scholarly journals Detecting a salt dome overhang with magnetotellurics: 3D inversion methodology and synthetic model studies

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. E251-E263 ◽  
Author(s):  
Anna Avdeeva ◽  
Dmitry Avdeev ◽  
Marion Jegen
Keyword(s):  
Laplace Operator ◽  
Salt Dome ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Data Set ◽  
Complementary Method ◽  
Model Studies ◽  
Spatial Gradients ◽  
The Laplace Operator ◽  
The Impact

Detecting a salt dome overhang is known to be problematic by seismic methods alone. We used magnetotellurics (MT) as a complementary method to seismics to investigate the detectability of a salt dome overhang. A comparison of MT responses for 3D synthetic salt models with and without overhang shows that MT is very sensitive to shallow salt structures and suggests that it should be possible to detect an overhang. To further investigate the resolution capability of MT for a salt dome overhang, we performed a 3D MT inversion study and investigated the impact of model parametrization and regularization. We showed that using the logarithms of the conductivities as model parameters is crucial for inverting data from resistive salt structures because, in this case, commonly used Tikhonov-type stabilizers work more equally for smoothing the resistive and conductive structures. The use of a logarithmic parametrization also accelerated the convergence and produced better inversion results. When the Laplace operator was used as a regularization functional, we still observed that the inversion algorithm allows spatial resistivity gradients. These spatial gradients are reduced if a regularization based on first derivatives in contrast to the Laplace operator is introduced. To demonstrate the favorable performance when logarithmic parametrization and gradient-based regularization are employed, we first inverted a data set simulated for a simple model of two adjacent blocks. Subsequently, we applied the code to a more realistic salt dome overhang detectability study. The results from the detectability study are encouraging and suggest that 3D MT inversion can be applied to decide whether the overhang is present in the shallow salt structure even in the case when only profile data are available. However, to resolve the overhang, a dense MT site coverage above the flanks of the salt dome is required.

scholarly journals Maximum Likelihood Estimation of the VAR(1) Model Parameters with Missing Observations

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Helena Mouriño ◽  
Maria Isabel Barão
Keyword(s):  
Stochastic Process ◽  
Missing Data ◽  
Maximum Likelihood ◽  
Moving Average ◽  
Practical Importance ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Missing Observations ◽  
Data Set ◽  
The Impact

Missing-data problems are extremely common in practice. To achieve reliable inferential results, we need to take into account this feature of the data. Suppose that the univariate data set under analysis has missing observations. This paper examines the impact of selecting an auxiliary complete data set—whose underlying stochastic process is to some extent interdependent with the former—to improve the efficiency of the estimators for the relevant parameters of the model. The Vector AutoRegressive (VAR) Model has revealed to be an extremely useful tool in capturing the dynamics of bivariate time series. We propose maximum likelihood estimators for the parameters of the VAR(1) Model based on monotone missing data pattern. Estimators’ precision is also derived. Afterwards, we compare the bivariate modelling scheme with its univariate counterpart. More precisely, the univariate data set with missing observations will be modelled by an AutoRegressive Moving Average (ARMA(2,1)) Model. We will also analyse the behaviour of the AutoRegressive Model of order one, AR(1), due to its practical importance. We focus on the mean value of the main stochastic process. By simulation studies, we conclude that the estimator based on the VAR(1) Model is preferable to those derived from the univariate context.

2.5‐D inversion of frequency‐domain electromagnetic data generated by a grounded‐wire source

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1753-1768 ◽  
Author(s):  
Yuji Mitsuhata ◽  
Toshihiro Uchida ◽  
Hiroshi Amano
Keyword(s):  
Frequency Domain ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
Magnetic Data ◽  
Statistical Criterion ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Gas Field ◽  
Data Set ◽  
Transient Electromagnetic

Interpretation of controlled‐source electromagnetic (CSEM) data is usually based on 1‐D inversions, whereas data of direct current (dc) resistivity and magnetotelluric (MT) measurements are commonly interpreted by 2‐D inversions. We have developed an algorithm to invert frequency‐Domain vertical magnetic data generated by a grounded‐wire source for a 2‐D model of the earth—a so‐called 2.5‐D inversion. To stabilize the inversion, we adopt a smoothness constraint for the model parameters and adjust the regularization parameter objectively using a statistical criterion. A test using synthetic data from a realistic model reveals the insufficiency of only one source to recover an acceptable result. In contrast, the joint use of data generated by a left‐side source and a right‐side source dramatically improves the inversion result. We applied our inversion algorithm to a field data set, which was transformed from long‐offset transient electromagnetic (LOTEM) data acquired in a Japanese oil and gas field. As demonstrated by the synthetic data set, the inversion of the joint data set automatically converged and provided a better resultant model than that of the data generated by each source. In addition, our 2.5‐D inversion accounted for the reversals in the LOTEM measurements, which is impossible using 1‐D inversions. The shallow parts (above about 1 km depth) of the final model obtained by our 2.5‐D inversion agree well with those of a 2‐D inversion of MT data.

Fast 2-D ray+Born migration/inversion in complex media

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 162-181 ◽  
Author(s):  
Philippe Thierry ◽  
Stéphane Operto ◽  
Gilles Lambaré
Keyword(s):  
Numerical Approximation ◽  
Reference Model ◽  
Real Data ◽  
Model Parameters ◽  
Complex Media ◽  
Inversion Algorithm ◽  
Numerical Approximations ◽  
Data Set ◽  
Cpu Time ◽  
Computational Evaluation

In this paper, we evaluate the capacity of a fast 2-D ray+Born migration/inversion algorithm to recover the true amplitude of the model parameters in 2-D complex media. The method is based on a quasi‐Newtonian linearized inversion of the scattered wavefield. Asymptotic Green’s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method. The model is described by velocity perturbations associated with diffractor points. Both the first traveltime and the strongest arrivals can be inverted. The algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm. Both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2-D Marmousi example. Comparison between logs extracted from the exact Marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations are recovered accurately in the regions of the model where the ray field is single valued. In the presence of caustics, neither the first traveltime nor the most energetic arrival inversion allow for a full recovery of the amplitudes although the latter improves the results. We conclude that all the arrivals associated with multipathing through transmission caustics must be taken into account if the true amplitude of the perturbations is to be found. Only 22 minutes of CPU time is required to migrate the full 2-D Marmousi data set on a Sun SPARC 20 workstation. The amplitude loss induced by the numerical approximations on the first traveltime and the most energetic migrated images are evaluated quantitatively and do not exceed 8% of the energy of the image computed without numerical approximation. Computational evaluation shows that extension to a 3-D ray+Born migration/inversion algorithm is realistic.

scholarly journals Chaos in overhead travelling cranes load motion

Mechanika ◽  
2019 ◽  
Vol 25 (3) ◽  
pp. 225-230
Author(s):  
Jerzy Margielewicz ◽  
Damian Gąska ◽  
Tadeusz Opasiak ◽  
Tomasz Haniszewski
Keyword(s):  
Cross Sections ◽  
Energy Losses ◽  
Largest Lyapunov Exponent ◽  
Model Parameters ◽  
Viscous Damper ◽  
Bifurcation Diagrams ◽  
Numerical Investigations ◽  
Model Studies ◽  
External Moment ◽  
The Impact

The paper presents the results of numerical investigations of the overhead travelling cranes load motion. The model studies assumes that the load is suspended on the inextensible rope. Conversely, its motion is triggered by an external moment. In addition, energy losses in the construction node connecting the rope to the drum are included. At the same time these losses were mapped through a linear viscous damper. The main objective was to evaluate the impact of individual mathematical model parameters on the dynamics of the transported load. The results were compared between two models: with/without crane structure vibrations included. The results were illustrated by multi-colored maps of the largest Lyapunov exponent, bifurcation diagrams, and Poincare cross-sections.

scholarly journals Joint stochastic constraint of a large data set from a salt dome

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. ID1-ID24 ◽  
Author(s):  
Alan W. Roberts ◽  
Richard W. Hobbs ◽  
Michael Goldstein ◽  
Max Moorkamp ◽  
Marion Jegen ◽  
...  
Keyword(s):  
Model Space ◽  
Salt Dome ◽  
Model Parameters ◽  
Data Sets ◽  
Data Set ◽  
Physical Relationship ◽  
Individual Parameter ◽  
Prior Model ◽  
Large Joint ◽  
Geophysical Surveys

Understanding the uncertainty associated with large joint geophysical surveys, such as 3D seismic, gravity, and magnetotelluric (MT) studies, is a challenge, conceptually and practically. By demonstrating the use of emulators, we have adopted a Monte Carlo forward screening scheme to globally test a prior model space for plausibility. This methodology means that the incorporation of all types of uncertainty is made conceptually straightforward, by designing an appropriate prior model space, upon which the results are dependent, from which to draw candidate models. We have tested the approach on a salt dome target, over which three data sets had been obtained; wide-angle seismic refraction, MT and gravity data. We have considered the data sets together using an empirically measured uncertain physical relationship connecting the three different model parameters: seismic velocity, density, and resistivity, and we have indicated the value of a joint approach, rather than considering individual parameter models. The results were probability density functions over the model parameters, together with a halite probability map. The emulators give a considerable speed advantage over running the full simulator codes, and we consider their use to have great potential in the development of geophysical statistical constraint methods.

Multivariate generalized linear mixed models for continuous bounded outcomes: Analyzing the body fat percentage data

2021 ◽  
pp. 096228022110432
Author(s):  
Ricardo R Petterle ◽  
Henrique A Laureano ◽  
Guilherme P da Silva ◽  
Wagner H Bonat
Keyword(s):  
Maximum Likelihood ◽  
Body Fat ◽  
The Body ◽  
Model Parameters ◽  
Body Fat Percentage ◽  
Fat Percentage ◽  
Data Set ◽  
Proposed Model ◽  
Computational Implementation ◽  
The Impact

We propose a multivariate regression model to handle multiple continuous bounded outcomes. We adopted the maximum likelihood approach for parameter estimation and inference. The model is specified by the product of univariate probability distributions and the correlation between the response variables is obtained through the correlation matrix of the random intercepts. For modeling continuous bounded variables on the interval [Formula: see text] we considered the beta and unit gamma distributions. The main advantage of the proposed model is that we can easily combine different marginal distributions for the response variable vector. The computational implementation is performed using Template Model Builder, which combines the Laplace approximation with automatic differentiation. Therefore, the proposed approach allows us to estimate the model parameters quickly and efficiently. We conducted a simulation study to evaluate the computational implementation and the properties of the maximum likelihood estimators under different scenarios. Moreover, we investigate the impact of distribution misspecification in the proposed model. Our model was motivated by a data set with multiple continuous bounded outcomes, which refer to the body fat percentage measured at five regions of the body. Simulation studies and data analysis showed that the proposed model provides a general and rich framework to deal with multiple continuous bounded outcomes.

scholarly journals Model-Based Geostatistics from a Bayesian Perspective: Investigating Area-to-Point Kriging with Small Data Sets

2019 ◽  
Vol 52 (3) ◽  
pp. 397-423
Author(s):  
Luc Steinbuch ◽  
Thomas G. Orton ◽  
Dick J. Brus
Keyword(s):  
Prior Distribution ◽  
Crop Yields ◽  
Simulated Data ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Small Data ◽  
Data Sets ◽  
Data Set ◽  
Minimal Impact ◽  
The Impact

AbstractArea-to-point kriging (ATPK) is a geostatistical method for creating high-resolution raster maps using data of the variable of interest with a much lower resolution. The data set of areal means is often considerably smaller ($$<\,50 $$<50 observations) than data sets conventionally dealt with in geostatistical analyses. In contemporary ATPK methods, uncertainty in the variogram parameters is not accounted for in the prediction; this issue can be overcome by applying ATPK in a Bayesian framework. Commonly in Bayesian statistics, posterior distributions of model parameters and posterior predictive distributions are approximated by Markov chain Monte Carlo sampling from the posterior, which can be computationally expensive. Therefore, a partly analytical solution is implemented in this paper, in order to (i) explore the impact of the prior distribution on predictions and prediction variances, (ii) investigate whether certain aspects of uncertainty can be disregarded, simplifying the necessary computations, and (iii) test the impact of various model misspecifications. Several approaches using simulated data, aggregated real-world point data, and a case study on aggregated crop yields in Burkina Faso are compared. The prior distribution is found to have minimal impact on the disaggregated predictions. In most cases with known short-range behaviour, an approach that disregards uncertainty in the variogram distance parameter gives a reasonable assessment of prediction uncertainty. However, some severe effects of model misspecification in terms of overly conservative or optimistic prediction uncertainties are found, highlighting the importance of model choice or integration into ATPK.

scholarly journals An Extension of the Kumaraswamy Distribution

2017 ◽  
Vol 6 (3) ◽  
pp. 61
Author(s):  
Jalmar M. F. Carrasco ◽  
Gauss M Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Integral Transform ◽  
Continuous Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Kumaraswamy Distribution ◽  
Special Cases ◽  
The Impact ◽  
Parameter Constraints

We propose and study a new five-parameter continuous distribution in the unit interval through a specific probability integral transform. The new distribution, under some parameter constraints, is an identified parametric model that includes as special cases six important models such as the Kumaraswamy and beta distributions. We obtain ordinary and incomplete moments, quantile and generating functions, mean deviations, R\'enyi entropy and moments of order statistics. The estimation of the model parameters is performed by maximum likelihood, and hypothesis tests are discussed. Additionally, through a simulation study we investigate the behavior of the maximum likelihood estimator, also we investigate the impact of ignoring identifiability problems. The usefulness of the proposed distribution is illustrated by means of a real data set.

scholarly journals Image-domain wavefield tomography for VTI media

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. C119-C128 ◽  
Author(s):  
Vladimir Li ◽  
Antoine Guitton ◽  
Ilya Tsvankin ◽  
Tariq Alkhalifah
Keyword(s):  
P Wave ◽  
Ocean Bottom ◽  
Inversion Algorithm ◽  
Borehole Data ◽  
Data Set ◽  
Acoustic Image ◽  
Image Domain ◽  
Image Guided ◽  
Time Migration ◽  
The Impact

Processing algorithms for transversely isotropic (TI) media are widely used in depth imaging and typically bring substantial improvements in reflector focusing and positioning. Here, we develop acoustic image-domain tomography (IDT) for reconstructing VTI (TI with a vertical symmetry axis) models from P-wave reflection data. The modeling operator yields an integral wave-equation solution, which is based on a separable dispersion relation and contains only P-waves. The zero-dip NMO velocity ([Formula: see text]) and anellipticity parameter [Formula: see text] are updated by focusing energy in space-lag images obtained by least-squares reverse-time migration (LSRTM). Application of LSRTM helps mitigate aperture- and illumination-induced artifacts in space-lag gathers and improve the robustness of [Formula: see text]-estimation. The impact of the trade-off between [Formula: see text] and [Formula: see text] is reduced by a three-stage inversion algorithm that gradually relaxes the constraints on the spatial variation of [Formula: see text]. Assuming that the depth profile of the Thomsen parameter [Formula: see text] is known at two or more borehole locations, we employ image-guided interpolation to constrain the depth scale of the parameter fields and of the migrated image. Image-guided smoothing is also applied to the IDT gradients to facilitate convergence towards geologically plausible models. The algorithm is tested on synthetic reflection and borehole data from the structurally complicated elastic VTI Marmousi-II model. Although the initial velocity field is purely isotropic and substantially distorted, all three relevant parameters ([Formula: see text], [Formula: see text], and [Formula: see text]) are estimated with sufficient accuracy. The algorithm is also applied to a line from a 3D ocean-bottom-node data set acquired in the Gulf of Mexico.

Age at Exposure to Parental Suicide and the Subsequent Risk of Suicide in Young People

Crisis ◽  
2018 ◽  
Vol 39 (1) ◽  
pp. 27-36 ◽  
Author(s):  
Kuan-Ying Lee ◽  
Chung-Yi Li ◽  
Kun-Chia Chang ◽  
Tsung-Hsueh Lu ◽  
Ying-Yeh Chen
Keyword(s):  
Young People ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Birth Registry ◽  
Data Set ◽  
Parental Suicide ◽  
The Impact ◽  
Age At Exposure

Abstract. Background: We investigated the age at exposure to parental suicide and the risk of subsequent suicide completion in young people. The impact of parental and offspring sex was also examined. Method: Using a cohort study design, we linked Taiwan's Birth Registry (1978–1997) with Taiwan's Death Registry (1985–2009) and identified 40,249 children who had experienced maternal suicide (n = 14,431), paternal suicide (n = 26,887), or the suicide of both parents (n = 281). Each exposed child was matched to 10 children of the same sex and birth year whose parents were still alive. This yielded a total of 398,081 children for our non-exposed cohort. A Cox proportional hazards model was used to compare the suicide risk of the exposed and non-exposed groups. Results: Compared with the non-exposed group, offspring who were exposed to parental suicide were 3.91 times (95% confidence interval [CI] = 3.10–4.92 more likely to die by suicide after adjusting for baseline characteristics. The risk of suicide seemed to be lower in older male offspring (HR = 3.94, 95% CI = 2.57–6.06), but higher in older female offspring (HR = 5.30, 95% CI = 3.05–9.22). Stratified analyses based on parental sex revealed similar patterns as the combined analysis. Limitations: As only register-­based data were used, we were not able to explore the impact of variables not contained in the data set, such as the role of mental illness. Conclusion: Our findings suggest a prominent elevation in the risk of suicide among offspring who lost their parents to suicide. The risk elevation differed according to the sex of the afflicted offspring as well as to their age at exposure.

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