the computational cost of an iteration, thereby enabling us to work with larger datasets, and (3) The nature of the algorithm makes it trivial to assimilate new data, as the new data can simply be added to the complete dataset from which the mini-batches are sampled.

To show the utility of this approach, we first apply it to an example where we invert for upper-mantle structure beneath the African Plate using data filtered down to 65 seconds. Starting from a 1-D model and with data recorded until 1995, we sequentially grow the dataset by incorporating more and more recent data into this ongoing inversion. Finally, we show our latest application, which started from the Collaborative Seismic Earth Model, where we incorporate periods down to 35 seconds.

“Extended Imaging: Convexification of Full-Waveform Inversion Problems and Target-Orient Elastic Inversion” Ettore Biondi, Stanford University

Full-waveform inversion (FWI) has proven its ability to invert high-resolution model parameters. However, its successful application is bounded by the knowledge of accurate initial model guesses. To avoid local minima and allow for inaccurate initial model estimates, we present a waveform inversion method that uses extended images to avoid the well-known issue of cycle skipping.

Moreover, in the context of seismic exploration, we demonstrate the ability of extended images to preserve the elastic amplitude response of pressure data and how they can be employed to perform a target-oriented elastic FWI method to obtain high-resolution elastic properties.

Finally, we apply the target-oriented methodology on an ocean bottom node field data 3D to characterize a potential target. We present the extended image space in the context of seismic exploration examples, but the theory can be easily applied to global seismology scenarios.

“Large-Scale Bayesian Full-Waveform Inversion using Hamiltonian Monte Carlo.” Lars Gebraad, ETH Zürich

Continental and global scale studies investigating mantle structure have in recent years been enhanced by advances in tomographic methods such as Full-Waveform Inversion (FWI), an approach that relies on the accurate simulation of wavefields using partial differential equations to reconstruct observed data. Methods such as these improve our ability to extract knowledge from data and thereby our capability of studying the inner Earth, at the cost of increased computational expense. Recent studies employing FWI acceleration techniques demonstrate that global scale deterministic FWI is within reach.

FWI problems can be recast as a Bayesian inference problems, using the data and prior knowledge to create a distribution over all possible models. Although this makes evaluating the solution of these problems computationally even more expensive, it also allows for powerful uncertainty quantification. Recent studies on the applicability of gradient-based Monte Carlo algorithms, such as Hamiltonian Monte Carlo (HMC), to seismological problems highlight their potential in this field.
The work presented shows how combining novel optimizations for both FWI and HMC create the powerful machinery needed to give Bayesian answers to tomographic questions on the scale of continents to the globe.

The product of combining these approaches yields efficient non-linear uncertainty quantification for FWI problems with favourable scaling properties w.r.t. many other available probabilistic algorithms. We’ll discuss the major ingedrients of such an approach, as well as preliminary considerations related to real data applications.

One major advantage of treating FWI problems probabilistically is that this allows one to distinguish between the effect of regularization (prior) and resolvability likelihood). This is important for studies involving parameters which are typically ill-recovered, such as density, attenuation and anisotropy.

“Downscaling Seismic Tomography.” Navid Hedjazian, Université de Lyon

In elastic full waveform inversion (FWI), scales smaller than a fraction of the minimum wavelength cannot be resolved, only a smoothed version of the true underlying medium can be recovered. Application of FWI to media containing small and strong heterogeneities therefore remains problematic. This smooth tomographic image is related to the effective elastic properties, which can be exposed with the homogenization theory of wave propagation. We study how this theory can be used in the FWI context. The seismic imaging problem is broken down in a two-stage multiscale approach. In the first step, called homogenized full waveform inversion (HFWI), observed waveforms are inverted for a macro-scale, fully anisotropic effective medium, smooth at the scale of the shortest wavelength present in the wavefield. The solution being an effective medium, it is difficult to directly interpret it. It requires a second step, called downscaling, where the macro-scale image is used as data, and the goal is to recover micro-scale parameters. All the information contained in the waveforms is extracted in the HFWI step. The solution of the downscaling step is highly non-unique as many fine-scale models may share the same long wavelength effective properties. We therefore rely on the introduction of external a priori information. In this step, the forward theory is the homogenization itself. It is computationally cheap, allowing to consider geological models with more complexity.

In a first approach to downscaling, the ensemble of potential fine-scale models is described with an object-based parametrization, and explored with a MCMC algorithm. We illustrate the method with a synthetic cavity detection problem. In a second approach, the prior information is introduced by the means of a training image, and the fine-scale model is recovered with a multi-point statistics algorithm. We apply this method on a subsurface synthetic problem, where the goal is to recover geological facies.