Surface‐consistent deconvolution in the log/Fourier domain

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 823-840 ◽  
Author(s):  
Guillaume Cambois ◽  
Paul L. Stoffa
Keyword(s):  
Seismic Data ◽  
Linear Problem ◽  
Real Data ◽  
Signal Amplitude ◽  
Fourier Domain ◽  
Subsurface Structure ◽  
Static Correction ◽  
Correction Problem ◽  
Band Limited ◽  
Hessian Method

In the surface‐consistent hypothesis, a seismic trace is the convolution of a source operator, a receiver operator, a reflectivity operator (representing the subsurface structure) and an offset‐related operator. In the log/Fourier domain, convolutions become sums and the log of signal amplitude at a given frequency is the sum of source, receiver, structural, and offset‐related terms. Recovering the amplitude of the reflectivity for a given frequency is then a linear problem (very similar to a surface‐consistent static correction problem). However, this linear system is underconstrained. Thus, among the infinite number of possible solutions, a particular one must be selected. Studies with real data support the choice of a spatially band‐limited solution. The surface‐consistent operators can then be calculated very efficiently using an inverse Hessian method. Applications to real seismic data show improvement compared with previous techniques. Surface‐consistent deconvolution is robust and fast in the log/Fourier domain. It allows the use of long operators, improves statics estimation, and removes the amplitude variations due to source or receiver coupling.

Surface‐consistent phase decomposition in the log/Fourier domain

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1099-1111 ◽  
Author(s):  
Guillaume Cambois ◽  
Paul Stoffa
Keyword(s):  
Seismic Data ◽  
Linear Problem ◽  
Phase Unwrapping ◽  
Fourier Domain ◽  
Minimum Phase ◽  
Phase Decomposition ◽  
Deconvolution Technique ◽  
Amplitude Spectra ◽  
Definition Of ◽  
Phase Spectra

In the log/Fourier domain, decomposing the amplitude spectra of seismic data into surface‐consistent terms is a linear problem that can be solved, very efficiently, one frequency at a time. However, the nonunique definition of the complex logarithm makes it much more difficult to decompose the phase spectra. The instability of phase unwrapping has previously prevented any attempt to decompose phase spectra in the log/Fourier domain. We develop a fast and robust partial unwrapping algorithm, which makes it possible to efficiently decompose the phase spectra of normal moveout‐corrected (NMO‐) data into surface‐consistent terms, in the log/Fourier domain. The dual recovery of amplitude and phase spectra yields a surface‐consistent deconvolution technique where only the average reflectivity is assumed to be white, and only the average wavelet is required to be minimum‐phase. Each individual deconvolution operator may be mixed‐phase, depending on its estimated phase spectra. For example, surface‐consistent time shifts and phase rotations, as well as any other surface‐consistent phase effects, are included in the phase spectra of the surface‐consistent deconvolution operators. Consequently, static shifts are estimated and removed without ever picking horizons or crosscorrelations.

Nonhyperbolic normal moveout stretch correction with deep learning automation

Geophysics ◽  
2021 ◽  
pp. 1-60
Author(s):  
Mohammad Mahdi Abedi ◽  
David Pardo
Keyword(s):  
Deep Learning ◽  
Seismic Data ◽  
Random Noise ◽  
Real Data ◽  
Correction Method ◽  
Heterogeneous Environments ◽  
Data Set ◽  
Nmo Correction ◽  
Band Limited ◽  
Nmo Stretch

Normal moveout (NMO) correction is a fundamental step in seismic data processing. It consists of mapping seismic data from recorded traveltimes to corresponding zero-offset times. This process produces wavelet stretching as an undesired byproduct. We address the NMO stretching problem with two methods: 1) an exact stretch-free NMO correction that prevents the stretching of primary reflections, and 2) an approximate post-NMO stretch correction. Our stretch-free NMO produces parallel moveout trajectories for primary reflections. Our post-NMO stretch correction calculates the moveout of stretched wavelets as a function of offset. Both methods are based on the generalized moveout approximation and are suitable for application in complex anisotropic or heterogeneous environments. We use new moveout equations and modify the original parameter functions to be constant over the primary reflections, and then interpolate the seismogram amplitudes at the calculated traveltimes. For fast and automatic modification of the parameter functions, we use deep learning. We design a deep neural network (DNN) using convolutional layers and residual blocks. To train the DNN, we generate a set of 40,000 synthetic NMO corrected common midpoint gathers and the corresponding desired outputs of the DNN. The data set is generated using different velocity profiles, wavelets, and offset vectors, and includes multiples, ground roll, and band-limited random noise. The simplicity of the DNN task –a 1D identification of primary reflections– improves the generalization in practice. We use the trained DNN and show successful applications of our stretch-correction method on synthetic and different real data sets.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

scholarly journals Deblending by direct inversion

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. A9-A12 ◽  
Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Jan Thorbecke
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Iterative Procedure ◽  
Inversion Process ◽  
Direct Inversion ◽  
Source Data ◽  
Band Limited ◽  
Blended Data ◽  
Simultaneous Source ◽  
Additional Constraints

Deblending of simultaneous-source data is usually considered to be an underdetermined inverse problem, which can be solved by an iterative procedure, assuming additional constraints like sparsity and coherency. By exploiting the fact that seismic data are spatially band-limited, deblending of densely sampled sources can be carried out as a direct inversion process without imposing these constraints. We applied the method with numerically modeled data and it suppressed the crosstalk well, when the blended data consisted of responses to adjacent, densely sampled sources.

scholarly journals Seismic Data Interpretation and Identification of Hydrocarbon-Bearing Zones of Rajian Area, Pakistan

Minerals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 891
Author(s):  
Naveed Ahmad ◽  
Sikandar Khan ◽  
Eisha Fatima Noor ◽  
Zhihui Zou ◽  
Abdullatif Al-Shuhail
Keyword(s):  
Seismic Data ◽  
Foreland Basin ◽  
Data Interpretation ◽  
Indus Basin ◽  
Subsurface Structure ◽  
Vertical Wells ◽  
Salt Range ◽  
Seismic Sections ◽  
The Given ◽  
Triangular Zone

The present study interprets the subsurface structure of the Rajian area using seismic sections and the identification of hydrocarbon-bearing zones using petrophysical analysis. The Rajian area lies within the Upper Indus Basin in the southeast (SE) of the Salt Range Potwar Foreland Basin. The marked horizons are identified using formation tops from two vertical wells. Seismic interpretation of the given 2D seismic data reveals that the study area has undergone severe distortion illustrated by thrusts and back thrusts, forming a triangular zone within the subsurface. The final trend of those structures is northwest–southeast (NW–SE), indicating that the area is part of the compressional regime. The zones interpreted by the study of hydrocarbon potential include Sakessar limestone and Khewra sandstone. Due to the unavailability of a petrophysics log within the desired investigation depths, lithology cross-plots were used for the identification of two potential hydrocarbon-bearing zones in one well at depths of 3740–3835 m (zone 1) and 4015–4100 m (zone 2). The results show that zone 2 is almost devoid of hydrocarbons, while zone 1 has an average hydrocarbon saturation of about 11%.

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