... to Gaussian and spike noises, even for a Dirac wavelet. Finally, we applied our method to real seismic data. The similarity between the observed and modeled seismic data, the higher resolution of the migration image, and flatter common image gathers corresponding to the inverted models proved the relevance...

... (discontinuities) of the signal that are localized near the wavefront. After convolution of the terms of such a series with a proper temporally short (high-frequency) wavelet, one obtains a synthetic seismic signal at a given point of interest. We present an outline of the proposed technique that yields integrals...

... to the events contained in the seismic data in the offset direction. In the time direction, however, the basis functions are Dirac delta functions, whereas seismic events exhibit a wavelet shape. This causes the RT to have high resolution in p but low resolution in τ . The proposed DecRT basis...

.... For the proposed method, we use equation  13 to compute a band-limited Dirac delta function. In the first setup, as shown in Figure  3a , we set the measured data d ( t ) to a Ricker wavelet with a main frequency of 10 Hz, whereas the predicted data p ( t ) is given by a time shift...

... a new misfit function by comparing the resulting matching filter with the band-limited Dirac delta function based on the Wasserstein distance. In the example section, we first use a shifted wavelet to analyze the properties of the proposed misfit function and compare it to other misfit functions...

... accurate, the resulting matching filter is close to a Dirac delta function. Its traveltime shift, which characterizes the defocusing of the matching filter, is computed by minimization of the crosscorrelation between a penalty function such as t 2 and the matching filter. ATI is constructed by minimization...

... into the invariant tensor form with the help of the Dirac tensors. The invariant Dirac tensors, γ α , are related to the coordinate system in such a way that their individual shapes are preserved in any coordinate system. The Dirac tensors fulfill the conditions where the space-time metric is Both...

... on forcing the deconvolution filter to reduce to the Dirac delta function. Wu et al. (2014) estimate an envelope function of the seismic trace along the time axis and invert it. The envelope function includes artificial low frequencies, which helps FWI to admit long-wavelength structure in the update...

.... On the left is a brute stack and on the right is a brute stack after free-surface multiple attenuation and source wavelet removal. Figure 6 shows common offset gathers from that project. A striking feature of the Weglein-Stolt approach is that it requires no model of the subsurface properties...

...Figure 3. Iterative-deconvolution principle. Here, there are five iterations shown in (a-e). At each of those iterations, an event is detected by identifying the maximum of the crosscorrelation of the source wavelet with the trace Y. The event is adaptively subtracted from the input trace...

... to the synthetic Marmousi model. Some practical issues (e.g., the source wavelet estimate and the scaling of the migrated image required by the VFSA optimization) are discussed with an application to a 2D real seismic multichannel reflection data set collected in the Gulf of Guayaquil (Ecuador). The postprocessing...

... ( 34 ) into equation ( 32 ) with ã = a and using the Dirac delta function property (35) yields (36) where the vertical wavenumber depends on the horizontal wavenumbers conjugate to the horizontal source coordinates. Note that the source wavelet a is required to calculate P d...

... in logarithmic scale. 27 04 2006 03 09 2006 Society of Exploration Geophysicists 2007 Matching pursuit expands a signal over a series of wavelets or atoms, selected from a dictionary composed of Gabor wavelets, supplemented with a canonical basis of discrete Dirac functions...

... of root-mean squared (rms) or stacking velocity, x is the offset, and m ( τ , p ) are the DecRT coefficients corresponding to the wavelet w . Obviously, for w ( t ) = δ ( t ) (the Dirac delta function), equation  2 reduces to the conventional hyperbolic RT...

... the wavelet, which includes the source amplitude and time evolution. In space, we recover a description of the source that is distributed and includes an estimate of the moment tensor at every point in the domain. A change of variables applied to the velocity-stress form of the elastic-wave equation ensures...