NMO in a horizontally stratified earth

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Seismic Data Analysis
Series Investigations in Geophysics
Author Öz Yilmaz
DOI http://dx.doi.org/10.1190/1.9781560801580
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store

We now consider a medium composed of horizontal isovelocity layers (Figure 3.1-6). Each layer has a certain thickness that can be defined in terms of twoway zero-offset time. The layers have interval velocities (v1, v2, …, vN), where N is the number of layers. Consider the raypath from source S to depth point D, back to receiver R, associated with offset x at midpoint location M. Cite error: Closing </ref> missing for <ref> tag that exactly describe wave propagation in a horizontally layered earth model with a given interval velocity function. We now replace the layers above the second shallow event at t0 = 0.8 s with a single layer with a velocity equal to the rms velocity down to this reflector — 2264 m/s. The resulting traveltime curve, computed using equation (4b), is shown in Figure 3.1-7b. This procedure is repeated for the deeper events at t0 = 1.2 and 1.6 s as shown in Figures 3.1-7c and d. Note that the traveltime curves in Figures 3.1-7b, c, and d are perfect hyperbolas. How different are the traveltime curves in Figure 3.1-7a from these hyperbolas? After careful examination, note that the traveltimes are slightly different for the shallow events at t0 = 0.8 and 1.2 s only at large offsets, particularly beyond 3 km. By dropping the higher order terms, we approximate the reflection times in a horizontally layered earth with a small-spread hyperbola.

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