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Apparatus, computer instructions and method for processing seismic data related to a subsurface of a body of water. The method includes inputting data indicative of recordings made by detectors provided on a curved profile in response to an acoustic wave reflected from the subsurface; applying a mat

Apparatus, computer instructions and method for processing seismic data related to a subsurface of a body of water. The method includes inputting data indicative of recordings made by detectors provided on a curved profile in response to an acoustic wave reflected from the subsurface; applying a matched mirror migration procedure to the data, where (i) actual positions of the detectors on the curved profile and corresponding recordings, and (ii) fictitious mirror positions of the actual detectors on the curved profile and corresponding recordings with a changed sign are added in the matched mirror migration; and generating a final image of the subsurface based on the matched mirror migration procedure.

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1. A method for processing seismic data related to a subsurface of a body of water and displaying a final image of the subsurface on a display, the method comprising: inputting data indicative of recordings made by detectors disposed on a curved, parameterized, depth-changing profile in response to

1. A method for processing seismic data related to a subsurface of a body of water and displaying a final image of the subsurface on a display, the method comprising: inputting data indicative of recordings made by detectors disposed on a curved, parameterized, depth-changing profile in response to an acoustic wave reflected from the subsurface;applying a matched mirror migration procedure to the data, wherein the matched mirror migration procedure uses a wave constructed based on (i) actual positions of the detectors disposed on the curved, parameterized, depth-changing profile and corresponding recordings, and (ii) fictitious mirror positions of the actual detectors on the curved, parameterized, depth-changing profile and corresponding recordings with a changed sign; andgenerating with a computing device the final image of the subsurface based on the matched mirror migration procedure. 2. The method of claim 1, wherein the (i) actual positions of the detectors on the curved, parameterized, depth-changing profile and corresponding recordings, and the (ii) fictitious mirror positions of the actual detectors on the curved, parameterized, depth-changing profile and corresponding recordings with a changed sign are applied to an up-traveling U wave that travels from reflectors in the subsurface to the detectors. 3. The method of claim 1, further comprising: calculating an up-travelling U wave and a down-travelling wave D; andtime cross-correlating the U wave with the D wave to generate the final image of the subsurface,wherein the U wave travels from reflectors in the subsurface to the detectors and the D wave travels from a sound source to the subsurface. 4. The method of claim 3, wherein only the step of calculating the up-travelling U wave is based on both (i) the actual positions of the detectors on the curved, parameterized, depth-changing profile and the corresponding recordings, and (ii) the fictitious mirror positions of the actual detectors on the curved, parameterized, depth-changing profile and the corresponding recordings with a changed sign. 5. The method of claim 4, wherein the step of calculating the down-travelling D wave does not take into consideration the fictitious mirror positions of the actual detectors and the corresponding recordings with a changed sign. 6. The method of claim 4, wherein the U wave and the D wave are calculated regressively based on a wave equation. 7. The method of claim 1, wherein a one-way wave equation is used to calculate the final image. 8. The method of claim 1, wherein no image from a migration step is added to the final image of the matched mirror migration. 9. The method of claim 1, wherein a step of datuming is not performed prior to calculating the final image, wherein datuming implies using data from the detectors provided at positions (xn, zn), where n=1, . . . N and N is a natural number, and synthesizing data that would have been recorded by the detectors if they had been placed at the same horizontal positions xn but at a same constant reference depth z0 for all the detectors. 10. The method of claim 1, wherein the data are collected from detectors being towed by a vessel and the detectors are submerged in water and distributed on the curved, parameterized, depth-changing profile underwater. 11. The method of claim 10, wherein the curved, parameterized, depth-changing profile is a hyperbola. 12. The method of claim 1, further comprising: calculating an up-travelling U wave from an initial altitude −zmax, where zmax is a maximum depth of the detectors;reverse propagating the up-travelling U wave from the initial altitude by a depth recursive calculation in which the up-travelling U wave is calculated at a current depth z+Δz from an up-travelling wave for a preceding depth z; andadding the detectors having a depth zr or a mirror depth −zr at a current z+Δz position of the up-travelling U wave when the detectors lie between z and z+Δz. 13. The method of claim 12, further comprising: propagating a down-travelling D wave emitted by a source of the acoustic wave, wherein the propagation is started at a depth equal to a depth of the source zs, and the propagation of the down-travelling D wave is carried out to obtain down-travelling waves for all depths greater than the depth of the source zs. 14. The method of claim 13, further comprising: correlating the down-travelling D wave and the up-travelling U wave for each depth greater than the depth of the source zs. 15. A method for processing seismic data related to a subsurface of a body of water, the method comprising: inputting data indicative of recordings made by detectors disposed on a curved, parameterized, depth-changing profile in response to an acoustic wave reflected from the subsurface;applying a matched mirror migration procedure to the data, wherein the matched mirror migration procedure uses a time migration procedure for calculating a wave based on both (i) actual positions of the detectors disposed on the curved, parameterized, depth-changing profile and corresponding recordings, and (ii) fictitious mirror positions of the actual detectors on the curved, parameterized, depth-changing profile and corresponding recordings with a changed sign;using free-surface boundary conditions for a surface of the water instead of absorbing boundary conditions, wherein the free-surface boundary conditions assume that a wave is reflected at the surface of the water while the absorbing boundary conditions assume that the wave moves from water into air at the surface of the water; andgenerating and displaying the final image of the subsurface based on the matched mirror migration procedure. 16. A method for processing seismic data related to a subsurface of a body of water and displaying a final image of the subsurface on a display, the method comprising: inputting data indicative of recordings made by detectors provided on a curved, parameterized, variable-depth profile in response to an acoustic wave reflected from the subsurface;applying a reverse time migration procedure for calculating a final image of the subsurface, wherein the reverse time migration procedures solves the full acoustic wave equation; andusing free-surface boundary conditions for a surface of the water instead of absorbing boundary conditions to calculate the final image, wherein the free-surface boundary conditions assume that a wave is reflected at the surface of the water while the absorbing boundary conditions assume that the wave moves from the water into air at the surface of the water. 17. The method of claim 16, wherein the data is collected from detectors being towed by a vessel and the detectors are submerged in water and distributed on the curved, parameterized, variable-depth profile underwater. 18. The method of claim 17, wherein the curved, parameterized, variable-depth profile is a hyperbola. 19. A computer program-implemented method for processing seismic data related to a subsurface of a body of water and displaying a final image of the subsurface on a display, the method comprising: inputting data indicative of recordings made by detectors provided on a curved, parameterized, depth-changing profile in response to an acoustic wave reflected from the subsurface;applying a matched mirror migration procedure to the data, wherein the matched mirror migration procedure uses a wave constructed based on (i) actual positions of the detectors and corresponding recordings, and (ii) fictitious mirror positions of the actual detectors and corresponding recordings with a changed sign, wherein the detectors are located on the curved, parameterized, depth-changing profile; andgenerating the final image of the subsurface based on the matched mirror migration procedure. 20. An apparatus for processing seismic data related to a subsurface of a body of water, the apparatus comprising: a processor programmed to perform the following method steps:receiving data indicative of recordings made by detectors provided on a curved, parameterized, depth-changing profile in response to an acoustic wave reflected from the subsurface;applying a matched mirror migration procedure to the data, wherein the matched mirror migration procedure uses a wave constructed based on (i) actual positions of the detectors on the curved, parameterized, depth-changing profile and corresponding recordings, and (ii) fictitious mirror positions of the actual detectors on the curved, parameterized, depth-changing profile and corresponding recordings with a changed sign; andgenerating a final image of the subsurface based on the matched mirror migration procedure. 21. A program storage device, readable by a computer, tangibly embodying a program of instructions executable by the computer for processing seismic data related to a subsurface of a body of water, the instructions comprising: inputting data indicative of recordings made by detectors provided on a curved, parameterized, depth-changing profile in response to an acoustic wave reflected from the subsurface;applying a matched mirror migration procedure to the data, wherein the matched mirror migration procedure uses a wave constructed based on (i) actual positions of the detectors on the curved, parameterized, depth-changing profile and corresponding recordings, and (ii) fictitious mirror positions of the actual detectors on the curved, parameterized, depth-changing profile and corresponding recordings with a changed sign; andgenerating a final image of the subsurface based on the matched mirror migration procedure. 22. A method for generating a final image of a subsurface of a body of water and for displaying the final image on a display, the method comprising: inputting recordings of plural detectors on a curved, parameterized, depth-changing profile in response to an acoustic wave reflected from the subsurface;applying a matched mirror migration procedure to the recordings, wherein the matched mirror migration procedure uses a wave constructed based on (i) actual positions of the detectors on the curved, parameterized, depth-changing profile and corresponding recordings, and (ii) fictitious mirror positions of the detectors on the curved, parameterized, depth-changing profile and corresponding recordings with a changed sign; andgenerating the final image of the subsurface based on the matched mirror migration procedure.