Michael Afanasiev

Ambient seismic source inversion in a heterogeneous Earth - Theory and application to the Earth's hum†

The sources of ambient seismic noise are extensively studied both to better understand their influence on ambient noise tomography and related techniques, and to infer constraints on their excitation mechanisms. Here we develop a gradient-based inversion method to infer the space-dependent and time-varying source power spectral density of the Earths hum from cross correlations of continuous seismic data. The precomputation of wavefields using spectral elements allows us to account for both finite-frequency sensitivity and for three-dimensional Earth structure. Although similar methods have been proposed previously, they have not yet been applied to data to the best of our knowledge. We apply this method to image the seasonally varying sources of Earths hum during North and South Hemisphere winter. The resulting models suggest that hum sources are localized, persistent features that occur at Pacific coasts or shelves and in the North Atlantic during North Hemisphere winter, as well as South Pacific coasts and several distinct locations in the Southern Ocean in South Hemisphere winter. The contribution of pelagic sources from the central North Pacific cannot be constrained. Besides improving the accuracy of noise source locations through the incorporation of finite-frequency effects and 3-D Earth structure, this method may be used in future cross-correlation waveform inversion studies to provide initial source models and source model updates.

The Collaborative Seismic Earth Model: Generation 1

Abstract We present a general concept for evolutionary, collaborative, multiscale inversion of geophysical data, specifically applied to the construction of a first‐generation Collaborative Seismic Earth Model. This is intended to address the limited resources of individual researchers and the often limited use of previously accumulated knowledge. Model evolution rests on a Bayesian updating scheme, simplified into a deterministic method that honors todays computational restrictions. The scheme is able to harness distributed human and computing power. It furthermore handles conflicting updates, as well as variable parameterizations of different model refinements or different inversion techniques. The first‐generation Collaborative Seismic Earth Model comprises 12 refinements from full seismic waveform inversion, ranging from regional crustal‐ to continental‐scale models. A global full‐waveform inversion ensures that regional refinements translate into whole‐Earth structure.

Automatic Global Multiscale Seismic Inversion: Insights into Model, Data, and Workflow Management

Modern global seismic waveform tomography is formulated as a PDE-constrained nonlinear optimization problem, where the optimization variables are Earths visco-elastic parameters. This particular problem has several defining characteristics. First, the solution to the forward problem, which involves the numerical solution of the elastic wave equation over continental to global scales, is computationally expensive. Second, the determinedness of the inverse problem varies dramatically as a function of data coverage. This is chiefly due to the uneven distribution of earthquake sources and seismometers, which in turn results in an uneven sampling of the parameter space. Third, the seismic wavefield depends nonlinearly on the Earths structure. Sections of a seismogram which are close in time may be sensitive to structure greatly separated in space. In addition to these theoretical difficulties, the seismic imaging community faces additional issues which are common across HPC applications. These include the storage of massive checkpoint files, the recovery from generic system failures, and the management of complex workflows, among others. While the community has access to solvers which can harness modern heterogeneous computing architectures, the computational bottleneck has fallen to these memory- and manpower-bounded issues. We present a two-tiered solution to the above problems. To deal with the problems relating to computational expense, data coverage, and the increasing nonlinearity of waveform tomography with scale, we present the Collaborative Seismic Earth Model (CSEM). This model, and its associated framework, takes an open-source approach to global-scale seismic inversion. Instead of attempting to monolithically invert all available seismic data, the CSEM approach focuses on the inversion of specific geographic subregions, and then consistently integrates these subregions via a common computational framework. To deal with the workflow and storage issues, we present a suite of workflow management software, along with a custom designed optimization and data compression library. It is the goal of this paper to synthesize these above concepts, originally developed in isolation, into components of an automatic global-scale seismic inversion.

MULTI-SCALE/MULTI-DATA INVERSION FOR ELASTIC EARTH STRUCTURE - A CONCEPT

Complex interactions of smalland large-scale processes are characteristic for the physics of the Earth, and their proper quantification is key to the integration of interdependent geophysical systems that are today mostly treated as isolated. Inferring Earth structure over a wide range of scales is the long-standing goal of seismic tomography. While much progress has been made in recent years, tomographic resolution remains limited by our inability to model and invert seismic wave propagation across the complete observable frequency band with the currently available computational resources. Here we propose a new concept for multi-scale seismic tomography intended to resolve Earth structure from local to global scales, including mantle as well as detailed crustal features. For this we develop a multi-scale full waveform inversion technique that assimilates complete teleseismic and regional seismograms in a broad frequency band. Being based on spectralelement modelling and adjoint techniques, our method simultaneously solves multiple regionaland continental-scale inverse problems in order to jointly resolve Earth structure with resolving lengths ranging from around 20 to more than 5000 km. To further increase the exploitable frequency band beyond what can be modelled numerically, we combine full waveform inversion with classical ray tomography that assimilates the arrival times of high-frequency body waves into the tomographic model. This combination results in an improved resolution of Earth structure, especially below 300 km depth. We apply our method to Europe and Western Asia, where resolution is particularly high beneath the North Atlantic, the Western Mediterranean and Anatolia. Quantitative resolution analysis based on second-order adjoints, as well as comparisons with observed ambient noise correlations, allow us to assess the quality and predictive power of the final model.