Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
2000-03-09
2004-02-10
Thomson, W. D. (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S009000, C703S010000, C703S006000, C702S014000, C702S016000, C702S017000, C702S018000, C367S073000, C367S014000, C367S025000
Reexamination Certificate
active
06691075
ABSTRACT:
FIELD OF THE INVENTION
This invention relates generally to the field of seismic prospecting. More particularly, the invention relates to a method for constructing a model seismic image of a subsurface seismic reflector.
BACKGROUND OF THE INVENTION
In the oil and gas industry, seismic prospecting techniques are commonly used to aid in the search for and evaluation of hydrocarbon deposits located in subterranean formations. In seismic prospecting, seismic energy sources are used to generate a seismic signal which propagates into the earth and is at least partially reflected by subsurface seismic reflectors. Such seismic reflectors typically are interfaces between subterranean formations having different elastic properties. The reflections are caused by differences in elastic properties, specifically wave velocity and rock density, which lead to differences in impedance at the interfaces. The reflections are recorded by seismic detectors at or near the surface of the earth, in an overlying body of water, or at known depths in boreholes. The resulting seismic data may be processed to yield information relating to the geologic structure and properties of the subterranean formations and potential hydrocarbon content.
The goal of all seismic data processing is to extract from the data as much information as possible regarding the subterranean formations. In order for the processed seismic data to fully represent geologic subsurface properties, the true amplitudes resulting from reflection of the input signal by the geologic target must be accurately represented. This requires that the amplitudes of the seismic data must be processed free from non-geologic seismic effects. Non-geologic amplitude effects include mechanisms that cause the measured seismic amplitudes to deviate from the amplitude caused by the reflection coefficient of the geologic target. These non-geologic amplitude effects can be related to acquisition of the data or to near surface effects. Examples of non-geologic amplitude effects that can be particularly troublesome are source and receiver variation, coherent noises, electrical noise or spikes, and overburden and transmission effects. If uncorrected, these effects can dominate the seismic image and obscure the true geologic picture.
A seismic wave source generates a wave that reflects from or “illuminates” a portion of a reflector. The collection of sources that comprises an entire 3-D survey generally illuminates a large region of the reflector. Conventional prestack 3-D migration algorithms can produce precise images of the reflector only if illumination is relatively uniform. Lateral velocity variations within the earth and nonuniformly sampled 3-D prestack seismic data, however, generally cause reflectors to be illuminated nonuniformly. Nonuniform illumination is generally due to varying azimuths and source-receiver midpoint locations. Consequently, prestack 3-D migrated images are often contaminated with non-geologic artifacts called an “acquisition footprint”. These artifacts can interfere with the ultimate interpretation of seismic images and attribute maps. Understanding and removing the effects of the acquisition footprint has thus become important for seismic acquisition design, to processing, and interpretation.
Let {right arrow over (S)}=(S
1
, S
2
)
T
and {right arrow over (G)}=(G
1
, G
2
)
T
denote two-dimensional coordinate vectors of a seismic source, commonly called a shot, and a seismic receiver, typically a geophone, respectively. These vectors {right arrow over (S)} and {right arrow over (G)} are defined with respect to a global Cartesian coordinate system {right arrow over (x)}=(x, y, z) in the plane given by z=0. Schleicher et al., “3-D True-Amplitude Finite-Offset Migration”,
Geophysics,
58, 1112-1126, (1993) showed that for any specified measurement configuration of sources and receivers, the vector pair ({right arrow over (S)},{right arrow over (G)}) can be described by a single position vector {right arrow over (&xgr;)}=(&xgr;
1
, &xgr;
2
)
T
according to the following relations
{right arrow over (S)}
({right arrow over (&xgr;)})=
{right arrow over (S)}
0
+&Ggr;
S
({right arrow over (&xgr;)}−{right arrow over (&xgr;)}
0
)
and
{right arrow over (G)}
({right arrow over (&xgr;)})=
{right arrow over (G)}
0
+&Ggr;
G
({right arrow over (&xgr;)}−{right arrow over (&xgr;)}
0
).
Here {right arrow over (S)}
0
and {right arrow over (G)}
0
are coordinate vectors describing a fixed source-receiver pair ({right arrow over (S)}
0
, {right arrow over (G)}
0
) defined by position vector {right arrow over (&xgr;)}={right arrow over (&xgr;)}
0
. Configuration matrices &Ggr;
S
and &Ggr;
G
are 2×2 constant matrices, depending only upon the measurement configuration. The configuration matrices are determined by
Γ
Sij
=
∂
S
i
∂
ξ
j
and
Γ
G
ij
=
∂
G
i
∂
ξ
j
,
for
i
=
1
,
2
and
j
=
1
,
2.
Examples of sets of configuration matrices for particular measurement configurations are:
&Ggr;
S
=I and &Ggr;
G
=I for common offset configuration,
&Ggr;
S
=0 and &Ggr;
G
=I for common shot configuration, and
&Ggr;
S
=I and &Ggr;
G
=0 for common receiver configuration.
Here I is the 2×2 identity matrix and 0 is the 2×2 zero matrix.
As discussed by Schleicher et al., (1993), supra, common offset 3-D migration can be formulated as a weighted summation along the diffraction traveltime surface, &tgr;
D
, also called the Huygens surface, through the following Kirchhoff migration equation
U
(
x
→
)
=
∑
j
Δ
ξ
→
j
w
(
ξ
→
j
,
x
→
)
U
.
(
ξ
→
j
,
t
+
τ
D
(
ξ
→
j
,
x
→
)
)
❘
t
=
0
.
(
1
)
Here U is the seismic amplitude sum; {right arrow over (x)} is the image point; {right arrow over (&xgr;)}
j
is the source-receiver midpoint for trace j; w is a weight chosen to preserve seismic amplitudes; and &tgr;
D
is the diffraction traveltime connecting source S, image point Q, and receiver G. The dot above U on the right hand side of equation (1) represents time differentiation. The term &Dgr;{right arrow over (&xgr;)}
j
in migration equation (1) is the two-dimensional element of surface area representing trace j, indicating that this equation is a discretized integral formula. Neglect of variations in &Dgr;{right arrow over (&xgr;)}
j
, caused by variations in source-receiver midpoint distribution, is in practice a significant cause of acquisition footprints. Migration implemented by equation (1) is referred to in the literature as “True Amplitude Kirchhoff Migration”.
Consider an image volume consisting of N points in each of the x, y, and z directions. Then imaging with migration equation (1) is an O(N
5
) process, because the two-dimensional summations over {right arrow over (&xgr;)}
j
must be performed at each point {right arrow over (x)} of the three-dimensional image space. O(N
5
) processes such as migration equation (1) must usually be implemented on supercomputers or on parallel networks of fast workstations.
Migration equation (1) only produces a good image under the assumptions that the source-receiver offset and azimuth are fixed in magnitude within a narrow range, and the data coverage is dense in {right arrow over (&xgr;)}
j
-space. This last assumption means that there are no large data gaps, which would give large &Dgr;{right arrow over (&xgr;)}
j
values. Failure of the data or the migration implementation to meet these assumptions generally results in an image that is contaminated with an acquisition footprint.
Schleicher et al., (1993), supra, show that synthetic seismic data may be written for one reflector and a collection of sources and receivers as the following data equation
U
({right arrow
Schneider, Jr. William A.
Winbow Graham A.
ExxonMobil Upstream Research Company
Schweppe Charles R.
Thomson W. D.
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