Device and method for estimating time-shifts
Computing device and method for calculating time-shifts associated with travel-times of seismic waves emitted by a source and recorded by plural seismic detectors after reflection from a subsurface structure. The method includes receiving seismic data (d) that includes plural traces related to a subsurface, wherein the seismic data (d) is in a time-space domain; transforming with a processor the seismic data (d) from the time-space domain to a radon domain; picking linear events from the seismic data in the radon domain; calculating the time-shifts associated with the picked linear events; correcting the seismic data (d) based on the time-shifts to obtain new seismic data (d′); and computing an image of the subsurface based on the new seismic data (d′). The time-shifts are calculated per trace and per event.
1. A method for calculating time-shifts associated with travel-times of seismic waves emitted by a source and recorded by plural seismic detectors after reflection from a subsurface structure, the method comprising:
receiving seismic data (d) that includes plural traces related to a subsurface, wherein the seismic data (d) is in a time-space domain;
transforming with a processor the seismic data (d) from the time-space domain to a radon domain;
picking linear events from the seismic data in the radon domain;
calculating the time-shifts associated with the picked linear events;
correcting the seismic data (d) based on the time-shifts to obtain new seismic data (d′); and
computing an image of the subsurface based on the new seismic data (d′),
wherein the time-shifts are calculated per trace and per event.
2. The method of claim 1 , wherein each time-shift of the time-shifts is calculated per trace and per event.
3. The method of claim 1 , further comprising:
applying an objective function for simultaneously calculating the time-shifts, slopes (p) and wavelets (S) for the seismic data, wherein the slopes (p) are radon transforms of space coordinates of the seismic data and the wavelets (S) are associated with energy amplitudes of the events.
4. The method of claim 3 , wherein the objective function is given by:
( p (j) ,S (j) ,σ i (j) )=arg min(Σ i=1 . . . N ∥d ( t,x i )−Σ j=1 . . . M S (j) ( t −(τ (j) +p (j) ·x i +σ i (j) ))∥ 2 ,
where σ i (j) is a time-shift per event j and per trace i.
5. The method of claim 1 , further comprising:
generating the new seismic data d′ as a sum of a set of the picked events calculated at times corrected with the time-shifts.
6. The method of claim 5 , wherein the new seismic data d′ is calculated as:
d ′( t,x )=Σ j=1 . . . M S (j) ( t−τ (j) −p (j) ·x−σ (j) ),
where S (j) is a wavelet associated with an event j, t is a time of the event, x is a space coordinate of the event, p is a slope of the event in the radon domain and σ (j) is a time-shift associated with the event.
7. The method of claim 1 , further comprising:
removing the picked linear events from the seismic data to generate residual data (r);
radon transforming the residual data;
automatic picking further events from the residual data; and
refining slopes, wavelets, and time-shifts associated with the picked further events.
8. The method of claim 7 , further comprising:
using the picked events and the further picked events to generate the image of the subsurface.
9. The method of claim 1 , further comprising:
filtering out events according to predetermined criteria related to a slope (p) in the radon domain.
10. A computing device for calculating time-shifts associated with travel-times of seismic waves emitted by a source and recorded by plural seismic detectors after reflection from a subsurface structure, the computing device comprising:
an interface configured to receive seismic data (d) that includes plural traces related to a subsurface, wherein the seismic data (d) is in a time-space domain; and
a processor connected to the interface and configured to,
transform the seismic data (d) from the time-space domain to a radon domain;
pick linear events from the seismic data in the radon domain;
calculate the time-shifts associated with the picked linear events;
correct the seismic data (d) based on the time-shifts to obtain new seismic data (d′); and
compute an image of the subsurface based on the new seismic data (d′),
wherein the time-shifts are calculated per trace and per event.
11. The computing device of claim 10 , wherein each time-shift of the time-shifts is calculated per trace and per event.
12. The computing device of claim 10 , wherein the computing device is further configured to:
apply an objective function for simultaneously calculating the time-shifts, slopes (p) and wavelets (S) for the seismic data, wherein the slopes (p) are radon transforms of space coordinates of the seismic data and the wavelets (S) are associated with energy amplitudes of the events.
13. The computing device of claim 12 , wherein the objective function is given by:
( p (j) ,S (j) ,σ i (j) )=arg min(Σ i=1 . . . N ∥d ( t,x i )−Σ j=1 . . . M S (j) ( t −(τ (j) +p (j) ·x i +σ i (j) ))∥ 2 ,
where σ i (j) is a time-shift per event j and per trace i.
14. The computing device of claim 10 , wherein the new seismic data d′ is calculated as:
d ′( t,x )=Σ j=1 . . . M S (j) ( t−τ (j) −p (j) ·x−σ (j) ),
where S (j) is a wavelet associated with an event j, t is a time of the event, x is a space coordinate of the event, p is a slope of the event in the radon domain and σ (j) is a time-shift associated with the event.
15. The computing device of claim 10 , wherein the computing device is further configured to:
remove the picked linear events from the seismic data to generate residual data (r);
radon transform the residual data;
automatic pick further events from the residual data; and
refine slopes, wavelets, and time-shifts associated with the picked further events.
16. The computing device of claim 15 , wherein the computing device is further configured to:
use the picked events and the further picked events to generate the image of the subsurface.
17. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a processor, implement a method for calculating time-shifts associated with travel-times of seismic waves emitted by a source and recorded by plural seismic detectors after reflection from a subsurface structure, the instructions comprising steps of:
receiving seismic data (d) that includes plural traces related to a subsurface, wherein the seismic data (d) is in a time-space domain;
transforming the seismic data (d) from the time-space domain to a radon domain;
picking linear events from the seismic data in the radon domain;
calculating the time-shifts associated with the picked linear events;
correcting the seismic data (d) based on the time-shifts to obtain new seismic data (d′); and
computing an image of the subsurface based on the new seismic data (d′),
wherein the time-shifts are calculated per trace and per event.
18. The medium of claim 17 , further comprising:
applying an objective function for simultaneously calculating the time-shifts, slopes (p) and wavelets (S) for the seismic data, wherein the slopes (p) are radon transforms of space coordinates of the seismic data and the wavelets (S) are associated with energy amplitudes of the events.
19. The medium of claim 18 , wherein the objective function is given by:
( p (j) ,S (j) ,σ i (j) )=arg min(Σ i=1 . . . N ∥d ( t,x i )−Σ j=1 . . . M S (j) ( t −(τ (j) +p (j) ·x i +σ i (j) ))∥ 2 ,
where σ i (j) is a time-shift per event j and per trace i.
20. The medium of claim 17 , wherein the new seismic data d′ is calculated as:
d ′( t,x )=Σ j=1 . . . M S (j) ( t−τ (j) −p (j) ·x−σ (j) ),
where S (j) is a wavelet associated with an event j, t is a time of the event, x is a space coordinate of the event, p is a slope of the event in the radon domain and σ (j) is a time-shift associated with the event.