Comparing time series using wavelet-based semblance analysis

Abstract

Similarity measures are becoming increasingly commonly used in comparison of multiple datasets from various sources. Semblance filtering compares two datasets on the basis of their phase, as a function of frequency. Semblance analysis based on the Fourier transform suffers from problems associated with that transform, in particular its assumption that the frequency content of the data must not change with time (for time-series data) or location (for data measured as a function of position). To overcome these problems, semblance is calculated here using the continuous wavelet transform. When calculated in this way, semblance analysis allows the local phase relationships between the two datasets to be studied as a function of both scale (or wavelength) and time. Semblance analysis is demonstrated on synthetic datasets and on gravity and aeromagnetic data from the Vredefort Dome, South Africa. Matlab source code is available from the IAMG server at www.iamg.org.