Gabor deconvolution of seismic data for source waveform and Q correction

Summary We present a novel approach to nonstationary seismic deconvolution using the Gabor transform. This nonstationary transform represents a signal as a superposition of sinusoids that are localized by time-shifted windows. The resulting time-frequency decomposition is a suite of local Fourier transforms that facilitates nonstationary spectral analysis or filtering. In a result that generalizes the seismic convolutional model, we show that the Gabor transform of a nonstationary seismic signal is the product of source signature, Q filter, and reflectivity effects. We use this spectral factorization theorem as a basis for a new deconvolution algorithm in the Gabor domain. We estimate the Gabor spectrum of the underlying reflectivity directly from the Gabor spectrum of an attenuated seismic signal. Tests on synthetic and real data show that our method works well and combines the effects of sourcesignature inversion and a data-driven inverse Q filter. In comparison with a stationary Wiener deconvolution, our Gabor deconvolution is similar within the Wiener design gate and superior elsewhere.