Method for removing coherent noise from seismic data through f-x filtering
AssigneeMobil Oil Corporation
InventorsRobert A. Meek, Andrew F. Linville, Jr.
Life of this patent
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Abstract
In seismic exploration, seismic reflections from subsurface formations are recorded in the form of a time-distance array of seismic traces. This array is transformed into a frequency-distance domain. Frequencies at which coherent noise resides within the frequency-distance domain are determined. Wavenumbers corresponding to such frequenices are removed by filtering. The wavenumber-filtered, frequency-distance domain of seismic traces are then transformed back into a time-distance array of seismic traces.
Claims4
In seismic exploration wherein seismic sources are activated at spaced locations along a line of exploration and the amplitude of reflections from subsurface formations are recorded as a function of time and distance along said line of exploration to produce a time-distance array of seismic traces, said traces comprised of a seismic signal component and a coherent noise component;
- a method of processing said seismic traces to remove said coherent noise component, comprising the steps of:
- a) transforming said time-distance (t-x) array of seismic traces with a fast Fourier transform into a frequency-distance (f-x) domain D (f,x) in accordance with the following:
- ##EQU5## where d(t,x) are the seismic traces in the t-x domain for x=1...n;
- n is the number of seismic traces;
- t=0,...,j;
- j is the number of time samples;
- D(f,x) are the seismic traces in the f-x domain;
- f=0 ... j.
- b) determining a frequency within a range wherein said coherent noise component resides, said frequency range being dependent on the bandwidth of said coherent noise component,
- c) determining a wavenumber corresponding to the coherent noise component of the determined frequency,
- d) determining a least squares filter a(m) for removing said determined wavenumber from the frequency-distance domain seismic traces, D(f,x), in accordance with the following:
- ##EQU6## where * means complex conjugate, R(m)=e.sup.i2.pi.km.DELTA.x for m=0...p-1;
- .sigma..sup.2 is a random noise term added to the diagonals;
- .sigma..sup.2 governs how deep the wavenumber notch will be (for small .sigma..sup.2 the notch will be deep and for a larger .sigma..sup.2 the notch will be shallow);
- and the width of the notch is controlled by the number (p) of coefficients generated,
- e) convolving said least squares filter a(m) with D(f,x), the (f,x) domain seismic traces to remove the determined wavenumber in accordance with the following:
- ##EQU7## where D'(f,x) is the filtered data and n is the number of traces, and f) transforming said filtered (f,x) domain seismic traces, D(f,x), with a fast Fourier transform back to the time-distance (t-x) domain to produce a time-distance (t-x) array of seismic traces with said coherent noise component removed in accordance with the following:
- ##EQU8## where d'(t,x) represents the data after coherent noise removal.
Dependencies are inferred from the claim text.