Absorption-Constrained Wavelet Power Spectrum Inversion for Robust Extraction From VSP Data

Extracting a reliable model of quality factor $Q$ from the spectral information of seismic signals is a significantly important step for seismic imaging and reservoir characterization. However, the conventional $Q$ estimation approach based on the frequency domain is susceptible to the high oscillative spectrum created by the unavoidable random and coherent noise in the observed signal. To address this issue, we introduce an absorption-constrained wavelet power spectrum inversion (AWPSI) method. The inversion involves absorption constraint (AC) and spectrum constraint (SC), where the AC term is a novel constraint for estimating the wavelet's amplitude spectrum or power spectrum. By treating medium absorption as a physical prior and utilizing information from all waveforms rather than individual ones, AWPSI can yield high-quality wavelet power spectra and ensure stable $Q$ estimation results. In addition, the proposed method has no limitations on the type of wavelet. Since its inversion target is wavelet power spectra, AWPSI is broadly applicable to various frequency-based $Q$ estimation approaches. We validate the effectiveness of the proposed method using both synthetic and actual vertical seismic profile (VSP) data.