High resolution least‐squares wave equation AVA imaging: Feasibility study with a data set from the Western Canadian Sedimentary Basin

Author(s):  
Juefu Wang ◽  
Henning Kuehl ◽  
Mauricio D. Sacchi
Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. S91-S99 ◽  
Author(s):  
Juefu Wang ◽  
Henning Kuehl ◽  
Mauricio D. Sacchi

This paper presents a 3D least-squares wave-equation migration method that yields regularized common-image gathers (CIGs) for amplitude-versus-angle (AVA) analysis. In least-squares migration, we pose seismic imaging as a linear inverse problem; this provides at least two advantages. First, we are able to incorporate model-space weighting operators that improve the amplitude fidelity of CIGs. Second, the influence of improperly sampled data (footprint noise) can be diminished by incorporating data-space weighting operators. To investigate the viability of this class of methods for oil and gas exploration, we test the algorithm with a real-data example from the Western Canadian Sedimentary Basin. To make our problem computationally feasible, we utilize the 3D common-azimuth approximation in the migration algorithm. The inversion algorithm uses the method of conjugate gradients with the addition of a ray-parameter-dependent smoothing constraint that minimizes sampling and aperture artifacts. We show that more robust AVA attributes can be obtained by properly selecting the model and data-space regularization operators. The algorithm is implemented in conjunction with a preconditioning strategy to accelerate convergence. Posing the migration problem as an inverse problem leads to enhanced event continuity in CIGs and, hence, more reliable AVA estimates. The vertical resolution of the inverted image also improves as a consequence of increased coherence in CIGs and, in addition, by implicitly introducing migration deconvolution in the inversion.


Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 262-273 ◽  
Author(s):  
Henning Kühl ◽  
Mauricio D. Sacchi

We present an acoustic migration/inversion algorithm that uses extended double‐square‐root wave‐equation migration and modeling operators to minimize a constrained least‐squares data misfit function (least‐squares migration). We employ an imaging principle that allows for the extraction of ray‐parameter‐domain common image gathers (CIGs) from the propagated seismic wavefield. The CIGs exhibit amplitude variations as a function of half‐offset ray parameter (AVP) closely related to the amplitude variation with reflection angle (AVA). Our least‐squares wave‐equation migration/inversion is constrained by a smoothing regularization along the ray parameter. This approach is based on the idea that rapid amplitude changes or discontinuities along the ray parameter axis result from noise, incomplete wavefield sampling, and numerical operator artifacts. These discontinuities should therefore be penalized in the inversion. The performance of the proposed algorithm is examined with two synthetic examples. In the first case, we generated acoustic finite difference data for a horizontally layered model. The AVP functions based on the migrated/inverted ray parameter CIGs were converted to AVA plots. The AVA plots were then compared to the true acoustic AVA of the reflectors. The constrained least‐squares inversion compares favorably with the conventional migration, especially when incompleteness compromises the data. In the second example, we use the Marmousi data set to test the algorithm in complex media. The result shows that least‐squares migration can mitigate kinematic artifacts in the ray‐parameter domain CIGs effectively.


Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA95-WCA107 ◽  
Author(s):  
Yaxun Tang

Prestack depth migration produces blurred images resulting from limited acquisition apertures, complexities in the velocity model, and band-limited characteristics of seismic waves. This distortion can be partially corrected using the model-space least-squares migration/inversion approach, where a target-oriented wave-equation Hessian operator is computed explicitly and then inverse filtering is applied iteratively to deblur or invert for the reflectivity. However, one difficulty is the cost of computing the explicit Hessian operator, which requires storing a large number of Green’s functions, making it challenging for large-scale applications. A new method to compute the Hessian operator for the wave-equation-based least-squares migration/inversion problem modifies the original explicit Hessian formula, enabling efficient computation of this operator. An advantage is that the method eliminates disk storage of Green’s functions. The modifications, however, also introduce undesired crosstalk artifacts. Two different phase-encoding schemes, plane-wave-phase encoding and random-phase encoding, suppress the crosstalk. When the randomly phase-encoded Hessian operator is applied to the Sigsbee2A synthetic data set, an improved subsalt image with more balanced amplitudes is obtained.


Author(s):  
D. E. Becker

An efficient, robust, and widely-applicable technique is presented for computational synthesis of high-resolution, wide-area images of a specimen from a series of overlapping partial views. This technique can also be used to combine the results of various forms of image analysis, such as segmentation, automated cell counting, deblurring, and neuron tracing, to generate representations that are equivalent to processing the large wide-area image, rather than the individual partial views. This can be a first step towards quantitation of the higher-level tissue architecture. The computational approach overcomes mechanical limitations, such as hysterisis and backlash, of microscope stages. It also automates a procedure that is currently done manually. One application is the high-resolution visualization and/or quantitation of large batches of specimens that are much wider than the field of view of the microscope.The automated montage synthesis begins by computing a concise set of landmark points for each partial view. The type of landmarks used can vary greatly depending on the images of interest. In many cases, image analysis performed on each data set can provide useful landmarks. Even when no such “natural” landmarks are available, image processing can often provide useful landmarks.


Author(s):  
Parisa Torkaman

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.


2020 ◽  
Author(s):  
Lian Duan ◽  
Alejandro Valenciano ◽  
Nizar Chemingui

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson

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.


Geophysics ◽  
2004 ◽  
Vol 69 (2) ◽  
pp. 378-385 ◽  
Author(s):  
Aristotelis Dasios ◽  
Clive McCann ◽  
Timothy Astin

We minimize the effect of noise and increase both the reliability and the resolution of attenuation estimates obtained from multireceiver full‐waveform sonics. Multiple measurements of effective attenuation were generated from full‐waveform sonic data recorded by an eight‐receiver sonic tool in a gas‐bearing sandstone reservoir using two independent techniques: the logarithmic spectral ratio (LSR) and the instantaneous frequency (IF) method. After rejecting unstable estimates [receiver separation <2 ft (0.61 m)], least‐squares inversion was used to combine the multiple estimates into high‐resolution attenuation logs. The procedure was applied to raw attenuation data obtained with both the LSR and IF methods, and the resulting logs showed that the attenuation estimates obtained for the maximum receiver separation of 3.5 ft (1.07 m) provide a smoothed approximation of the high‐resolution measurements. The approximation is better for the IF method, with the normalized crosscorrelation factor between the low‐ and high‐resolution logs being 0.90 for the IF method and 0.88 for the LSR method.


2018 ◽  
Vol 91 (1092) ◽  
pp. 20180319 ◽  
Author(s):  
Amy R McDowell ◽  
Susan C Shelmerdine ◽  
David W Carmichael ◽  
Owen J Arthurs

2002 ◽  
Vol 5 (3) ◽  
pp. 212-212 ◽  
Author(s):  
U. Tiede ◽  
A. Pommert ◽  
B. Pflesser ◽  
E. Richter ◽  
M. Riemer ◽  
...  

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