Instantaneous frequency and amplitude at the envelope peak of a constant‐phase wavelet

Abstract

Robertson and Nogami (1984) have shown that the instantaneous frequency at the peak of a zero‐phase Ricker wavelet is exactly equal to that wavelet’s average Fourier spectral frequency weighted by its amplitude spectrum. Bodine (1986) gave an example which shows this is also true for constant‐phase bandpass wavelets. Here I prove that this holds for any constant‐phase wavelet. I then develop an equation expressing this quantity as a function of propagation time through an attenuating medium. A corresponding equation is derived for the amplitude of the envelope peak. Taken together, these may aid in the analysis of seismic data as suggested by Robertson and Nogami (1984), Bodine (1986), and Robertson and Fisher (1988).