Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2002-05-21
2004-07-13
Barow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C703S005000
Reexamination Certificate
active
06763304
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to the field of geophysical prospecting. More particularly, the invention relates to the field of seismic data processing. Specifically, the invention is a method for attenuating multiples in seismic data using a high-resolution Radon transform.
2. Description of the Related Art
In the field of geophysical prospecting, the knowledge of the subsurface structure of the earth is useful for finding and extracting valuable mineral resources, such as oil and natural gas. A well-known tool of geophysical prospecting is a seismic survey. A seismic survey transmits acoustic waves emitted from appropriate energy sources into the earth and collects the reflected signals using an array of receivers. Then seismic data processing techniques are applied to the collected data to estimate the subsurface structure.
In a seismic survey, the seismic signal is generated by injecting an acoustic signal from on or near the earth's surface, which then travels downwardly into the earth's subsurface. The acoustic signal may also travel downwardly through a body of water, in a marine survey. Appropriate energy sources may include explosives or vibrators on land and air guns or marine vibrators in water regimes. When the acoustic signal encounters a seismic reflector, an interface between two subsurface strata having different acoustic impedances, a portion of the acoustic signal is reflected back to the surface, where the reflected energy is detected by a receiver. Appropriate detectors may include particle motion detectors (such as geophones) on land and pressure detectors (such as hydrophones) in water regimes. Both sources and receivers may be deployed by themselves or, more commonly, in arrays.
The seismic energy recorded by each source and receiver pair during the data acquisition stage is known as a seismic trace. Seismic data traces contain the desired seismic reflections, known as the primary reflections or primaries. A primary reflection comes from the detection of an acoustic signal that travels from a source to a receiver with but a single reflection from a subsurface seismic reflector. Unfortunately, the seismic traces often contain many unwanted additional reflections known as multiple reflections or multiples, which can obscure and even overwhelm the sought-after primary reflections. A multiple reflection comes from the recording of an acoustic signal that has reflected more than once before being detected by a receiver. The additional multiple reflections could come from subsurface reflectors or from the surface of the earth in a land seismic survey and the water-earth or air-water interfaces in a water seismic survey. The recorded signals from multiples obscure the recorded signals from the primaries, making it harder to identify and interpret the desired primaries. Thus, the removal, or at least attenuation, of multiples is a desired step in seismic data processing in many environments. This is particularly so in marine seismic surveys, where multiples are especially strong relative to primaries. This is because the water-earth and, particularly, the air-water interfaces are strong seismic reflectors due to their high acoustic impedance contrasts.
One of many techniques well known in the art of seismic data processing for attenuating multiples is the use of a Radon transform. First, a single Fourier transform takes data from the space-time domain, or (x, t) domain, to the Fourier domain, or (x, &ohgr;) domain. Here, co is the frequency. Then, for each frequency c, the Radon transform, or decomposition, transforms data to the Radon domain, or (q, &tgr;) domain. Here, q is a parameter associated with the curvature of the curvilinear trajectory describing the seismic event in the (x, t) domain and X (tau) is the zero offset intercept time. The Radon transform is given in simplest terms by the equation
Lm=d,
(1)
where L is a matrix representing the Radon transform, m is a vector representing the model being solved for in the Radon domain, and d is a vector containing the seismic data set being processed. The vector d is size M, where M is the number of available seismic traces d
i
in the seismic data set d. Typically, M is the number of digitized seismic traces in a gather. The vector m is size N, where N is the number of spectral curvature components m
i
that d is being decomposed into by the Radon transform L. Thus, the matrix L representing the Radon transform is size M×N and decomposes the seismic data samples d
i
in d into the spectral components m
i
in m.
In general, problems like Equation (1) can be solved by a least squares approach, such as
m
=(
L
H
L
)
−1
L
H
d.
(2)
However, the matrix L
H
L may not be invertible for the Radon transform matrix L. Thus, Equation (1) is typically solved as a diagonally stabilized least squares problem given by
m
=(
L
H
L+kI
)
−1
L
H
d.
(3)
Here k is a pre-whitening factor or diagonal stabilization constant and I is the N×N identity matrix. The diagonal stabilization matrix kI is added to the matrix L
H
L to avoid numerical instabilities in the matrix inversion. The superscript H indicates the Hermitian transpose of a matrix. The matrix (L
H
L+kI) to be inverted has Toeplitz structure and thus the inversion can be done using Levinson recursion.
Once the data has been transformed into the Radon domain as the model solution m, the primaries can be muted from m. Then, the multiples remaining in m can be transformed back into the spatial domain by the inverse transform
d
m
=Lm
m
, (4)
where d
m
is the data vector containing substantially just multiples and m
m
is the model containing substantially just multiples. Now the multiples in multiple data vector d
m
can be subtracted from the data vector d to give substantially just the desired primaries. The matrix to be inverted, (L
H
L+kI), has Toeplitz structure and can be inverted using the Levinson recursion scheme, since the stabilization matrix kI is constant.
Hampson, D., 1986, “Inverse Velocity Stacking for Multiple Elimination”, J. Can. Soc. of Expl. Geophys., 22(1): 44-55, describes a parabolic Radon transform. It is used to attenuate multiples in a computer-efficient way. This is the method described above. However, it only works well with large move outs. These large move outs are, for example, twenty or more milliseconds at the farthest usable offset.
Sacchi, M. D. and Ulrych, T. J., 1995, “High-Resolution Velocity Gathers and Offset Space Reconstruction”, Geophysics, 60, 4, 1169-1177, describe a high-resolution Radon transform for attenuating multiples. The high-resolution transform constrains the Radon spectra to be sparse, using a sparseness prior for the curvature direction. This could also be called a re-weighted iterative approach. However, the high-resolution transform can show extra artifacts, which may compromise amplitude preservation. In addition, amplitudes may be affected if the induced sparseness is too strong.
Hunt, L., Cary, P., and Upham, W., 1996, “The Impact of an Improved Radon Transform on Multiple Attenuation”, 66
th
Ann. Internat. Mtg.: Soc. of Expl. Geophys., 1535-1538, shows that a high-resolution parabolic Radon transform based on Sacchi and Ulrych's 1995 publication improves the separation of primaries from multiples that have a small move-out difference. However, the techniques still suffers from the same deficits as Sacchi and Ulrych does.
Zwartjes, P. and Duijndam, A., 2000, “Optimizing Reconstruction for Sparse Spatial Sampling, 70
th
Ann. Internat. Mtg.: Soc. of Expl. Geophys., 2162-2165, show that high-resolution Fourier regularization shows a better reconstruction in large gaps than standard least squares regularization.
In a high-resolution Radon transform, the diagonal matrix kI in the diagonally stabilized least squares approach given by Equation (3) is replaced by a N×N diagonal matrix Q. The matrix Q is a stabilization matrix.
Barow John
PGS Americas, Inc.
Schweppe Charles R.
Taylor Victor J.
Thigpen Eugene
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