Interferometric redatuming by sparse inversion

Assuming that exact transmission responses are known between the surface and a particular depth level in the subsurface, seismic sources can be effectively mapped to that level by a process called interferometric redatuming. After redatuming, the obtained wavefields can be used for imaging below this particular depth level. Interferometric redatuming consists of two steps, namely (i) the decomposition of the observed wavefields into up- and down-going constituents and (ii) a multidimensional deconvolution of the up- and downgoing wavefields. While this method works in theory, sensitivity to noise and artifacts due to incomplete acquisition call for a different formulation. In this letter, we demonstrate the benefits of formulating the two steps that undergird interferometric redatuming in terms of a transform-domain sparsity-promoting program. By exploiting compressibility of seismic wavefields in the curvelet domain, we not only become robust with respect to noise but we are also able to remove certain artifacts while preserving the frequency content. These improvements lead to a better image of the target from the redatumed data.