Using the wavelet transform for seismic wave impedance inversion

Model-based inversion technology has become one of the necessary technologies in the seismic exploration industry. It is frequently used to estimate many subsurface attributes, i.e., velocity, impedance, attenuation, etc. It is important to note that the accuracy of model-based inversion relies on the precision of the initial model, which suffers from insufficiency of low-frequency information in seismic data. Enhancing the high-frequency content and accuracy of low frequencies in the initial model can improve solution accuracy. Conventional initial models fail to adequately represent the high-frequency details of lateral geologic variations and to capture low-frequency components accurately. We develop a wavelet transform solution for this problem. Initially, we demonstrate that seismic records approximate the wavelet transform of logarithmic impedance. Consequently, we use the wavelet inverse transform to reconstruct the mid- and high-frequency information of seismic impedance, highlighting the detailed spatial variations. Furthermore, we apply kriging interpolation, based on subspace interpolation principles, using well impedance and seismic record waveforms to derive the low-frequency impedance from the scale inverse transform. Wavelet transform theory ensures a perfect match between the low- and high-frequency components in the inversion result. The frequency components of the inversion result are balanced, with no deficiencies or redundancies within the seismic data’s high cutoff frequency band. Thus, our method of initial model building is a type of inversion method. In addition, this method is simple and efficient because fast convolution processing can be performed. Model experiments and practical data inversions confirm the method’s feasibility and its ability to enhance resolution.