Patent Document ID: 8981971
Application ID: 14224916

Base Claim:
1. A method for seismic exploration of the earth comprising the steps of applying to the earth a seismic input signal which is characterized by a seismic source wavelet I(t), recording a seismic trace f(t) in response to said seismic source wavelet, and transforming said seismic source wavelet I(t) into a zero-degree phase wavelet φ p (t) and a shifted 90 degree phase wavelet Ψ p (t), where the wavelets φ p (t) and Ψ p (t) span a two dimensional sub-space, creating a sub-space dictionary as 
 D s ={(φ p ,Ψ p )} pεΓ where Γ is a set of wavelets which are derived using φ p (t) wavelet and Ψ p (t) wavelet, and projecting said seismic trace f(t) onto said dictionary D s to find the best matching projection, with a residual determined after each projection matching, wherein the sum of said residuals determines the fidelity in data compression.

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Claim 5:
5. The method of claim 1 wherein, R m f represents the residual after the m-th projection, with R o f=f, the initial residual being the response trace f(t) itself, and the m-th order residual R m f computed from m≧0, where (φ pm ,Ψ pm )εD s , finding a sub-set of the input wavelet φ pm , Ψ pm in the dictionary D s such that the m-th order residual has the biggest energy projected thereon such that, 
 |< R m f,φ pm >|+|<R m f,Ψ pm >|=max(|< R m f,φ p >|+|<R m f,Ψ p >|) pεΓ, projecting R m f on (φ pm ,Ψ pm ), wherein 
 R m f=<R m f,φ pm >φ pm +>R m f,Ψ pm >Ψ pm +R m+1 f, stopping at the m-th iteration when the norm of the residual satisfies 
 ∥ R m f ∥<ε where ε is a predefined small, positive value, and the compressed wave is represented by f = ∑ m = 0 M - 1 ⁢ ⁢ ( 〈 R m ⁢ f , ϕ pm 〉 ⁢ ϕ pm + 〈 R m ⁢ f , Ψ pm 〉 ⁢ Ψ pm ) + R M ⁢ f .