Turning-ray tomography

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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

Rapid discharge of the sediments by the Mississippi River has given rise to an accumulation of gas-charged mudflows within complex, meandering channels down the slopes of its delta. Velocities within these mudflows are significantly lower than the surrounding deltaic sediments and can be as low as 300 m/s. The underlying predeltaic Holocene sequence also is characterized by sediments with lateral velocity variations [1] [2].

Because of the absence of a near-surface refractor with a strong velocity contrast, first arrivals on shot gathers recorded over the Mississippi Delta often do not represent the typical refracted arrivals associated with a head wave. Therefore, neither refraction traveltime tomography (Section C.9) is applicable to estimate a near-surface model nor refraction statics (refraction statics corrections) may be a rigorous solution to resolving the near-surface complexity in the Mississippi Delta.

Figure 9.5-55  (a) A map of statics derived from turning-ray tomography applied to a 3-D seismic data set, (b) an inline stack along the traverse indicated by the horizontal line in (a) with refraction statics corrections, and (c) the same inline stack with turning-ray tomographic statics corrections. [3]; courtesy Geosignal, Western Geophysical.

Instead, the first arrivals are often associated with diving waves through the deltaic and predeltaic Holocene sediments [4]. Because of the unusual velocity gradients within the near-surface layers, the downgoing incident wave rapidly turns around before being reflected and is recorded by the receiver as the first arrival.

Just as reflection traveltime tomography (Section J.6) can be used to update an initial estimate of a subsurface velocity-depth model, turning-ray tomography may be used to update an initial estimate of a near-surface velocity-depth model [4] [5].

  1. Begin with the picking of the first arrivals that represent the diving waves through the near surface.
  2. Define an initial velocity-depth model by a set of near-surface layers with constant velocities and thicknesses, and model the first-arrival times by ray tracing.
  3. Compute the difference between the modeled and observed first-arrival times.
  4. Estimate the change in parameters vector Δp of equation (10), by way of the GLI solution given by equation (J-88) by perturbing the velocities of the near-surface layers only.
  5. Update the parameter vector p + Δp to obtain a new near-surface velocity-depth model.
  6. Iterate steps (a) through (e) as necessary to minimize the discrepancy between the modeled and actual first-arrival times.


The final velocity-depth model resulting from the iterative application of turning-ray tomography is then used to compute the one-way traveltimes through the near-surface model along vertical raypaths. These are then used to apply the necessary source and receiver statics corrections to the prestack data. Figure 9.5-55a shows the statics solution derived from turning-ray tomography applied to a 3-D offshore seismic data set from the Mississippi Delta [3]. Note the mudflows characterized by the strings of negative statics shifts. Figure 9.5-55b shows a stacked section along an inline traverse with refraction statics corrections (refraction statics corrections), and Figure 9.5-55c shows the stacked section along the same traverse with statics corrections as in (a) based on turning-ray tomography. Note the significant improvement of event continuity in the central part of the section.


  1. Coleman et al., 1980, Coleman, J. M., Prior, D. B., and Garrison, L. E., 1980, Subaqueous sediment instabilities in the offshore Mississippi River Delta: USGS Open-File Report 80-01, 60.
  2. May et al., 1988, May, J. A., Meeder, C. A., Tinkle, A. R., and Wener, K. R., 1988, Seismic no-data zone, Offshore Mississippi Delta: Part II: using geologic information to predict acoustic properites: Proc. Offshore Tech. Conf., 75–84.
  3. 3.0 3.1 Kim and Bell, 2000, Kim, H. S. and Bell, M. L., 2000, 3-D turning-ray tomography and its application to Mississippi Delta: 70th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 593–596.
  4. 4.0 4.1 Zhou et al., 1992, Zhou, X., Sixta, D. P. and Angstman, B. G., 1992, Tomostatics: turning-ray tomography and statics corrections: The Leading Edge, 11, No. 12, 15–23.
  5. Bell et al., 1994, Bell, M. L., Lara, R., and Gray, W. C., 1994, Application of turning-ray tomography to the offshore Mississippi Delta: 64th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1509–1512.

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Turning-ray tomography
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