A forward acoustic model shows that geologic lithofacies groups can be identified by the character of the wavelet transform of their seismic response even for incident signals with wavelength much larger than the dominant bed thickness. The same model shows that multiple interbed reflections can be neglected. This allows the use of a simple 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 (FT) methods; good agreement is obtained between the well log wavelet spectrum and both the forward modeled seismic data and the real seismic data.

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