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Suppose we have a trace representative of a seismic horizon, apply cosine tapering to its edges, and pad it with zeros. This ideal horizon reference trace is called
. To create a measure of how well this ideal waveform matches with other traces throughout a seismic volume, the crosscorrelation is calculated throughout the volume over shift
,
![$\displaystyle \gamma(\tau,\mathbf{x}) = \int h(t+\tau)d(t,\mathbf{x}) d\tau,$](img133.png) |
(9) |
where
is the seismic image. In order to ensure that the volume we generate is non-negative, let
![$\displaystyle \alpha(\tau,\mathbf{x}) = \gamma(\tau,\mathbf{x}) - \min_{\left(\tau,\mathbf{x}\right)} \left[ \gamma(\tau,\mathbf{x})\right] .$](img135.png) |
(10) |
Automatic picking may be performed on the semblance-like volume
to determine the shifts defining the horizon corresponding to reference trace
. Those shifts may be converted back to time in the image domain by adding a reference time for the ideal horizon trace, taken here to be that trace's midpoint.
This is a basic method for creating a horizon probability volume, which is intended for use in this paper as part of a proof of concept for automatic horizon interpretation using the variational picking algorithm. It could encounter difficulties in areas where significant lateral wavelet variation or faulting occurs.
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2022-05-24