Geologic lithofacies identification using the multiscale character of seismic reflections

A forward acoustic model shows that geologic lithofacies groups can be identified by the character of the wavelet transform of their seismic reflection response even for incident signals with a wavelength much larger than the dominant bed thickness. The same model shows that multiple interbed reflections can be neglected. This allows the use of an analytical relation of the linear reflection response expressed as a convolution between the incident signal and the scaled derivative of the acoustic impedance. The relation is applied to solve the inverse problem for the acoustic impedance, using orthogonal discrete wavelet transform (DWT) and Fourier transform methods; good agreement is obtained between the well log wavelet spectrum and both the forward modeled seismic data and the real seismic data. It is found that the DWT approach is superior, having a better signal-to-noise ratio and more localized deconvolution artifacts. A population of well logs containing a wide range of lithologies and bed thicknesses, which are categorized into lithofacies groups, is used to define the conditional probability of a wavelet transform response given a lithofacies group. These conditional probabilities are used to estimate the lithofacies probability given a seismic wavelet response via a Bayesian inversion.