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.