The wavelet transform as a tool for geophysical data integration

In geophysical exploration different types of measurements are used to probe the same subsurface region. In this paper we show that the wavelet transform can aid the process of linking different data types. The continuous wavelet transform, and in particular the analysis of amplitudes along wavelet transform modulus maxima lines, is a powerful tool to analyze the characteristic properties of local variations in a signal. The amplitude-versus-scale curve of a particular transition in a signal can be seen as its fingerprint. Hence, local variations in different data types can be linked by comparing their fingerprints in the wavelet transform domain. Insight in the physics underlying the different types of measurements is required to ‘tune’ the different wavelet transforms in such a way that a particular geological transition in the Earth’s subsurface leaves the same fingerprint in the wavelet transform of each data type. We discuss the wavelet transform as a tool for geophysical data integration for three situations. First we discuss how one can link the scale-dependent properties of outliers in borehole data to those of reflection events in surface seismic data. We use wave theory to derive relations between the two data types in the wavelet transform domain. Next we analyze the relation between the wavelet transforms of detailed geological models and (simulated) migrated seismic data, with the aim of improving the geological interpretation. A spatial resolution function provides the link between the wavelet transforms of the geological model and the migrated seismic data. Finally we consider the integration of geotechnical (cone penetration test) data with shallow shear wave seismic data. We illustrate with a real data example that specific geological features of the shallow subsurface can be identified in the wavelet transforms of both data types. We conclude that the wavelet transform can be used as a tool that aids the integration of different types of data.