Estimating primaries by sparse inversion and application to near-offset data reconstruction

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. A23-A28 ◽  
Author(s):  
G. J. van Groenestijn ◽  
D. J. Verschuur
Keyword(s):  
Missing Data ◽  
Estimation Method ◽  
Synthetic Data ◽  
Estimation Procedure ◽  
Data Reconstruction ◽  
Multiple Model ◽  
Inversion Process ◽  
Sparse Inversion ◽  
Multiple Elimination

Accurate removal of surface-related multiples remains a challenge in many cases. To overcome typical inaccuracies in current multiple-removal techniques, we have developed a new primary-estimation method: estimation of primaries by sparse inversion (EPSI). EPSI is based on the same primary-multiple model as surface-related multiple elimination (SRME) and also requires no subsurface model. Unlike SRME, EPSI estimates the primaries as unknowns in a multidimensional inversion process rather than in a subtraction process. Furthermore, it does not depend on interpolated missing near-offset data because it can reconstruct missing data simultaneously. Sparseness plays a key role in the new primary-estimation procedure. The method was tested on 2D synthetic data.

Estimation of primaries by sparse inversion with scattering-based multiple predictions for data with large gaps

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. V183-V197 ◽  
Author(s):  
Tim T.Y. Lin ◽  
Felix J. Herrmann
Keyword(s):  
Free Surface ◽  
Computational Cost ◽  
Estimation Method ◽  
Synthetic Data ◽  
Real Data ◽  
Memory Efficiency ◽  
Forward Prediction ◽  
Primary Model ◽  
Estimated Green’S Function ◽  
Sparse Inversion

We have solved the estimation of primaries by sparse inversion problem for a seismic record with large near-offset gaps and other contiguous holes in the acquisition grid without relying on explicit reconstruction of the missing data. Eliminating the unknown data as an explicit inversion variable is desirable because it sidesteps possible issues arising from overfitting the primary model to the estimated data. Instead, we have simulated their multiple contributions by augmenting the forward prediction model for the total wavefield with a scattering series that mimics the action of the free surface reflector within the area of the unobserved trace locations. Each term in this scattering series involves convolution of the total predicted wavefield once more with the current estimated Green’s function for a medium without the free surface at these unobserved locations. It is important to note that our method cannot by itself mitigate regular undersampling issues that result in significant aliases when computing the multiple contributions, such as source-receiver sampling differences or crossline spacing issues in 3D acquisition. We have investigated algorithms that handle the nonlinearity in the modeling operator due to the scattering terms, and we also determined that just a few of the terms can be enough to satisfactorily mitigate the effects of near-offset data gaps during the inversion process. Numerical experiments on synthetic data found that the final derived method can significantly outperform explicit data reconstruction for large near-offset gaps, with a similar computational cost and better memory efficiency. We have also found on real data that our scheme outperforms the unmodified primary estimation method that uses an existing Radon-based interpolation of the near-offset gap.

scholarly journals Estimation of primaries and near-offset reconstruction by sparse inversion: Marine data applications

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. R119-R128 ◽  
Author(s):  
G. J. A. van Groenestijn ◽  
D. J. Verschuur
Keyword(s):  
Shallow Water ◽  
Input Data ◽  
Field Data ◽  
Waveform Inversion ◽  
Multiple Model ◽  
Data Set ◽  
Water Field ◽  
Sparse Inversion ◽  
Band Limited ◽  
Multiple Elimination

Most wave-equation-based multiple removal algorithms are based on prediction and subtraction of multiples. Especially for shallow water, the prediction strongly relies on a correct interpolation of the missing near offsets. The subtraction of predicted multiples from the data can easily lead to the distortion of primaries if primaries and multiples overlap. Recently, a new approach for surface-related multiple removal was proposed: the estimation of primaries by sparse inversion (EPSI), which is based on a full waveform inversion approach. EPSI is based on the same primary-multiple model as surface-related multiple elimination (SRME) and does not require a subsurface model. In contrast to SRME, EPSI estimates the primaries as unknowns in a multidimensional inversion process rather than a subtraction process.The multidimensional primary impulse responses are parameterized by band-limited spikes, which are estimated such that they, along with their corresponding multiples, match the input data. An interesting aspect of the EPSI method is that it produces a residual, which is the part of the input data not explained by primaries and multiples. This residual can be analyzed and may provide useful information on the primary estimation process. Furthermore, it has been demonstrated that EPSI is also capable of reconstructing the missing near offsets from the multiples. The proposed method is applied to a field data set with moderate water depth, where it is demonstrated that the results are comparable with SRME. This data set is used to illustrate the residual. For a shallow-water field data set, it is shown that EPSI gives a better result than the standard SRME result caused by EPSI’s capability to reconstruct the missing near offsets.

scholarly journals 3D surface-related multiple prediction: A sparse inversion approach

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. V31-V43 ◽  
Author(s):  
E. J. van Dedem ◽  
D. J. Verschuur
Keyword(s):  
Input Data ◽  
Synthetic Data ◽  
Data Set ◽  
3D Surface ◽  
Parametric Inversion ◽  
Sparse Inversion ◽  
Marine Data ◽  
Multiple Prediction ◽  
Multiple Elimination

The theory of iterative surface-related multiple elimination holds for 2D as well as 3D wavefields. The 3D prediction of surface multiples, however, requires a dense and extended distribution of sources and receivers at the surface. Since current 3D marine acquisition geometries are very sparsely sampled in the crossline direction, the direct Fresnel summation of the multiple contributions, calculated for those surface positions at which a source and a receiver are present, cannot be applied without introducing severe aliasing effects. In this newly proposed method, the regular Fresnel summation is applied to the contributions in the densely sampled inline direction, but the crossline Fresnel summation is replaced with a sparse parametric inversion. With this procedure, 3D multiples can be predicted using the available input data. The proposed method is demonstrated on a 3D synthetic data set as well as on a 3D marine data set from offshore Norway.

Estimation of primaries by sparse inversion from passive seismic data

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. SA61-SA69 ◽  
Author(s):  
G. J. van Groenestijn ◽  
D. J. Verschuur
Keyword(s):  
Seismic Data ◽  
Large Scale ◽  
Synthetic Data ◽  
Point Sources ◽  
Impulse Responses ◽  
Inversion Process ◽  
Amplitude Estimation ◽  
Passive Seismic ◽  
Sparse Inversion ◽  
Data Surface

For passive seismic data, surface multiples are used to obtain an estimate of the subsurface responses, usually by a crosscorrelation process. This crosscorrelation process relies on the assumption that the surface has been uniformly illuminated by subsurface sources in terms of incident angles and strengths. If this is not the case, the crosscorrelation process cannot give a true amplitude estimation of the subsurface response. Furthermore, cross terms in the crosscorrelation result are not related to actual subsurface inhomogeneities. We have developed a method that can obtain true amplitude subsurface responses without a uniform surface-illumination assumption. Our methodology goes beyond the crosscorrelation process and estimates primaries only from the surface-related multiples in the available signal. We use the recently introduced estimation of primaries by sparse inversion (EPSI) methodology, in which the primary impulse responses are considered to be the unknowns in a large-scale inversion process. With some modifications, the EPSI method can be used for passive seismic data. The output of this process is primary impulse responses with point sources and receivers at the surface, which can be used directly in traditional imaging schemes. The methodology was tested on 2D synthetic data.

scholarly journals Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 674
Author(s):  
Kushani De De Silva ◽  
Carlo Cafaro ◽  
Adom Giffin
Keyword(s):  
State Of The Art ◽  
Estimation Method ◽  
Synthetic Data ◽  
Noisy Data ◽  
Bayesian Framework ◽  
Physical Systems ◽  
Gradient Profile ◽  
Ill Posed ◽  
Profile Estimation ◽  
Different Levels

Attaining reliable gradient profiles is of utmost relevance for many physical systems. In many situations, the estimation of the gradient is inaccurate due to noise. It is common practice to first estimate the underlying system and then compute the gradient profile by taking the subsequent analytic derivative of the estimated system. The underlying system is often estimated by fitting or smoothing the data using other techniques. Taking the subsequent analytic derivative of an estimated function can be ill-posed. This becomes worse as the noise in the system increases. As a result, the uncertainty generated in the gradient estimate increases. In this paper, a theoretical framework for a method to estimate the gradient profile of discrete noisy data is presented. The method was developed within a Bayesian framework. Comprehensive numerical experiments were conducted on synthetic data at different levels of noise. The accuracy of the proposed method was quantified. Our findings suggest that the proposed gradient profile estimation method outperforms the state-of-the-art methods.

Estimation of the Shape Evolution and the Growth History of an Embedded Crack by Fatigue Loading

2011 ◽  
Author(s):  
Koji Gotoh ◽  
Keisuke Harada ◽  
Yosuke Anai
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Fatigue Cracks ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Fatigue Loading ◽  
Shape Evolution ◽  
Crack Growth Behaviour ◽  
Embedded Crack

Fatigue life estimation for planar cracks, e.g. part-through surface cracks or embedded cracks is very important because most of fatigue cracks found in welded built-up structures show planar crack morphologies. Fatigue crack growth behaviour of an embedded crack in welded joints is investigated in this study. The estimation procedure of crack shape evolution for an embedded crack is introduced and validation of the estimation procedure of fatigue crack growth based on the numerical simulation of fatigue crack growth with EDS concept for an embedded crack is performed. The validity of the proposed shape evolution estimation method and the fatigue crack growth simulation based on the fracture mechanics approach with EDS concept are confirmed.

scholarly journals Gaussian process regression for monitoring and fault detection of wastewater treatment processes

2017 ◽  
Vol 75 (12) ◽  
pp. 2952-2963 ◽  
Author(s):  
Oscar Samuelsson ◽  
Anders Björk ◽  
Jesús Zambrano ◽  
Bengt Carlsson
Keyword(s):  
Wastewater Treatment ◽  
Missing Data ◽  
Fault Detection ◽  
Gaussian Process ◽  
Flow Rate ◽  
Sequential Monte Carlo ◽  
Estimation Method ◽  
Gaussian Process Regression ◽  
Local Optima ◽  
Efficient Operation

Monitoring and fault detection methods are increasingly important to achieve a robust and resource efficient operation of wastewater treatment plants (WWTPs). The purpose of this paper was to evaluate a promising machine learning method, Gaussian process regression (GPR), for WWTP monitoring applications. We evaluated GPR at two WWTP monitoring problems: estimate missing data in a flow rate signal (simulated data), and detect a drift in an ammonium sensor (real data). We showed that GPR with the standard estimation method, maximum likelihood estimation (GPR-MLE), suffered from local optima during estimation of kernel parameters, and did not give satisfactory results in a simulated case study. However, GPR with a state-of-the-art estimation method based on sequential Monte Carlo estimation (GPR-SMC) gave good predictions and did not suffer from local optima. Comparisons with simple standard methods revealed that GPR-SMC performed better than linear interpolation in estimating missing data in a noisy flow rate signal. We conclude that GPR-SMC is both a general and powerful method for monitoring full-scale WWTPs. However, this paper also shows that it does not always pay off to use more sophisticated methods. New methods should be critically compared against simpler methods, which might be good enough for some scenarios.

Imputed Estimation For Varying Coefficient Models with Missing Covariates

2013 ◽  
Vol 787 ◽  
pp. 1089-1092
Author(s):  
Pei Xin Zhao
Keyword(s):  
Missing Data ◽  
Estimation Procedure ◽  
Estimating Equation ◽  
Equation Method ◽  
Missing Covariates ◽  
Varying Coefficient Models ◽  
Finite Sample ◽  
Varying Coefficient

By using the imputation-based estimating equation method, an imputed estimation procedure for the coefficient functions is proposed. The proposed procedure can attenuate the effect of the missing data, and performs well for the finite sample.

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