spectral decomposition or time-frequency representation (tfr) is a powerful tool for analyzing time varying nature of seismic data. mapping of a one dimensional seismic time trace to a two dimensional function of time and frequency reveals some characteristics of seismic signals that are not available in only time or frequency representations. this approach has been widely used in seismic explo...

If the Navier-Stokes equations are averaged with a local, spacial convolution type filter, φ = gδ∗φ, the resulting system is not closed due to the filtered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which satisfies u = D(u) + O(δ), where δ is the filter width and α ≥ 2. Using a deconvolution operator as an approximate filter inverse, yields the closu...

where d(t) is the recorded signal and n(t) is the additive sensor noise signal. Some methods (Champagnat et al., 1996; Lavielle, 1993) used in Bayesian formulation the prior hypothesis that the reflectivity signal r(t) is a Bernouilli-Gaussian process. The first step is a detection of the reflectors and it follows by a magnitude estimation. The high noise level on recordings limits the performa...

The extended Euler deconvolution algorithm is shown to be a generalization and unification of 2-D Euler deconvolution and Werner deconvolution. After recasting the extended Euler algorithm in a way that suggests a natural generalization to three dimensions, we show that the 3-D extension can be realized using generalized Hilbert transforms. The resulting algorithm is both a generalization of ex...

In this study, simultaneous deconvolution and reconstruction of peak profiles in the first ((1)D) and second dimension ((2)D) of comprehensive two-dimensional (2D) gas chromatography (GC×GC) is achieved on the basis of the property of this new type of instrumental data. First, selective information, where only one component contributes to the peak elution window of a given modulation event, is ...

In this paper, we present a novel method for inverse filtering a two dimensional (2-D) signal using phase-based processing techniques. A 2-D sequence can be represented by a sufficient number of samples of the phase of its Fourier transform and its region of support. This is exploited to perform deconvolution. We examine the effects of additive noise and incomplete knowledge of the point spread...

Being interested by a field data application of Marchenko imaging, I identify a Gulf of Mexico 2-D line that I deem appropriate for the job. One of the main requirements of Marchenko imaging is to have deconvolved data. For this dataset and task, I use a non-minimum phase deconvolution approach in the lag-log domain: It can estimate wavelets of any length, shape and amplitude, and yields deconv...