Seismic processing with continuous wavelet transform maxima

Kristopher A. H. Innanen

Sophisticated signal analysis methods have been in existence since the 1990s, formalizing the older idea of edge detection and characterization. Amongst the better known of these is one focusing on the portions of continuous wavelet transforms thought to contain most of the signal's information content-its maxima. While analysis of continuous wavelet transform maxima (CWTMs) has been applied in exploration seismology, processing of these data have not. Simple methods exist to do this, and we discuss and implement one-the model of Mallat and Zhong-in this paper. The approach requires a bit of conceptual explanation, as it has not appeared in the exploration geophysics literature before, and we devote most of this paper to that task; our primary goal is logically develop the implementation, and leave relatively open the many possible applications to the seismic trace it seems to have in potential. However, we end the paper with a simple example of thresholding of CWTMs, and the resulting reduction in noise. In a companion paper we use such data to produce internal multiple prediction operators.