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On the inverse problem of soil profile reconstruction: a comparison of time-domain approaches

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Abstract

We discuss a one-dimensional inverse material profile reconstruction problem that arises in layered media underlain by a rigid bottom, when total wavefield surficial measurements are used to guide the reconstruction. To tackle the problem, we adopt the systematic framework of PDE-constrained optimization and construct an augmented misfit functional that is further endowed by a regularization scheme. We report on a comparison of spatial regularization schemes such as Tikhonov and total variation against a temporal scheme that treats the model parameters as time-dependent. We study numerically the effects of inexact initial estimates, data noise, and regularization parameter choices for all three schemes, and report inverted profiles for the modulus, and for simultaneous inversion of both the modulus and viscous damping. Our numerical experiments demonstrate comparable or superior performance of the time-dependent regularization over the Tikhonov and total variation schemes for both smooth and sharp target profiles, albeit at increased computational cost.

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Authors and Affiliations

  1. Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, 1 University Station, C1748, Austin, TX, 78712, USA

    Seong-Won Na & Loukas F. Kallivokas

Authors
  1. Seong-Won Na
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  2. Loukas F. Kallivokas
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Correspondence to Loukas F. Kallivokas.

Additional information

Support for this work was provided by the US National Science Foundation under grant awards ATM-0325125 and CMS-0348484.

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Na, SW., Kallivokas, L.F. On the inverse problem of soil profile reconstruction: a comparison of time-domain approaches. Comput Mech 42, 921–942 (2008). https://doi.org/10.1007/s00466-008-0295-x

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  • DOI: https://doi.org/10.1007/s00466-008-0295-x

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