Interpolation and/or extrapolation of seismic data

Abstract

A method of processing seismic data is provided in the seismic data is acquired at a plurality of locations and the method comprises interpolating and/or extrapolating the seismic data, thereby to estimate seismic data at a target location different from the plurality of locations. The interpolating and/or extrapolating the seismic data is performed in a polar co-ordinate system. The method may provide for, among other things, accuracy of estimation; particularly at short offsets from the seismic source. The polar co-ordinate system used may be chosen to approximate the seismic wavefront in an earth model, for example in an earth model in which properties vary only with depth.

1 . A method of processing seismic data acquired at a plurality of locations, the method comprising:
 using a processor to read a non-transitory computer-readable medium and/or computer readable signals containing instructions that when executed by the processor provide for:
 interpolating and/or extrapolating the seismic data to estimate seismic data at a target location different from the plurality of locations, wherein the seismic data comprise measurements of one or more attributes of a wavefield generated by a seismic source and/or a spatial derivative of said wavefield and interpolating and/or extrapolating of the seismic data is performed in a polar co-ordinate system, and wherein a coordinate origin of the polar co-ordinate system is configured to be substantially coincident with a location of the seismic source that generated the wavefield. 
   
     
     
         2 . The method of  claim 1 , wherein the interpolating and/or extrapolating of the seismic data comprises using at least one of a matching pursuit interpolation method and a matching pursuit extrapolation method. 
     
     
         3 . The method of  claim 2 , wherein the matching pursuit interpolation method comprises one of an interpolation by matching pursuit method, a multichannel interpolation by matching pursuit method and a matching pursuit Fourier interpolation method. 
     
     
         4 . The method of  claim 1 , wherein the one or more attributes of the wavefield comprise at least one of pressure, particle displacement, particle velocity and particle acceleration. 
     
     
         5 . The method of  claim 1 , wherein the measurements of the spatial derivative of said wavefield comprise measurements of a parameter that can be transformed into the spatial derivative. 
     
     
         6 . The method of  claim 1 , wherein the measurements of the one or more attributes of the wavefield generated by the seismic source and/or the spatial derivative of said wavefield comprise measurements of a pressure and a spatial derivative of the wavefield. 
     
     
         7 . The method as claimed in  claim 1 , wherein the interpolating and/or extrapolating the seismic data is performed in a 2-D polar coordinate system. 
     
     
         8 . The method as claimed in  claim 1 , wherein the interpolating and/or extrapolating the seismic data is performed in a polar co-ordinate system that approximates a seismic wavefront in an earth model. 
     
     
         9 . The method as claimed in  claim 8 , wherein the interpolating and/or extrapolating the seismic data is performed in the polar co-ordinate system that approximates the seismic wavefront in the earth model in which properties vary only with depth. 
     
     
         10 . The method as claimed in  claim 1 , wherein the interpolating and/or extrapolating the seismic data is performed using an expansion series defined in a polar coordinate system. 
     
     
         11 . The method as claimed in  claim 10 , wherein the expansion series is a Taylor expansion series. 
     
     
         12 . The method as claimed in  claim 1 , wherein the seismic data is acquired using at least one seismic cable comprising a plurality of seismic receivers. 
     
     
         13 . The method as claimed in  claim 1 , wherein the seismic data comprises multi-component seismic data. 
     
     
         14 . The method as claimed in  claim 13 , wherein the seismic data is recorded by a plurality of multi-component seismic receivers. 
     
     
         15 . The method as claimed in  claim 12 , further comprising:
 estimating a spatial derivative of a first component of the seismic data using a second component of the seismic data.   
     
     
         16 . The method as claimed in  claim 15 , wherein the spatial derivative of the first component of the seismic data is a derivative along a direction substantially perpendicular to the at least one of the seismic cables. 
     
     
         17 . The method as claimed in  claim 1 , wherein the origin of the polar co-ordinate system is substantially coincident with a horizontal position of an acoustic centre of the seismic source. 
     
     
         18 . The method as claimed in  claim 1 , wherein the seismic data is recorded by a plurality of seismic receivers in a survey area, wherein each of the plurality of seismic receivers is located at a one of the plurality of locations. 
     
     
         19 . The method as claimed in  claim 1 , wherein the seismic data is recorded by a first seismic cable and a second seismic cable, and wherein the target location comprises a location disposed between the first seismic cable and the second seismic cable. 
     
     
         20 . The method as claimed in  claim 1 , wherein the seismic data is recorded by a first seismic cable and the target location comprises a location disposed between the first seismic cable and the seismic source. 
     
     
         21 . The method as claimed in  claim 1 , further comprising:
 processing the estimated seismic data for the target location to obtain information about one or more parameters of an interior section of the earth.