Instantaneous spectral bandwidth and dominant frequency with applications to seismic reflection data

Abstract

Fourier power spectra are often usefully characterized by average measures. In reflection seismology, the important average measures are center frequency, spectral bandwidth, and dominant frequency. These quantities have definitions familiar from probability theory: center frequency is the spectral mean, spectral bandwidth is the standard deviation about that mean, and dominant frequency is the square root of the second moment, which serves as an estimate of the zero‐crossing frequency. These measures suggest counterparts defined with instantaneous power spectra in place of Fourier power spectra, so that they are instantaneous in time though they represent averages in frequency. Intuitively reasonable requirements yield specific forms for these instantaneous quantities that can be computed with familiar complex seismic trace attributes. Instantaneous center frequency is just instantaneous frequency. Instantaneous bandwidth is the absolute value of the derivative of the instantaneous amplitude divided by the instantaneous amplitude. Instantaneous dominant frequency is the square root of the sum of the squares of the instantaneous frequency and instantaneous bandwidth. Instantaneous bandwidth and dominant frequency find employment as additional complex seismic trace attributes in the detailed study of seismic data. Instantaneous bandwidth is observed to be nearly always less than instantaneous frequency; the points where it is larger may mark the onset of distinct wavelets. These attributes, together with instantaneous frequency, are perhaps, of greater use in revealing the time‐varying spectral properties of seismic data. They can help in the search for low frequency shadows or in the analysis of frequency change due to effects of data processing. Instantaneous bandwidth and dominant frequency complement instantaneous frequency and should find wide application in the analysis of seismic reflection data.