Three-Dimensional P- and S-Wave Velocity Profiling of Geotechnical Sites Using Full-Waveform Inversion Driven by Field Data
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Soil Dynamics and Earthquake Engineering 87 (2016) 63–81 Contents lists available at ScienceDirect Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn Three-dimensional P- and S-wave velocity profiling of geotechnical sites using full-waveform inversion driven by field data Arash Fathi a, Babak Poursartip b, Kenneth H. Stokoe II b, Loukas F. Kallivokas a,b,n a Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA b Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, TX, USA article info abstract Article history: We discuss the application of a recently developed full-waveform-inversion-based technique to the Received 22 December 2015 imaging of geotechnical sites using field-collected data. Specifically, we address the profiling of arbitrarily Received in revised form heterogeneous sites in terms of P- and S-wave velocities in three dimensions, using elastic waves as 18 April 2016 probing agents. We cast the problem of finding the spacial distribution of the elastic soil properties as an Accepted 19 April 2016 inverse medium problem, directly in the time domain, and use perfectly-matched-layers (PMLs) to ac- Available online 7 May 2016 count for the semi-infinite extent of the site under investigation. Keywords: After briefly reviewing the theoretical and computational aspects of the employed technique, we Site characterization focus on the characterization of the George E. Brown Jr. Network for Earthquake Engineering Simulation Full-waveform inversion (FWI) site in Garner Valley, California (NEES@UCSB). We compare the profiles obtained from our full-wave- Elastic waves form-inversion-based methodology against the profiling obtained from the Spectral-Analysis-of-Surface- perfectly-matched-layers (PMLs) Spectral-Analysis-of-Surface-Waves (SASW) Waves (SASW) method, and report agreement. In an attempt to validate our methodology, we also Vibroseis compare the recorded field data at select control sensors that were not used for the full-waveform in- Field data processing version, against the response at the same sensors, computed based on the full-waveform-inverted profiles. We report very good agreement at the control sensors, which is a strong indicator of the cor- rectness of the inverted profiles. Overall, the systematic framework discussed herein seems robust, general, practical, and promising for three-dimensional site characterization purposes. & 2016 Elsevier Ltd. All rights reserved. 1. Introduction profiling of the soil shares common elements with medical ima- ging [17]. In both cases, elastic waves are used to interrogate the Reliable three-dimensional P- and S-wave velocity profiles of unseeable medium, and the medium's response to this probing is the near-surface soil have great value in geotechnical engineering subsequently used for driving the imaging. In the mathematical practice, and can play a vital role in the safe design of critical sciences, this process is referred to as solving an inverse medium components of the civil infrastructure, such as nuclear power problem. fi plants, bridges, and hospitals, among others. Wave velocity pro- Our goal is to nd the distribution of the P-wave velocity cp(x), 1 filing of the soil is referred to as seismic site characterization. and S-wave velocity cs(x) of the soil in three-space dimensions. We use a seismic vibrator to apply loads on the ground surface, Seismic site characterization techniques can be broadly classified which results in the propagation of elastic waves in the soil. Due to into two categories: invasive and non-invasive. Invasive techni- the possibly heterogeneous character of the site, multiple reflec- ques, such as borehole-based methods, are costly and can typically tions and refractions occur. The time-history response of the soil provide only localized information of the site under investigation, medium to this loading is recorded by using geophones, spatially while, non-invasive techniques are capable of providing global arranged over the formation's surface, and is, hereafter, referred to fi imaging, and are generally more cost-ef cient. Non-invasive as measured response (Fig. 1). Arriving at a material profile can then be achieved by minimizing the difference between the measured n Corresponding author at: Department of Civil, Architectural and Environmental response at sensor locations, and a computed response corre- Engineering, The University of Texas at Austin, Austin, TX, USA. sponding to a trial distribution of the material parameters, under E-mail addresses: [email protected] (A. Fathi), [email protected] (B. Poursartip), [email protected] (K.H. Stokoe II), [email protected] (L.F. Kallivokas). 1 x =(xyz,,) is the position vector. http://dx.doi.org/10.1016/j.soildyn.2016.04.010 0267-7261/& 2016 Elsevier Ltd. All rights reserved. 64 A. Fathi et al. / Soil Dynamics and Earthquake Engineering 87 (2016) 63–81 Fig. 1. Problem definition: (a) interrogation of a heterogeneous semi-infinite domain by an active source; and (b) computational model truncated from the semi-infinite medium via the introduction of perfectly-matched-layers (PMLs). the same loading, using a computational model. The computa- data, which are inherently three-dimensional, into two-dimensional tional model should mimic the physics of the problem as closely as full-waveform-inversion-based software, whenever the site condi- possible. A key challenge is proper termination of the semi-infinite tions would support plane strain assumptions. We demonstrated the extent of the domain of interest.2 We use perfectly matched-layers method's viability by characterizing a site in Austin, Texas [19].Inthis (PMLs) for domain truncation (Fig. 1) [5,15,39], since they are communication, we abandon the plane strain assumption, and con- among the best available tools in the presence of heterogeneity sider arbitrary heterogeneity in three space dimensions. To be able to [15]. A PML is a (practically reflectionless) buffer zone that sur- extend the framework described in [19] to the fully three-dimen- rounds the domain of interest, where outgoing waves are forced to sional case, various algorithmic modifications are needed, including decay. modifications to the forward three-dimensional wave simulator, per Obtaining the P- and S-wave velocity profiles of the soil in [15], to the inversion methodology, per [14], and to the manner the three-dimensional, arbitrarily heterogeneous domains, remains a field experiment is designed and the associated field data are pro- challenging problem. The inverse medium problem at hand is cessed post-recording. We use the mathematical apparatus that we notoriously ill-posed, computationally expensive, posed over a described recently in [13-15], and excerpt herein, but focus on the semi-infinite medium, and has challenging physics. Due to these three-dimensional characterization of the NEES@UCSB site in Garner complexities, and in order to render the problem tractable, current Valley, California, as a case study. To this end, we integrate recent techniques rely on simplifying assumptions. We classify these advances in several areas. Specifically, we use: (a) a parallel, three- simplifications as follows: (a) limiting the spatial variability of the dimensional, state-of-the-art wave simulation tool for domains ter- soil properties, whereby it is assumed that the soil is horizontally minated by PMLs [15]; (b) a partial-differential-equation (PDE)-con- layered (one-dimensional) [25,29,33], or has properties varying strained optimization framework, through which the misfit mini- only within a plane (two-dimensional) [3,12,19,21]; (b) assuming mization between the measured response and the computed response that the measured response of the soil at sensor locations is due is enforced [14]; (c) regularization schemes to alleviate the ill-po- only to Rayleigh waves, thus neglecting other wave types, such as sedness and solution multiplicity inherent in inverse problems, compressional and shear waves, as is the case in the SASW [33],or where the regularization factor is computed adaptively at each in- its close variant, the MASW method [30]; (c) idealizing the soil version iteration [14,20]; (d) continuation schemes that provide al- medium, which is porous, and, generally, partially or fully satu- gorithmic robustness [20]; and (e) a biasing scheme for the robust rated, as an elastic solid; (d) imaging only one elastic property, fi simultaneous inversion of both cp(x) and cs(x) pro les [14,21]. such as the shear wave velocity or an equivalent counterpart Most inversion approaches result in profile reconstructions that [2,11,27,28]; and (e) grossly simplifying the boundary conditions are physically acceptable. Validation of the inverted profiles, in the fi associated with the semi-in nite extent of the medium, due to the absence of borehole data, becomes challenging, if not impossible. complexity and computational cost that a rigorous treatment Herein, to aid in the validation of the inverted profiles, we use a set would require [11,36]. In recent years, the ubiquity of parallel of control sensors. Specifically, out of the 35 sensors that we de- computers, and significant advances in computational geosciences, ployed at the NEES@UCSB site, we use only 30 of them to feed our has created the opportunity of developing a toolkit that is capable full-waveform-inversion algorithms. The remaining 5 sensors of robust, accurate, and three-dimensional characterization