Online Journal for E&P Geoscientists

Tsingas, Constantine ^*1; Verschuur, Eric ²
(1) EXPEC ARC, Saudi Aramco, Dhahran, Saudi Arabia. (2) Delphi Studio For Imaging, Delft, Netherlands.

While, historically, the number of seismic recording channels increases by orders of magnitude every 10 years, current 3D Wide Azimuth field acquisition geometries usually have poor spatial sampling in at least one dimension. Most of the demultiple and imaging algorithms, such as reverse time migration, wave equation imaging algorithms and 3D SRME, assume regularly and densely sampled data. A number of data reconstruction techniques have been published in the last few years. These can be categorized as local or global methods. Local methods tend to be robust and easy to implement, but they suffer when attempting to interpolate large gaps. Alternatively, global methods are slower and harder to implement, but can interpolate larger data gaps.

In this presentation, we will outline and demonstrate, on synthetic and field data reconstruction technique and methodology that relies on the fact that the seismic data is redundant and can be represented in a suitable transform domain, in our case, the linear/parabolic Radon domain. By imposing sparseness in the transform domains (i.e. assuming the data can be represented by a limited number of model parameters), transformation from this sparse model domain to the original data domain allows the generation of data for any desired output location. Examples of these model domains are the plane wave domain (i.e. the Fourier domain), the curvelet domain, and the linear or parabolic Radon domain. Since these transforms are usually ill-posed, we need to include an extra constraint, which is typically done in the transform domain. We will illustrate with several examples the effect of employing the L1, L2 and Cauchy constraints in the data reconstruction process using sparse Radon transforms