... stationary. We construct a set of specific windows, called molecular-Gabor (MG) windows, by solving an optimization problem, such that the seismic trace in each of the MG windows is stationary. A time-frequency ( t - f ) transform, called MG transform, can be obtained from a MG frame constructed using the MG...

...-shift method of wavefield extrapolation is fast and stable; however, it can be cumbersome to adapt to lateral velocity variations. We address the extension of phase-shift extrapolation to lateral velocity variations by using a spatial Gabor transform instead of the normal Fourier transform. The Gabor...

... the discrete Gabor transform, or complex-valued time-frequency decomposition, of any signal. Although the Fourier transform renders stationary convolution into exact, multiplicative factors, the Gabor transform, or windowed Fourier transform, induces only an approximate factorization of the nonstationary...

... was resolved here by introducing an alternative approach in resolution enhancement. Our method uses Gabor deconvolution (GD) combined with wavelet scaling. First, the seismic trace is transformed in the time-frequency domain using the Gabor transform. Subsequently, the Gabor magnitude spectrum of the seismic...

.... However, their precision rates often are low, thus requiring substantial manual labor to select desired events of interest. This study investigates two time-frequency methods which combine signal enhancement with automated event detection and selection, namely, (1) the sparse Gabor transform and (2...

... the short-time Fourier transform and Gabor transform. The S-transform and continuous wavelet transform are analyzed as the variable-length transforms. First we conduct a synthetic transmission experiment, and compare the frequency-dependent scattering attenuation to the theoretically predicted values. From...

... inversion results will be easily yielded. To deal with this problem, we decompose nonstationary seismic inversion into three subproblems. First, Q e curves are estimated at well locations using a novel scheme. Because the Gabor transform can induce approximate factorization of NSCM, the time-varying wavelet...

... correction. The corresponding procedure considers frequency content of each time sample along each trace in the time-frequency domain using the Gabor transform. As such, the dominant frequency of the seismic wavelets is increased in a nonstationary manner. Performance of our method is evaluated by applying...

... of noise. We find that having an approximate estimate for intrinsic attenuation, even when these effects are strong, leads to improvements in resolution and a more accurate recovery of the P-wave velocity. Then, we implement and develop our method on a 2D field data set using Gabor transforms to obtain...

...Figure 2. Synthetic seismic traces ( Q = 88 ) and their Gabor transform spectra (a) before and (b) after inverse Q -filtering. ...