{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T20:34:56Z","timestamp":1765485296604,"version":"3.48.0"},"reference-count":38,"publisher":"Society of Exploration Geophysicists","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In most geometries in which seismic-traveltime tomography is applied (e.g., crosswell, surface-reflection, and VSP), determination of the slowness field using only traveltimes is not a well-conditioned problem. Nonuniqueness is common. Even when the slowness field is uniquely determined, small changes in measured traveltimes can cause large errors in the computed slowness field. A priori information often is available \u2014 well logs, initial rough estimates of slowness from structural geology, etc. \u2014 and can be incorporated into a traveltime-inversion algorithm by using penalty terms. To further regularize the problem, smoothing constraints also can be incorporated using penalty terms by penalizing derivatives of the slowness field. What weights to use on the penalty terms is a major decision, particularly the smoothing-penalty weights. We use a continuation approach in selecting the smoothing-penalty weights. Instead of using fixed smoothing-penalty weights, we decrease them step by step, using the slowness model computed with the previous, larger weights as the initial slowness model for the next step with the new, smaller weights. This continuation approach can solve synthetic problems more accurately than does one that uses fixed smoothing-penalty weights, and it appears to yield more features of interest in real-data applications of traveltime tomography. We have formulated guidelines for making the many choices needed to implement this continuation strategy effectively and have developed specific choices for crosswell-traveltime tomography.<\/jats:p>","DOI":"10.1190\/1.2969460","type":"journal-article","created":{"date-parts":[[2008,10,6]],"date-time":"2008-10-06T16:46:49Z","timestamp":1223311609000},"page":"VE337-VE351","source":"Crossref","is-referenced-by-count":17,"title":["A continuation approach to regularization of ill-posed problems with application to crosswell-traveltime tomography"],"prefix":"10.1190","volume":"73","author":[{"given":"Kenneth P.","family":"Bube","sequence":"first","affiliation":[{"name":"1University of Washington, Department of Mathematics, Seattle, Washington, U.S.A. E-mail: bube@math.washington.edu."}]},{"given":"Robert T.","family":"Langan","sequence":"additional","affiliation":[{"name":"2Chevron Energy Technology Company, San Ramon, California, U.S.A. E-mail: bob.langan@chevron.com."}]}],"member":"186","published-online":{"date-parts":[[2008,10,1]]},"reference":[{"key":"2025121113083035200_R1","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1190\/1.1441970","article-title":"Tomographic determination of velocity and depth in laterally varying media","volume":"50","author":"Bishop","year":"1985","journal-title":"Geophysics"},{"key":"2025121113083035200_R2","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1190\/1.1444089","article-title":"Inversion of seismic refraction data using genetic algorithms","volume":"61","author":"Boschetti","year":"1996","journal-title":"Geophysics"},{"key":"2025121113083035200_R3","unstructured":"Bregman\n              N. 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