Seismic data processing including variable water velocity estimation and compensation therefor
Effects of time variability of water velocities in seismic surveys are addressed. Traveltime discontinuities in the input seismic data which are associated with the time-variable water velocities are determined. The input seismic data is transformed from a data space that contains the traveltime discontinuities into a model space which does not contain the traveltime discontinuities. Then the transformed seismic data is reverse transformed from the model space back into the data space.
1. A method, stored in a memory and executing on a processor, for correcting input seismic data for time-variable water velocities comprising the steps of:
determining traveltime discontinuities in the input seismic data which are associated with the time-variable water velocities;
transforming the input seismic data from a data space that contains the traveltime discontinuities into a model space which does not contain the traveltime discontinuities; and
reverse transforming the transformed seismic data from the model space back into the data space,
wherein the transforming includes using a conjugate gradients solver and an equation which includes operators based on the traveltime discontinuities to estimate the model-domain signal which reverse transforms to give the input seismic data.
2. The method of claim 1 , further comprising:
generating an image of a subsurface from which the input seismic data was recorded based on the reverse transformed seismic data.
3. The method of claim 1 , wherein the time-variable water velocities include a first water velocity associated with a subsurface region at a first time and a second water velocity, which is different than the first water velocity, associated with the subsurface region at a second time.
4. The method of claim 1 , wherein the step of reverse transforming further comprises:
using an operator without time variability associated with the traveltime discontinuities to perform the reverse transformation.
5. The method of claim 1 , wherein the step of determining further comprises:
approximating a point-of-entry for each datapoint in the input seismic data; and
determining extrapolation-time differences between sources used to generate the input seismic data and respective approximated points-of entry to generate the traveltime discontinuities.
6. The method of claim 1 , wherein the method is operable to correct both primary waves and multiple waves in the input seismic data for time variable water velocities by:
generating a set of model-domain weights to separate primary and multiple arrivals during an inversion associated with the conjugate-gradients solver using iteratively re-weighted methods;
generating two or more models of the seismic data using the set of model-domain weights to separate energy between the models in the inversion; and
updating the two or more models such that, after reverse transformation using variable-velocity operators and re-combination in a data domain, a result describes the input seismic data.
7. A computer system programmed to correct input seismic data for time-variable water velocities comprising:
at least one memory device configured to store the input seismic data and computer program instructions; and
at least one processor for executing the computer program instructions to:
determine traveltime discontinuities in the input seismic data which are associated with the time-variable water velocities;
transform the input seismic data from a data space that contains the traveltime discontinuities into a model space which does not contain the traveltime discontinuities; and
reverse transform the transformed seismic data from the model space back into the data space,
wherein the processor transforms the seismic data by using a conjugate gradients solver and an equation which includes operators based on the traveltime discontinuities to estimate the model-domain signal which reverse transforms to give the input seismic data.
8. The computer system of claim 7 , further comprising:
an output device configured to generate an image of a subsurface from which the input seismic data was recorded based on the reverse transformed seismic data.
9. The computer system of claim 7 , wherein the time-variable water velocities include a first water velocity associated with a subsurface region at a first time and a second water velocity, which is different than the first water velocity, associated with the subsurface region at a second time.
10. The computer system of claim 7 , wherein the processor is further configured to perform the reverse transform by using an operator without time variability associated with the traveltime discontinuities to perform the reverse transformation.
11. The computer system of claim 7 , wherein the processor is further configured to determining the traveltime discontinuities by:
approximating a point-of-entry for each datapoint in the input seismic data; and
determining extrapolation-time differences between sources used to generate the input seismic data and respective approximated points-of entry to generate the traveltime discontinuities.
12. A method, stored in a memory and executing on a processor, for correcting input seismic data for time-variable water velocities, the method comprising:
transforming input seismic data from a data acquisition space to a model space depending on slant coordinates and enabling decomposition into plane waves, the transforming incorporating travel-time discontinuities;
compensating for water-column velocity variations by phase-shifting the plane waves to eliminate the travel-time discontinuities;
reverse transforming recombined phase-shifted plane waves back into the data acquisition domain to obtain seismic data corrected for time-variable water velocities; and
generating an image of a formation under the seafloor using the seismic data corrected for time-variable water velocities.
13. The method of claim 12 , wherein the transforming input seismic data employs normalized weights to account for irregular distribution of the input data.
14. The method of claim 13 , wherein the transforming, the compensating and the reverse transforming are treated as an inverse problem using a conjugate gradients solver of a transform
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where d is input data, ψ is data in the model space, ω is a temporal frequency, x and y are spatial positions for 1, . . . , N data traces, g k is a data weight appropriate for the k th trace, {tilde over (g)} is the normalization factor, e iθ for imaginary number i and phase angle θ is used to define a slanting path, p x and p y are slownesses that define slants in x and y spatial dimensions, and Δt e represent travel time discontinuities which are functions of acquisition times t ai .