Patent Application
20070258323
The present invention relates generally to the field of seismic data processing and interpretation. More specifically, the invention relates to decompose a prestack or poststack seismic trace into a set of predefined wavelets of different shapes and reconstruct a new seismic trace using a subset of the wavelets or the original seismic trace with all the wavelets.
In seismic prospecting, a seismic source is used to generate a seismic wave that propagates into the earth and is at least partially reflected by subsurface seismic reflectors. The reflected signals are recorded by seismic receivers located at or near the surface of the earth, in an overlying body of water, or at known depths in boreholes, and the resulting seismic data are seismic data traces and may be processed to yield information relating to the subsurface formations.
Seismic prospecting consists of three separate stages: data acquisition, data processing, and data interpretation. The seismic energy recorded by each seismic receiver is known as a “seismic data trace”. Seismic data traces typically contain both the desired seismic reflections and one or more unwanted noise components that can overwhelm the wanted seismic reflections.
One method for attenuating unwanted noise components in seismic data traces is through the common-midpoint (CMP) stacking process. the “midpoint” for a seismic data trace is the point midway between the source location and the receiver location for that trace. According to the CMP method, the recorded seismic data traces are sorted into common-midpoint gathers each of which contains a number of different seismic data traces of the same midpoint but different source-to-receiver offset distances. The seismic data traces within each CMP gather are corrected for statics and normal moveout and are then summed or “stacked” to yield a stacked data trace which is a composite of the individual seismic data traces in the CMP gather. Before the summing process, the individual seismic data traces are normally called pre-stack seismic traces. After the summing process, the summed or stacked data traces are normally called post-stack seismic traces. Typically, the post-stack data trace has a significantly improved signal-to-noise ratio compared to that of the pre-stack seismic data traces.
In seismic prospecting, it is well known that the conventionally and commonly used model for a seismic trace is the mathematical convolutional model (Sheriff, 1999), which is defined as the convolution of a single source wavelet with a seismic reflection coefficient function:
x(t)=w(t)*r(t)+n(t),
where x(t) is the recorded seismic trace, w(t) is the seismic source wavelet, r(t) is the earth's reflectivity function, n(t) is random noise, and “*” represents mathematical convolution. This model is used and implied in seismic data processing and interpretation, such as deconvolution and inversion.
One of the assumptions of the convolutional model is the single Wavelet assumption, which assumes that the source wavelet remain invariant as it travels through the subsurface. This single wavelet model is, however, far from the real situation. It is an obvious fact that the frequency of a seismic trace becomes lower when depth increases.
The seismic response of a subsurface layer with different physical properties is different. The shapes of a seismic wavelet will change when the wavelet passes through the layer. The changes will be different at different locations where the physical properties of the layer are different. The difference in wavelet shape changes is valuable information to predict the changes in formation and petrophysical properties.
Without implying the single wavelet assumption, the current invention establishes a method for decomposing seismic traces into multiple wavelets of different shapes. This approach is obviously more realistic and provides more capabilities in seismic data processing and interpretation.
The present invention has established a method for decomposing a seismic trace that can be a prestack or poststack seismic trace, into a set of predefined seismic wavelets of different shapes and reconstructing the original seismic trace with the set of wavelets and a new seismic trace with a selected subset of the set of wavelets. This invention can be divided into two parts: decomposition of a seismic trace and reconstruction of a new or original seismic trace.
The interval of the dominant frequencies can be made smaller for higher accuracy of the decomposition and larger for fast decomposition computation. An interval of 1 Hz is normally used in this invention.
For easy description, a wavelet trace is defined as a data vector that has only one wavelet in the data vector and has the same number of amplitude samples as the seismic data trace to be decomposed.
With the wavelet base or a subset of the wavelets in the base, a linear program can be established as shown below for each seismic data trace to be decomposed.
Minimize: CX
Subject to: AX=B and X>=0
where X is the vector of variables to be solved for, C is the vector of weights for X, matrix A is of wavelet trace columns and B is the seismic trace vector to be decomposed.
For each wavelet in the wavelet base or in the selected subset of the wavelets, a wavelet trace or vector is formed for each of the amplitude samples of the seismic trace to be decomposed. The wavelets of the wavelet traces are positioned at the positions of the amplitude samples of the seismic trace to be decomposed. The wavelet traces form the columns of matrix A. The above wavelet traces are multiplied by −1 and also added into matrix A.
For more accurate decomposition, maximum and minimum positions of the seismic trace are computed. Wavelet traces are then generate for the positions and added to the matrix A.
The expression “CX” is called objective function. C is a vector of weights for the corresponding wavelet traces in matrix A. The same values of 1 can be used.
The above linear program can be solved by one of the many linear optimization methods. A good presentation and reference of the interior point method can be found in Ross, et al. (1997).
Once the linear program is solved, the elements of vector X represent the amplitudes of the wavelet traces in matrix A. The wavelet traces with amplitudes that are larger than a certain threshold are kept and information required to recover the wavelet traces is saved to a computer file. The other wavelet traces are discarded.
a and 3b show the original seismic section and the reconstruction of the original seismic section.
REFERENCE:
Sheriff, R. E., 1999, Encyclopedic Dictionary of Exploration Geophysics, Third edition, Society of Exploration Geophysicists, p 52-53.
Ross, C., Terlaky, T. and Vial, J.-Ph, 1997, Theory and Algorithms for Linear Optimization, John Wiley & Sons.
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