Article,
Lateral velocity resolution from three-dimensional seismic refraction data
Geophysical Journal International, 135 (3): 1101--1112 (December 1998)
DOI: 10.1046/j.1365-246X.1998.00695.x
Abstract
A method for estimating the lateral velocity resolution from 3-D seismic
refraction traveltimes is presented. The method is non-linear in
that synthetic data calculated from 'checkerboard' models are inverted
using an iterative tomographic approach incorporating smoothness
constraints and updated ray paths at each iteration. Two applications
are presented: (1) real data from the Faeroe Basin experiment using
the ray coverage and noise level of approximately 50 000 picks, and
(2) ideal data from the same experiment corresponding to 100 per
cent data recovery, equivalent to about three times as many ray paths.
The refraction data constrain the sedimentary and basement structure
to approximately 12 km depth. A comparison of the results from the
two data sets provides a qualitative check on the resolution method,
illustrates the pitfalls of using ray coverage as an indicator of
resolution, and demonstrates the potential resolution of currently
feasible 3-D refraction experiments. 32 checkerboard models consisting
of alternating positive and negative velocity anomalies superimposed
on the preferred final model of the basin were tested, each with
a different cell size, position or orientation. The problem of ray
bending associated with the 5 per cent checkerboard anomalies is
shown to be small. Using models with four cell sizes allowed for
resolution estimates from 3 to 15 km, this range being imposed by
the frequency content of the data and the areal dimensions of the
study area (44x26 km). An operator centred on each model node measures
the local semblance between the known and recovered checkerboard
models. A determination of the smallest well-resolved cell size at
each model node is then made using a 0.7 semblance threshold to provide
a spatially dependent lateral resolution estimate. Resolution for
the real data set varies from an average of just over 3 km at 2 km
depth, to 10 km at 10 km depth, where there is a local maximum in
ray coverage due to a concentration of ray-bottoming points. For
the ideal data set, the average lateral resolution drops off roughly
linearly from better than 3 km at 2 km depth, to 6.3 km at 10 km
depth. The largest difference between the resolution associated with
the ideal and real data occurs at 7.2 km depth, where it averages
4.6 km for the former and 10.8 km for the latter due to the near
absence of ray-bottoming points between 7 and 9 km. The results show
that the final model for the Faeroe Basin obtained by regularized
inversion with smoothness constraints is consistent with the resolution
estimates in the sense that the model does not contain structure
with a wavelength smaller than the resolution estimate at any point.
The results for the ideal data show that good-quality 3-D refraction
experiments can provide a lateral resolution of no worse than the
receiver spacing (shot spacing for land data) throughout most of
the sampled volume.
