{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:40:44Z","timestamp":1787323244954,"version":"build-2736575974"},"reference-count":61,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Polish National Science Center","award":["2022\/46\/E\/ST10\/00266"],"award-info":[{"award-number":["2022\/46\/E\/ST10\/00266"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2026,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Full waveform inversion (FWI) is a powerful wave-based imaging technique, but its inherent ill-posedness and nonconvexity make it prone to local minima and poor convergence. Regularization techniques are commonly employed to stabilize FWI by incorporating prior information that enforces structural constraints, such as smooth variations or piecewise-constant behavior. Among them, Tikhonov regularization promotes smoothness, while total variation (TV) regularization preserves sharp boundaries; both are widely used in solving ill-posed inverse problems. However, in the context of FWI, we highlight two key shortcomings of these regularization methods. First, subsurface model parameters (P- and S-wave velocities, density) often exhibit complex geological formations with sharp discontinuities separating distinct layers, while parameters within each layer vary smoothly. Neither Tikhonov nor TV regularization alone can effectively constrain such piecewise-smooth structures. Second, and more critically, when the initial model is far from the true model, these regularization assumptions can lead to convergence toward a local minimum. To address these limitations, we propose an adaptive Tikhonov-TV (TT) regularization method that decomposes the model into smooth and blocky components, enabling robust recovery of piecewise-smooth structures. The method is implemented within the alternating direction method of multipliers (ADMM) framework and incorporates an automated balancing strategy based on robust statistical analysis. Extensive numerical experiments on both acoustic and elastic FWI are conducted using challenging benchmark geological models. The results demonstrate that TT regularization significantly improves convergence and reconstruction accuracy compared to Tikhonov and TV regularization when applied separately. We show that for complex models and remote initial models, both Tikhonov and TV regularization tend to converge to local minima, whereas the TT regularization effectively mitigates cycle skipping through its adaptive combination of the two regularization strategies.<\/jats:p>","DOI":"10.1137\/25m1748238","type":"journal-article","created":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T07:59:22Z","timestamp":1773129562000},"page":"480-518","source":"Crossref","is-referenced-by-count":2,"title":["Robust Acoustic and Elastic Full Waveform Inversion by Adaptive Tikhonov-TV Regularization"],"prefix":"10.1137","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2080-9697","authenticated-orcid":true,"given":"Kamal","family":"Aghazade","sequence":"first","affiliation":[{"name":"Institute of Geophysics, Polish Academy of Sciences, Warsaw, 01-452, Poland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8403-1434","authenticated-orcid":true,"given":"Ali","family":"Gholami","sequence":"additional","affiliation":[{"name":"Institute of Geophysics, Polish Academy of Sciences, Warsaw, 01-452, Poland."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,3,10]]},"reference":[{"key":"ref1","first-page":"1253","author":"Aghamiry H.","year":"2018","journal-title":"Expanded Abstracts, 88 Annual SEG Meeting (Anaheim)"},{"key":"ref2","first-page":"855","volume":"218","author":"Aghamiry H.","year":"2019","journal-title":"Geophys. 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