Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2001-06-28
2004-02-03
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C702S017000
Reexamination Certificate
active
06687617
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to seismic data processing, and more particularly to a more rapid method of migrating seismic data for steeply-dipping reflectors and large lateral variations in velocity.
Typically, seismic data is arranged in arrays representing an acoustic signal received by sensors. Often the seismic data represents signal values as a function of geometric location and frequency content of the signal. Geological sensors, like geophones and hydrophones, measure the wavefields at a multitude of positions. The measured seismic data characterized by wavefields are processed to identify useful geological formations. One such processing step is called seismic data migration.
Seismic data migration requires solving the wave equation in the earth volume. Measured wavefield data points are used in conjunction with the wave equation to identify useful geological formations. It is well known in the art that the seismic data requires migration in order to restore the apparent positions of reflections to their correct locations (Claerbout
1
, 1999; Stolt and Benson
2
, 1986). Numerous techniques of seismic data migration are known in the art (Bording and Lines
3
, 1997; Claerbout
4
, 1999; Stolt and Benson
5
, 1986). Different techniques provide differing degrees of accuracy. In general, more accurate methods require greater computational resources. In order to use available computer resources in a cost-effective manner, computation-intensive algorithms must be designed as efficiently as possible.
1
Incorporated herein by reference.
2
Incorporated herein by reference.
3
Incorporated herein by reference.
4
Incorporated herein by reference.
5
Incorporated herein by reference.
Conventional finite difference methods of migration are valued for their accuracy, but they are computationally intensive. Because of its expense, the finite difference method is most appropriate for use in regions where the acoustic signal velocity strongly varies laterally, as well as with depth (or time).
Most conventional finite difference methods of migration represent “one-way” approximations of the two-way acoustic wave equation for constant density, which has the form:
∂
2
P/∂x
2
+∂
2
P/∂y
2
+∂
2
P/∂z
2
=(1
/c
2
)∂
2
P/∂t
2
(1)
where
P=acoustic pressure,
x, y, z=position coordinates, and
c=acoustic velocity
Examples of known methods of finite difference solutions for the “two-way” wave equation can be found, for example, in Bording and Lines
6
, 1997, and Smith, U.S. Pat. No. 5,999,488. These methods are particularly slow, since they independently account for downgoing and upgoing propagation of the wavefield. In addition, in order to use equation (1) effectively, the spatial distribution of the velocity, C(x,y,z), must be known very precisely. This level of precision is difficult to obtain. Thus, there is a long felt need for a method and system to retain the accuracy of the finite difference method at increased speed and reduced cost, without having a highly detailed knowledge of the spatial distribution for the propagation velocity.
6
Incorporated herein by reference.
REFERENCES:
patent: 5696733 (1997-12-01), Zinn et al.
patent: 5995904 (1999-11-01), Willen et al.
patent: 6317695 (2001-11-01), Zhou et al.
“Compensating Finite-Difference Errors in 3-D Migration and Modeling”, 10/91, Li in Geophysics, vol. 56, No. 10.*
“Migration of Seismic Data by Phase Shift Plus Interpolation”, 2/84, Gazdag et al. in Geophysics, vol. 49, No. 2.*
“Wave Equation Migration with the Phase-Shift Method”, 12/78, Gazdag in Geophysics, vol. 43, No. 7.*
Ralph Phillip Bording and Larry R. Lines, 1997, “Seismic Modeling and Imaging with the Complete Wave Equation,” Course Notes Series No. 8, SEG.
Charles Cerjan, Dan Kosloff, Ronnie Kosloff and Moshe Reshef, 1985, “A nonreflecting boundary condition for discrete and elastic wave equations,” Geophysics, 50, 4, 705-708.
Jon Claerbout, 1985, 1999, “Imaging the Earth's Interior,” Blackwell Scientific Publications, Ltd.
Robert W. Clayton and Bjorn Engquist, 1980, “Absorbing boundary conditions for wave-equation migration,” Geophysics, 45, 5, 895-904.
Jeno Gazdag, 1978, Wave equation migration with the phase-shift method: Geophysics, 43, 1342-1351.
E. Kjartansson, 1979, “Attenuation of seismic waves in rocks and applications in energy exploration,” Ph.D. thesis, Stanford Univ.
Jeno Gazdag and Piero Sgua, zero, 1984, Migration of seismic data by phase shift plus . . . , Geophysics, 49, 124-131.
R. Kosloff and D. Kosloff, 1986, Absorbing Boundaries for Wave Propagation Problems, Journal of Computational Physics, 63, 363-376, Wave equation migration with the phase-shift method, Geophysics, 43, 1342-1351.
Myung W. Lee and Sang Y. Suh, 1985, “Optimization of one-way wave equations,” Geophysics, 50, 10, 1634-1637.
Zhiming Li, 1991, “Compensating finite-difference errors in 3-D migration and modeling,” Geophysics, 56, 10, 1650-1660.
Curtis Ober, Rob Gjertsen and David Womble, 1999, “Salvo: A Seismic Migration Code for Complex geology,” A report prepared for members to the ACTI consortium, Sandia National Lab, Albuquerque, N.M.
Robert Stolt and Alvin Benson, 1986, “Seismic Migration: Theory and Practice, vol. 5” Geophysical Press.
Le Toan M
PGS America, Inc.
Thigpen E. Eugene
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