Estimation of propagation angles of seismic waves in geology with application to determination of propagation velocity and angle-domain imaging

1. A method in a host of determining the propagation angles of reflected seismic waves, comprising:

inputting data representing reflected seismic waves in a memory;

inputting a propagation velocity field in the memory;

using the propagation velocity field to migrate the data with a downward continuation Fourier domain shot record migration by multiplying, for each frequency, each point of a conjugate of a source wave field with a receiver wave field to obtain a result, then summing the results over all frequencies;

computing, using a processor that communicates with the memory, propagation direction vectors of the source wave field and the receiver wave field, wherein the source wave field and the receiver wave field are propagated by the downward continuation Fourier domain shot record migration using the data of the reflected seismic waves and the propagation velocity field; and

transforming the propagation direction vectors into propagation angles of the reflected seismic waves.

2. The method of claim 1 , wherein the propagation angles include an incidence angle, a dip angle, and an azimuth angle of the reflected seismic waves.

3. The method of claim 1 , wherein computing the propagation direction vectors includes encoding propagation direction information from the source wave field and the receiver wave field into Fourier domain carrier wave fields and decoding propagation direction information in space domain.

4. The method of claim 1 , wherein computing the propagation direction vectors Includes interpolating the source wave field, the receiver wave field, and the Fourier domain carrier wave fields in a phase shift plus interpolation downward continuation step.

5. The method of claim 4 , wherein computing the propagation direction vectors includes interpolating the source wave field, the receiver wavefield, and the Fourier domain carrier wave fields, and dividing the interpolated Fourier domain carrier wave fields by the magnitude of the interpolated source wave field or the receiver wave field.

6. The method of claim 1 , further comprising using the propagation direction vectors to compute the propagation angles of reflected seismic waves.

7. The method of claim 1 , wherein the propagation direction vectors are computed at a subsurface reflection point.

8. A method in a host of determining a three-dimensional Image of earth's geology, comprising:

inputting data representing reflected seismic waves in a memory;

inputting a propagation velocity field in the memory;

using the propagation velocity field to migrate the data with a downward continuation Fourier domain shot record migration by multiplying, for each frequency, each point of a conjugate of a source wave field with a receiver wave field to obtain a result, then summing the results over all frequencies;

computing, using a processor that communicates with the memory, propagation direction vectors of the source wave field and the receiver wave field, wherein the source wave field and the receiver wave field are propagated by the downward continuation Fourier domain shot record migration using the data of the reflected seismic waves and the propagation velocity field;

transforming the propagation direction vectors into propagation angles of the reflected seismic waves; and

using the downward continuation Fourier domain shot record migration and the propagation direction vectors to compute a three-dimensional image, wherein an amplitude of the reflected seismic waves and a set of propagation angles is associated with each point in the three-dimensional image.

9. The method of claim 8 , further comprising using the downward continuation Fourier domain shot record migration and the propagation direction vectors to apply an angle-dependent imaging condition including inputting axis parameters defining a plurality of angle volumes in the memory, wherein each angle volume represents a range of propagation angles, wherein the propagation angles at each point in the three-dimensional image connects the point to one of the angle volumes, and wherein the amplitude of the reflected seismic waves of each point of the three-dimensional Image is added to the corresponding point of one of the angle-volumes.

10. The method of claim 8 , wherein the propagation direction vectors are computed at a subsurface reflection point.

11. A non-transitory computer-readable medium storing program instructions that cause a host to perform steps, comprising:

inputting data representing reflected seismic waves;

inputting a propagation velocity field;

using the propagation velocity field to migrate the data with a downward continuation Fourier domain shot record migration by multiplying, for each frequency, each point of a conjugate of a source wave field with a receiver wave field to obtain a result, then summing the results over all frequencies;

computing propagation direction vectors of the source wave field and the receiver wave field, wherein the source wave field and the receiver wave field are propagated by the downward continuation Fourier domain shot record migration using the data of the reflected seismic waves and the propagation velocity field; and

transforming the propagation direction vectors into propagation angles of reflected seismic waves.

12. The non-transitory computer-readable medium of claim 11 , wherein the propagation direction vectors are computed at a subsurface reflection point.

13. A non-transitory computer-readable medium storing program instructions that cause a host to perform steps, comprising:

inputting data representing reflected seismic waves;

inputting a propagation velocity field;

using the propagation velocity field to migrate the data with a downward continuation Fourier domain shot record migration by multiplying, for each frequency, each point of a conjugate of a source wave field with a receiver wave field to obtain a result, then summing the results over all frequencies;

computing propagation direction vectors of the source wave field and the receiver wave field, wherein the source wave field and the receiver wave field are propagated by the downward continuation Fourier domain shot record migration using the data of the reflected seismic waves and the propagation velocity field;

transforming the propagation direction vectors into propagation angles of reflected seismic waves; and

generating a three-dimensional image for each shot record, wherein an amplitude of the reflected seismic waves and a set of propagation angles is associated with each point in the image.

14. The non-transitory computer-readable medium of claim 13 , wherein the propagation direction vectors are computed at a subsurface reflection point.