Resolution enhancement of seismic data using spectral modeling based on dominant Ricker components and separable nonlinear least squares

Seismic resolution enhancement has a key role in seismic interpretation, especially in reservoir characterization and geologic interpretation. Exploration seismology has a limitation in temporal resolution and thin-layer detection, so any effort to improve the resolution of available data is valuable. Seismic deconvolution is one of the main steps in seismic processing and is intensively used for enhancing the vertical resolution. In this procedure, the seismic wavelet is compressed in order to decrease wavelet interferences and improve temporal resolution. In the common method of seismic deconvolution — i.e., Wiener deconvolution — the seismic wavelet is estimated by using the early part of autocorrelation of traces. Assuming the reflection series is a random function, the smoothed version of the amplitude spectrum of traces can be considered as the amplitude spectrum of the seismic wavelet. The wavelet spectrum can be properly reconstructed by the linear combination of a number of Ricker wavelets with different peak frequencies. The authors aim to introduce a novel method for resolution improvement based on fitting and finding main Ricker components of the source-wavelet spectrum. This attempt is classified under the group of the separable nonlinear least squares (SNLS), the objective function of which is a combination of linear and nonlinear functions. A variable projection method is applied to recognize the optimum peak frequency of Ricker wavelets involved in the wavelet spectrum. Our synthetic tests indicate that the SNLS algorithm is able to achieve a very close approximation of dominant Ricker components of the source spectrum. Considering the minimum phase assumption of the wavelet, the phase spectrum is also computed by Hilbert transform of the estimated amplitude spectrum. Once the amplitude and phase information are available, the deconvolution operator can be designed. Our synthetic and real tests indicate that, in comparison with Wiener deconvolution, spectral modeling based on dominant Ricker components (SMDRC) has improved the deconvolution outputs.