scholarly journals Applying compactness constraints to differential traveltime tomography

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. R67-R75 ◽  
Author(s):  
Jonathan B. Ajo-Franklin ◽  
Burke J. Minsley ◽  
Thomas M. Daley
Keyword(s):  
Stable Solution ◽  
Model Space ◽  
Time Lapse ◽  
Process Time ◽  
Spatial Process ◽  
Weighted Norm ◽  
Inversion Algorithm ◽  
Time Data ◽  
Data Set ◽  
Traveltime Tomography

Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizing functionals may not always be appropriate, particularly in cases where the anomaly being imaged is generated by a nonsmooth spatial process. Time-lapse imaging of flow-induced velocity anomalies is one such case; flow features are often characterized by spatial compactness or connectivity. By performing inversions on differenced arrival time data, the properties of the time-lapse feature can be directly constrained. We develop a differential traveltime tomography algorithm whichselects for compact solutions, i.e., models with a minimum area of support, through application of model-space iteratively reweighted least squares. Our technique is an adaptation of minimum support regularization methods previously explored within the potential theory community. We compare our inversion algorithm to the results obtained by traditional Tikhonov regularization for two simple synthetic models: one including several sharp localized anomalies and a second with smoother features. We use a more complicated synthetic test case based on multiphase flow results to illustrate the efficacy of compactness constraints for contaminant infiltration imaging. We apply the algorithm to a [Formula: see text]-sequestration-monitoring data set acquired at the Frio pilot site. We observe that in cases where the assumption of a localized anomaly is correct, the addition of compactness constraints improves image quality by reducing tomographic artifacts and spatial smearing of target features.

High-resolution wave-equation AVA imaging: Algorithm and tests with a data set from the Western Canadian Sedimentary Basin

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. S91-S99 ◽  
Author(s):  
Juefu Wang ◽  
Henning Kuehl ◽  
Mauricio D. Sacchi
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Least Squares ◽  
Oil And Gas ◽  
Sedimentary Basin ◽  
Model Space ◽  
Sampled Data ◽  
Inversion Algorithm ◽  
Data Set ◽  
Data Space

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.

scholarly journals Ground-penetrating-radar reflection attenuation tomography with an adaptive mesh

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. WA251-WA261 ◽  
Author(s):  
Emily A. Hinz ◽  
John H. Bradford
Keyword(s):  
Ground Penetrating Radar ◽  
Fluid Transport ◽  
Computation Time ◽  
Model Space ◽  
Adaptive Mesh ◽  
Adaptive Meshing ◽  
Inversion Algorithm ◽  
Data Set ◽  
Data Limitations ◽  
Ground Penetrating

Ground-penetrating radar (GPR) attenuation-difference analysis can be a useful tool for studying fluid transport in the subsurface. Surface-based reflection attenuation-difference tomography poses a number of challenges that are not faced by crosshole attenuation surveys. We create and analyze a synthetic attenuation-difference GPR data set to determine methods for processing amplitude changes and inverting for conductivity differences from reflection data sets. Instead of using a traditional grid-based inversion, we use a data-driven adaptive-meshing algorithm to alter the model space and to create a more even distribution of resolution. Adaptive meshing provides a method for improving the resolution of the model space while honoring the data limitations and improving the quality of the attenuation difference inversion. Comparing inversions on a conventional rectangular grid with the adaptive mesh, we find that the adaptively meshed model reduces the inversion computation time by an average of 75% with an improvement in the root mean square error of up to 15%. While the sign of the conductivity change is correctly reproduced by the inversion algorithm, the magnitude varies by as much as much as 50% from the true values. Our heterogeneous conductivity model indicates that the attenuation difference inversion algorithm effectively locates conductivity changes, and that surface-based reflection surveys can produce models as accurate as traditional crosshole surveys.

Stochastic inversion of pressure and saturation changes from time-lapse AVO data

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. C81-C92 ◽  
Author(s):  
Helene Hafslund Veire ◽  
Hilde Grude Borgos ◽  
Martin Landrø
Keyword(s):  
Stochastic Model ◽  
Seismic Data ◽  
Synthetic Data ◽  
Time Lapse ◽  
Bayesian Framework ◽  
Reservoir Modeling ◽  
Data Set ◽  
The North ◽  
Fluid Saturation ◽  
Likelihood Model

Effects of pressure and fluid saturation can have the same degree of impact on seismic amplitudes and differential traveltimes in the reservoir interval; thus, they are often inseparable by analysis of a single stacked seismic data set. In such cases, time-lapse AVO analysis offers an opportunity to discriminate between the two effects. We quantify the uncertainty in estimations to utilize information about pressure- and saturation-related changes in reservoir modeling and simulation. One way of analyzing uncertainties is to formulate the problem in a Bayesian framework. Here, the solution of the problem will be represented by a probability density function (PDF), providing estimations of uncertainties as well as direct estimations of the properties. A stochastic model for estimation of pressure and saturation changes from time-lapse seismic AVO data is investigated within a Bayesian framework. Well-known rock physical relationships are used to set up a prior stochastic model. PP reflection coefficient differences are used to establish a likelihood model for linking reservoir variables and time-lapse seismic data. The methodology incorporates correlation between different variables of the model as well as spatial dependencies for each of the variables. In addition, information about possible bottlenecks causing large uncertainties in the estimations can be identified through sensitivity analysis of the system. The method has been tested on 1D synthetic data and on field time-lapse seismic AVO data from the Gullfaks Field in the North Sea.

A hybrid regularization scheme for the inversion of magnetotelluric data from natural and controlled sources to layer and distortion parameters

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. E301-E315 ◽  
Author(s):  
Thomas Kalscheuer ◽  
Juliane Hübert ◽  
Alexey Kuvshinov ◽  
Tobias Lochbühler ◽  
Laust B. Pedersen
Keyword(s):  
Transfer Functions ◽  
Homogeneous Distribution ◽  
Stable Configuration ◽  
Inversion Algorithm ◽  
Magnetotelluric Data ◽  
Data Set ◽  
Near Surface ◽  
Minimum Solution ◽  
Magnetic Transfer ◽  
Distortion Parameters

Magnetotelluric (MT), radiomagnetotelluric (RMT), and, in particular, controlled-source audiomagnetotelluric (CSAMT) data are often heavily distorted by near-surface inhomogeneities. We developed a novel scheme to invert MT, RMT, and CSAMT data in the form of scalar or tensorial impedances and vertical magnetic transfer functions simultaneously for layer resistivities and electric and magnetic galvanic distortion parameters. The inversion scheme uses smoothness constraints to regularize layer resistivities and either Marquardt-Levenberg damping or the minimum-solution length criterion to regularize distortion parameters. A depth of investigation range is estimated by comparing layered model sections derived from first- and second-order smoothness constraints. Synthetic examples demonstrate that earth models are reconstructed properly for distorted and undistorted tensorial CSAMT data. In the inversion of scalar CSAMT data, such as the determinant impedance or individual tensor elements, the reduced number of transfer functions inevitably leads to increased ambiguity for distortion parameters. As a consequence of this ambiguity for scalar data, distortion parameters often grow over the iterations to unrealistic absolute values when regularized with the Marquardt-Levenberg scheme. Essentially, compensating relationships between terms containing electric and/or magnetic distortion are used in this growth. In a regularization with the minimum solution length criterion, the distortion parameters converge into a stable configuration after several iterations and attain reasonable values. The inversion algorithm was applied to a CSAMT field data set collected along a profile over a tunnel construction site at Hallandsåsen, Sweden. To avoid erroneous inverse models from strong anthropogenic effects on the data, two scalar transfer functions (one scalar impedance and one scalar vertical magnetic transfer function) were selected for inversion. Compared with a regularization of distortion parameters with the Marquardt-Levenberg method, the minimum-solution length criterion yielded smaller absolute values of distortion parameters and a horizontally more homogeneous distribution of electrical conductivity.

Replicating the Recovery following the 2014 South Napa Earthquake using Stochastic Process Models

2018 ◽  
Vol 34 (3) ◽  
pp. 1247-1266 ◽  
Author(s):  
Hua Kang ◽  
Henry V. Burton ◽  
Haoxiang Miao
Keyword(s):  
Stochastic Process ◽  
Repair Time ◽  
Process Models ◽  
Time Data ◽  
Data Set ◽  
Damage Data ◽  
Exogenous Factors ◽  
Recovery Models ◽  
Statistical Relationships ◽  
Recovery Trajectory

Post-earthquake recovery models can be used as decision support tools for pre-event planning. However, due to a lack of available data, there have been very few opportunities to validate and/or calibrate these models. This paper describes the use of building damage, permitting, and repair data from the 2014 South Napa Earthquake to evaluate a stochastic process post-earthquake recovery model. Damage data were obtained for 1,470 buildings, and permitting and repair time data were obtained for a subset (456) of those buildings. A “blind” prediction is shown to adequately capture the shape of the recovery trajectory despite overpredicting the overall pace of the recovery. Using the mean time to permit and repair time from the acquired data set significantly improves the accuracy of the recovery prediction. A generalized model is formulated by establishing statistical relationships between key time parameters and endogenous and exogenous factors that have been shown to influence the pace of recovery.

scholarly journals A fast methodology for large-scale focusing inversion of gravity and magnetic data using the structured model matrix and the 2-D fast Fourier transform

2020 ◽  
Vol 223 (2) ◽  
pp. 1378-1397
Author(s):  
Rosemary A Renaut ◽  
Jarom D Hogue ◽  
Saeed Vatankhah ◽  
Shuang Liu
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Linear Systems ◽  
Large Scale ◽  
Surface Measurement ◽  
Magnetic Data ◽  
Uniform Grid ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Data Set

SUMMARY We discuss the focusing inversion of potential field data for the recovery of sparse subsurface structures from surface measurement data on a uniform grid. For the uniform grid, the model sensitivity matrices have a block Toeplitz Toeplitz block structure for each block of columns related to a fixed depth layer of the subsurface. Then, all forward operations with the sensitivity matrix, or its transpose, are performed using the 2-D fast Fourier transform. Simulations are provided to show that the implementation of the focusing inversion algorithm using the fast Fourier transform is efficient, and that the algorithm can be realized on standard desktop computers with sufficient memory for storage of volumes up to size n ≈ 106. The linear systems of equations arising in the focusing inversion algorithm are solved using either Golub–Kahan bidiagonalization or randomized singular value decomposition algorithms. These two algorithms are contrasted for their efficiency when used to solve large-scale problems with respect to the sizes of the projected subspaces adopted for the solutions of the linear systems. The results confirm earlier studies that the randomized algorithms are to be preferred for the inversion of gravity data, and for data sets of size m it is sufficient to use projected spaces of size approximately m/8. For the inversion of magnetic data sets, we show that it is more efficient to use the Golub–Kahan bidiagonalization, and that it is again sufficient to use projected spaces of size approximately m/8. Simulations support the presented conclusions and are verified for the inversion of a magnetic data set obtained over the Wuskwatim Lake region in Manitoba, Canada.

scholarly journals Time-Lapse Seismic Monitoring of Onshore Reservoirs in Niger Delta, Field ‘K’ as a Case Study

2017 ◽  
Vol 1 (1) ◽  
pp. 23-27 ◽  
Author(s):  
A. Ogbamikhumi ◽  
T. Tralagba ◽  
E. E. Osagiede
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Niger Delta ◽  
Rock Physics ◽  
Time Lapse ◽  
Seismic Survey ◽  
Impedance Change ◽  
Data Set ◽  
Reservoir Fluid ◽  
4D Seismic

Field ‘K’ is a mature field in the coastal swamp onshore Niger delta, which has been producing since 1960. As a huge producing field with some potential for further sustainable production, field monitoring is therefore important in the identification of areas of unproduced hydrocarbon. This can be achieved by comparing production data with the corresponding changes in acoustic impedance observed in the maps generated from base survey (initial 3D seismic) and monitor seismic survey (4D seismic) across the field. This will enable the 4D seismic data set to be used for mapping reservoir details such as advancing water front and un-swept zones. The availability of good quality onshore time-lapse seismic data for Field ‘K’ acquired in 1987 and 2002 provided the opportunity to evaluate the effect of changes in reservoir fluid saturations on time-lapse amplitudes. Rock physics modelling and fluid substitution studies on well logs were carried out, and acoustic impedance change in the reservoir was estimated to be in the range of 0.25% to about 8%. Changes in reservoir fluid saturations were confirmed with time-lapse amplitudes within the crest area of the reservoir structure where reservoir porosity is 0.25%. In this paper, we demonstrated the use of repeat Seismic to delineate swept zones and areas hit with water override in a producing onshore reservoir.

Inversion and uncertainty estimation of gravity data using simulated annealing: An application over Lake Vostok, East Antarctica

Geophysics ◽  
2005 ◽  
Vol 70 (1) ◽  
pp. J1-J12 ◽  
Author(s):  
Lopamudra Roy ◽  
Mrinal K. Sen ◽  
Donald D. Blankenship ◽  
Paul L. Stoffa ◽  
Thomas G. Richter
Keyword(s):  
Simulated Annealing ◽  
Gravity Data ◽  
A Priori ◽  
Model Space ◽  
Uncertainty Estimation ◽  
East Antarctica ◽  
Airborne Gravity ◽  
Model Parameters ◽  
Data Set ◽  
Lake Vostok

Interpretation of gravity data warrants uncertainty estimation because of its inherent nonuniqueness. Although the uncertainties in model parameters cannot be completely reduced, they can aid in the meaningful interpretation of results. Here we have employed a simulated annealing (SA)–based technique in the inversion of gravity data to derive multilayered earth models consisting of two and three dimensional bodies. In our approach, we assume that the density contrast is known, and we solve for the coordinates or shapes of the causative bodies, resulting in a nonlinear inverse problem. We attempt to sample the model space extensively so as to estimate several equally likely models. We then use all the models sampled by SA to construct an approximate, marginal posterior probability density function (PPD) in model space and several orders of moments. The correlation matrix clearly shows the interdependence of different model parameters and the corresponding trade-offs. Such correlation plots are used to study the effect of a priori information in reducing the uncertainty in the solutions. We also investigate the use of derivative information to obtain better depth resolution and to reduce underlying uncertainties. We applied the technique on two synthetic data sets and an airborne-gravity data set collected over Lake Vostok, East Antarctica, for which a priori constraints were derived from available seismic and radar profiles. The inversion results produced depths of the lake in the survey area along with the thickness of sediments. The resulting uncertainties are interpreted in terms of the experimental geometry and data error.

Common-focus point-based target-oriented imaging approach for continuous seismic reservoir monitoring

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. M41-M48 ◽  
Author(s):  
Hongwei Liu ◽  
Mustafa Naser Al-Ali
Keyword(s):  
Seismic Data ◽  
Rock Physics ◽  
Time Lapse ◽  
Velocity Estimation ◽  
Estimation Methods ◽  
Data Sets ◽  
Data Set ◽  
Velocity Models ◽  
Reservoir Monitoring ◽  
Focus Point

The ideal approach for continuous reservoir monitoring allows generation of fast and accurate images to cope with the massive data sets acquired for such a task. Conventionally, rigorous depth-oriented velocity-estimation methods are performed to produce sufficiently accurate velocity models. Unlike the traditional way, the target-oriented imaging technology based on the common-focus point (CFP) theory can be an alternative for continuous reservoir monitoring. The solution is based on a robust data-driven iterative operator updating strategy without deriving a detailed velocity model. The same focusing operator is applied on successive 3D seismic data sets for the first time to generate efficient and accurate 4D target-oriented seismic stacked images from time-lapse field seismic data sets acquired in a [Formula: see text] injection project in Saudi Arabia. Using the focusing operator, target-oriented prestack angle domain common-image gathers (ADCIGs) could be derived to perform amplitude-versus-angle analysis. To preserve the amplitude information in the ADCIGs, an amplitude-balancing factor is applied by embedding a synthetic data set using the real acquisition geometry to remove the geometry imprint artifact. Applying the CFP-based target-oriented imaging to time-lapse data sets revealed changes at the reservoir level in the poststack and prestack time-lapse signals, which is consistent with the [Formula: see text] injection history and rock physics.

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