Robust detection of weak acoustic signals in noise using near optimal shrinkage in radon domain

In this work we present methods and strategies for robust detection of weak compressional (P) and shear (S) wave arrivals in acoustic data collected in subsurface oilwells especially in noisy environments such as with logging while drilling (LWD) acquisition. First, we propose a novel de-noising method to combat random additive noise and reflections by employing space time shrinkage in the Discrete Radon Transform (DRT) domain. The novelty of our approach lies in a proposed class of space-time shrinkage operators for this purpose derived from a quantity called the semblance used in velocity (slowness) processing. The algorithm is validated on synthetic and real data and shows significant improvement in log coverage.