Processing seismic data representing a physical system
View Patent ↗A method of processing seismic data representing a physical system, the method comprising a difference between first and second seismic data representing the system in first and second states, respectively, and inverting the difference in accordance with a parameterized model of the physical system to obtain changes in the parameters of the model.
1. A method of processing seismic data representing a physical system, the method comprising:
forming a difference between first and second measurements of seismic data representing the system in first and second states, respectively; and
inverting the difference in accordance with a parameterized model of the physical system to obtain changes in the parameters of the model.
2. A method as claimed in claim 1 , wherein the first and second states represent the physical system at different times.
3. A method as claimed in claim 1 , wherein the inversion is performed in a statistical environment.
4. A method as claimed in claim 3 , wherein the inversion is a least squares inversion.
5. A method as claimed in claim 3 , wherein the inversion is a Bayesian inversion.
6. A method as claimed in claim 4 , wherein a first part of the solution to the inversion is a posterior expectation.
7. A method as claimed in claim 6 , wherein the posterior expectation corresponds to changes in the parameters of the model.
8. A method as claimed in claim 4 , wherein a second part of the solution to the inversion is a posterior covariance.
9. A method as claimed in claim 8 , wherein the posterior covariance corresponds to the uncertainty in the posterior expectation.
10. A method as claimed in claim 1 , wherein changes in the parameters of the model follow Gaussian statistics.
11. A method as claimed in claim 1 , wherein the difference has an associated error model with a corresponding error term e.
12. A method as claimed in claim 11 , wherein the error term e corresponds to the difference between (i) the difference between the first and second measured data, and (ii) the changes in the parameters of the model when operated upon by a forward modelling operator.
13. A method as claimed in claim 11 , wherein the error term e is related to the difference d between the first and second measured data and the changes δ in the parameters of the model when operated upon by a forward modelling operator G via the matrix-vector expression d=Gδ+e.
14. A method as claimed in claim 11 , wherein the statistical properties of the error term is described via an expectation and a covariance.
15. A method as claimed in claim 14 wherein the error term follows Gaussian statistics.
16. A method as claimed in claim 11 , wherein the error term is used to determine the posterior expectation.
17. A method as claimed in claim 11 , wherein the error term is used to determine the posterior covariance.
18. A method as claimed in claim 11 , wherein the physical system has a part which is the same in the first and second states, measurements of this part being used to determine statistical properties of the error term.
19. A method as claimed in claim 1 , wherein prior knowledge about the changes of the parameters of the model is defined in a prior model.
20. A method as claimed in claim 19 , where the prior model is defined via a prior expectation and a prior covariance.
21. A method as claimed in claim 20 , where the prior model follows Gaussian statistics.
22. A method as claimed in claim 19 , wherein a first part of a solution to the inversion is a posterior expectation and where the prior model for the changes of the parameters of the model is used to determine the posterior expectation.
23. A method as claimed in claim 19 , wherein a second part of a solution to the inversion is a posterior covariance and where the prior model for the changes of the parameters of the model is used to determine the posterior covariance.
24. A method as claimed in claim 1 , wherein the seismic data are reflection data.
25. A method as claimed in claim 1 , wherein the parameters of the model are any complete set of elastic properties that can be used to formulate a linear expression of reflectivity.
26. A method as claimed in claim 25 , wherein the parameters of the model are the P-wave velocity, the S-wave velocity, and the density.
27. A method as claimed in claim 25 , wherein the parameters of the model are the acoustic impedance, the shear impedance, and the density.
28. A method as claimed in claim 1 , wherein the physical system includes a region containing a hydrocarbon reservoir.
29. A method as claimed in claim 1 , wherein the obtained changes in the parameters of the model are used to assess where changes in the physical system have occurred between the first and second states.
30. A method as claimed in claim 29 , wherein the obtained changes in the parameters of the model are used to assess the change in hydrocarbon content in the hydrocarbon reservoir.
31. A method as claimed in claim 1 , wherein the obtained changes in the parameters of the model are used to assess the probabilities of changes in the physical system between the first and second states.
32. A method as claimed in claim 31 , wherein the probabilities of changes in the physical system are used to generate a probability density map of changes in the physical system.
33. A computer-readable storage medium storing a computer program executable by a computer a computer to perform a method as claimed in claim 1 .
34. A computer programmed to perform a method as claimed in claim 1 .
35. An apparatus for processing data representing a physical system, the apparatus comprising:
a computer-implemented means for forming a difference between first and second measured data representing the system in first and second states, respectively; and
a computer-implemented means for inverting the difference in accordance with a parameterized model of the physical system to obtain changes in the parameters of the model.