2013
DOI: 10.1190/geo2012-0327.1
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Dynamic warping of seismic images

Abstract: The problem of estimating relative time (or depth) shifts between two seismic images is ubiquitous in seismic data processing. This problem is especially difficult where shifts are large and vary rapidly with time and space, and where images are contaminated with noise or for other reasons are not shifted versions of one another. A new solution to this problem requires only simple extensions of a classic dynamic time warping algorithm for speech recognition. A key component of that classic algorithm is a nonli… Show more

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Cited by 275 publications
(133 citation statements)
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References 14 publications
(14 reference statements)
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“…We will discuss how to specify the constraint bounds of ds∕dτ in computing the shifts. One potential problem of the common DTW method (Hale, 2013; is that the estimated shifts are limited to integers, which may not be sufficient to accurately correlate the synthetic and real seismograms. We use the smooth DTW method, proposed by Compton and Hale (2014), to compute smoothly varying shifts, which are often more accurate than those from the common DTW method, as suggested by Muñoz and Hale (2015).…”
Section: Dtwmentioning
confidence: 99%
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“…We will discuss how to specify the constraint bounds of ds∕dτ in computing the shifts. One potential problem of the common DTW method (Hale, 2013; is that the estimated shifts are limited to integers, which may not be sufficient to accurately correlate the synthetic and real seismograms. We use the smooth DTW method, proposed by Compton and Hale (2014), to compute smoothly varying shifts, which are often more accurate than those from the common DTW method, as suggested by Muñoz and Hale (2015).…”
Section: Dtwmentioning
confidence: 99%
“…The shifts sðτÞ are often large and nonlinear ) and therefore are difficult to estimate using windowed crosscorrelation methods. The DTW method, first proposed by Sakoe and Chiba (1978) in speech recognition, is a better method to estimate nonlinear and rapidly varying shifts (Hale, 2013;Muñoz and Hale, 2015). DTW corresponds in solving the following constrained optimization problem:…”
Section: Dtwmentioning
confidence: 99%
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“…As described by Hale (2013), a migration image I based on the incorrect velocity can be considered a warped version of the true imageĨ based on the correct velocity. In equation 1, hðx; zÞ and lðx; zÞ are warping functions that specify how much the image point at ðx; zÞ inĨ is shifted from the same image point in I in the horizontal (h) and vertical (l) directions:…”
Section: Theorymentioning
confidence: 99%
“…With the assumptions above, depth differences between images should be primarily caused by time-lapse changes in the velocity and not by physical changes in reflector position. Dynamic image warping (Hale, 2013) is used to measure the image shifts in a way that is robust to cycle skipping and amplitude differences between images. By minimizing the warping function (the shifts between baseline and monitor images), we invert for velocity changes iteratively using the adjoint-state method (Plessix, 2006).…”
Section: Introductionmentioning
confidence: 99%