Method of representing seismic signals

A method for seismic surveying, the method comprising the steps of:

• performing a seismic survey using one or more seismic sources, wherein performing the seismic survey comprises using a plurality of seismic receivers disposed at a plurality of irregularly spaced locations to record multichannel seismic data generated by the one or more seismic sources, wherein the plurality of seismic receivers measure seismic signals at the plurality of irregularly spaced locations and the plurality of irregularly spaced locations comprise discrete points spread in space and/or time, and wherein the measured seismic signals comprise a time series of waves and the multichannel seismic data comprises the measured seismic signals and a first order derivative of the measured seismic signals;
• receiving the multichannel seismic data from the plurality of seismic receivers;
• using a processor to regularize the received multichannel seismic data, wherein the processor executes a series of instructions stored thereon, the instructions comprising:
• selecting a set of iterative basis functions to model said multichannel seismic data, wherein each of the set of iterative basis functions is fully defined by n unknown parameters;
• producing a representative model of the multichannel seismic data by iteratively estimating the n unknown parameters, wherein the step of producing the representative model of the multichannel seismic data, comprises:
• (a) applying an estimate of the n unknown parameters to each of the set of iterative basis functions;
• (b) combining results of the application of the estimate of the n unknown parameters to each of the set of iterative basis functions to produce an iterative representative model of the multichannel seismic data;
• (c) comparing the iterative representative model of the multichannel seismic data with the measured seismic signals and the derivatives of the measured seismic signals at said discrete points;
• (d) adjusting the estimate of the n unknown parameters and repeating steps (a), (b) and (c) until a difference between the iterative representative model of the multichannel seismic data and the measured seismic signals and the derivatives of the measured seismic signals at said discrete points is minimized;
• and
• (e) determining the representative model of the measured seismic signals from the set of iterative basis functions and values of the adjusted n unknown parameters when the difference between the iterative representative model of the multichannel seismic data and the measured seismic signals and the derivatives of the measured seismic signals at said discrete points is minimized;
• transforming the multichannel seismic data received from the plurality of seismic receivers disposed at the plurality of irregularly spaced locations in the seismic survey into regularized seismic signals, wherein the transforming of the multichannel seismic data from the seismic survey to regularized seismic signals comprises using the representative model of the multichannel seismic data to regularize the measured seismic signals by interpolating values for the measured seismic signals at regularized positions;
• and
• using the regularized seismic signals to obtain an image of a subsurface of the Earth.