The limits of resolution of zero‐phase wavelets

Abstract

This investigation deals with resolving reflections from thin beds rather than the detection of events that may or may not be resolved. Resolution is approached by considering a thinning bed and how accurately measured times on a seismic trace represent actual, vertical two‐way traveltimes through the bed. Theoretical developments are in terms of frequency and time rather than wavelength and thickness because the latter two variables require knowledge of interval velocities. These results are compared with similar studies by Rayleigh, Ricker (1953), and Widess (1973, 1980). We show that the temporal resolution of a broadband wavelet with a white spectrum is controlled by its highest terminal frequency [Formula: see text], and the resolution limit approximates 1/(1.5 [Formula: see text]), provided the wavelet’s band ratio exceeds two octaves. The practical limit of resolution, however, occurs at a one‐quarter wavelength condition and approximates 1/(1.4 [Formula: see text]). The resolving power of zero‐phase wavelets can be compared quantitatively once a wavelet is known in the time domain.