NEESR-SG: High-Fidelity Site Characterization by Experimentation, Field Observation, and Inversion-Based Modeling Dominic Assimaki 2 (Co-PI), Jacobo Bielak 3 (PI), Arash Fathi 4, Omar Ghattas 4, Loukas F. Kallivokas 4 (Co-PI), Sezgin Kucukcoban 4, Jamie Steidl 5 (Co-PI), Kenneth H. Stokoe II 4, and Leticia Velazquez 1 (Co-PI) Forward Modeling Main objective: To develop the capability for estimating the geological structure and mechanical properties both of individual sites and of complete basins, and to demonstrate this capability at the site at the Garner Valley Downhole Array (GVDA). Site characterization: To date, the majority of techniques employed in site characterization hinge on one-dimensional assumptions, allowing material variability along the depth direction only. Even in exploration geophysics, where the problem is similar, albeit at much larger scales, many of the methods used are based on two- dimensional hypotheses, despite the fact that the sources (loads that probe the structure), and the receivers (data recorders), generate and record three- dimensional wavefields, and the structure itself exhibits material variability in three dimensions. A key focal point of this project is the development of three-dimensional inversion methodologies, based on complete waveforms, for reconstructing the three-dimensional profile of probed sites. Key ingredients: Our work entails integrating several individual components: New inversion methods based on partial-differential-equation-(PDE)-constrained optimization approaches In-situ dynamic testing using the equipment Validation using records and experimentation at the well–instrumented site in Garner Valley, CA Earthquake records from new strong-motion and broadband sensor networks New inversion techniques for nonlinear soil behavior Forward and inverse modeling: At the heart of the site characterization problem using active (or passive) dynamic sources lies an inverse wave-based problem. Inverse problems are notoriously more difficult than the corresponding forward wave propagation problems. In the forward problem, one wishes to determine the soil response due to a prescribed excitation under the assumption that the source and the material properties are known. By contrast, in the inverse problem one wants to estimate the spatial distribution of the soil properties that results in a predicted response that most closely matches the observed records generated by either an active source or a seismic signal. The forward problems are, thus, but a mere “inner iteration” of the inverse problem, which entails multiple forward wave propagation simulations. It is thus important that forward wave simulations are carried out fast and accurately. Summary II. At large scales (UTA) A new framework for petascale full-waveform seismic inversion is being developed at UTA/CMU. The image illustrates the first component of this framework, a new state- of-the-art code for elastic wave propagation. This code has the following features: discontinuous Galerkin discretization in space with Godunov fluxes and 4 th -order explicit Runge-Kutta in time; arbitrary-order spectral elements on mapped hexahedral elements; dynamic adaptive mesh coarsening and refinement in space using forest-of-octree meshes; support for hanging nodes for arbitrary-order elements; and parallel dynamic load balancing via space filling curves on forest-of-octree meshes. The code has been scaled up to 16K processor cores (and the adaptivity kernels to 62K cores). The image depicts a snapshot from propagating elastic waves generated by a double-couple source on a spherical domain with several Earth-like layers. Adaptation of the mesh to several wavefronts can be seen in the image. Inverse Modeling Field Tests We have conducted two major field experiments using the equipment: a 2D test at the Hornsby Bend site in Austin, Texas; and a 3D test at the site using the Garner Valley Downhole Array (GVDA) facility. The inverted profiles for Hornsby Bend site are presented here. Results for Garner Valley site will be communicated in the future. CMMI Cognizant NSF Officer: Dr Richard Fragaszy 4 The University of Texas at Austin (UTA) 1 The University of Texas at El Paso (UTEP) 2 Georgia Institute of Technology (GT) 3 Carnegie Mellon (CMU) 5 University of California at Santa Barbara (UCSB) Our small group I. At small scales (UTA/CMU) At small scales, pertinent to individual site characterization efforts, forward wave simulations must allow for proper truncation of the computational domain. New perfectly-matched-layers (PML), embedded within new mixed and hybrid finite element approaches are being developed at UTA/CMU. The images illustrate developments along these lines for 2D SH-wave propagation, and 2D elastic waves. The images show perfect absorption for heterogeneous domains under either surficial or interior explosive sources. 2D PML-truncated forward SH wave simulation 2D PML-truncated forward elastic wave simulation Elastic wave simulations due to explosive sources near the top and bottom of elongated PML- truncated sites I. Inversion based on total wavefields using synthetic data (UTA/CMU) A target shear wave velocity profile with 5 layers and inclusion Inverted 5 layer profile with inclusion Elastic-wave-based inversion (2 parameters) SH-wave-based inversion (1 parameter) Inverted P-wave velocity profile Inverted S-wave velocity profile II. Inversion based on total wavefields using field data (UTA/UCSB) Objective functional: (UCSB/UTA) Discrete state, adjoint, and control problems: Gradient-based optimization: Iteratively update material properties: We invert for a layered medium with an elliptic inclusion. We use a source continuation scheme with four distinct Gaussian pulses to probe the medium. Inverted S-wave velocity profile using full-waveform inversion Inverted P-wave velocity profile using full-waveform inversion Inverted S-wave velocity profile via the SASW method Comparison of S-wave velocity profiles obtained via full-waveform inversion and the SASW method (at locations marked by the solid lines) Currently, our inversion code supports 2D problems. Hence, a key challenge is to generate plane-strain conditions in a field experiment, so that its results can be used in a 2D code. This can be done, theoretically, by applying loads that extends to infinity. In practice, few point sources along a line can approximately generate a similar condition. This process is illustrated in the following images. We attempt to invert soil properties for a site 200 m long. We use five “line loads”, each comprising 21 point sources. 36 sensors are deployed to record data. We use chirp signals to probe the medium. The frequency content of these signals increases linearly from 3Hz to 8Hz and are widely used in radar and geophysical applications. After performing the field experiment, we process the collected data by removing parts with low signal to noise ratio via using an FIR filter. We use superposition to prepare the data for our 2D code. Inversion results are displayed below. We also compare our results with the widely used SASW method. The agreement between the two methods is good. We perform forward wave simulations based on the profiles obtained via the full-waveform inversion, and the SASW method. Time history results at two sensor locations are shown here and demonstrate good agreement between the recorded field data and the computed response using the inversion-based profiles.