A comparison of performances of linearized and global nonlinear 2-D inversions of VLF and VLF-R electromagnetic data

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 462-475 ◽  
Author(s):  
P. Kaikkonen ◽  
S. P. Sharma
Keyword(s):  
A Priori ◽  
Low Frequency ◽  
Model Parameters ◽  
Nonlinear Inversion ◽  
Stable Model ◽  
Very Fast Simulated Annealing ◽  
Iterative Inversion ◽  
Priori Information ◽  
The One ◽  
Nonlinear Joint

The performances of linearized (local) and global nonlinear joint 2-D inversions of very low frequency (VLF) and VLF resistivity electromagnetic measurements are analyzed. A stable iterative inversion scheme is used in linearized inversion while the very fast simulated annealing approach is used in global nonlinear inversion. Synthetic noise‐free and noisy data due to three different models in complexity and two field examples are considered. Synthetic examples show that linearized inversion reveals the subsurface structure better than global nonlinear inversion provided the model has only a few parameters under inversion. Both linearized and global nonlinear inversions must be performed combining all available data in order to obtain the most reliable estimates of the subsurface parameters. Complex models with a large number of parameters are better to invert using global nonlinear inversion although the CPU time needed is always much longer than the one used in linearized inversion. Contrary to global nonlinear inversion, success in linearized inversion requires the good a priori information of all the model parameters under inversion. Noise in data influences the linearized inversion results more than those provided by global inversion. Linearized inversion using as an initial model the mean model due to a few global inversion runs is also a good approach. Even in this case, if there are a large number of model parameters in inversion, linearized inversion can lead to an unstable solution. To overcome such a problem, one can fix the important and stable model parameters from the first step of linearized inversion and then vary and stabilize unstable parameters in the second step.

scholarly journals How to average logarithmic retrievals?

2012 ◽  
Vol 5 (4) ◽  
pp. 831-841 ◽  
Author(s):  
B. Funke ◽  
T. von Clarmann
Keyword(s):  
Maximum Likelihood ◽  
A Priori ◽  
Mean Value ◽  
Natural Variability ◽  
High Signal ◽  
Method Of Averaging ◽  
Signal To Noise ◽  
Mixing Ratios ◽  
Priori Information ◽  
The One

Abstract. Calculation of mean trace gas contributions from profiles obtained by retrievals of the logarithm of the abundance rather than retrievals of the abundance itself are prone to biases. By means of a system simulator, biases of linear versus logarithmic averaging were evaluated for both maximum likelihood and maximum a priori retrievals, for various signal to noise ratios and atmospheric variabilities. These biases can easily reach ten percent or more. As a rule of thumb we found for maximum likelihood retrievals that linear averaging better represents the true mean value in cases of large local natural variability and high signal to noise ratios, while for small local natural variability logarithmic averaging often is superior. In the case of maximum a posteriori retrievals, the mean is dominated by the a priori information used in the retrievals and the method of averaging is of minor concern. For larger natural variabilities, the appropriateness of the one or the other method of averaging depends on the particular case because the various biasing mechanisms partly compensate in an unpredictable manner. This complication arises mainly because of the fact that in logarithmic retrievals the weight of the prior information depends on abundance of the gas itself. No simple rule was found on which kind of averaging is superior, and instead of suggesting simple recipes we cannot do much more than to create awareness of the traps related with averaging of mixing ratios obtained from logarithmic retrievals.

Smoothing operators for waveform tomographic imaging

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1646-1654 ◽  
Author(s):  
Steve Cardimona ◽  
Jan Garmany
Keyword(s):  
Fresnel Zone ◽  
A Priori ◽  
Approximate Solutions ◽  
Velocity Model ◽  
Forward Problem ◽  
Nonlinear Inversion ◽  
Approximation Solution ◽  
Waveform Data ◽  
Sensitivity Functions ◽  
Priori Information

The analytic kernel in the space‐time domain for the Frechet derivative of acoustic waveform data with respect to changes in the slowness model is given by the Born approximation solution to the integral equation of waveform scattering. Preconditioning operators in the solution of this forward problem, which may incorporate a priori information and approximate solutions, are smoothing operators in the imaging problem, the first iteration of a nonlinear inversion for the slowness model. Some preconditioning operators are determined for solutions to the parabolic wave equation, and then used to create new sensitivity functions that retain appropriate characteristics of the true Frechet kernel in forward calculations. The new sensitivity functions define near‐source, near‐receiver and far‐field kernels, as well as kernels that exhibit an amplitude decay off the ray yielding ray‐perpendicular sensitivity that scales with the Fresnel zone size. A sample calculation from a synthetic cross‐well imaging experiment shows the usefulness of introducing physically appropriate model smoothing directly into the sensitivity function of the forward problem, helping to obtain a geologically reasonable image of the velocity model when ray coverage is insufficient.

scholarly journals How to average logarithmic retrievals

2011 ◽  
Vol 4 (6) ◽  
pp. 7159-7183 ◽  
Author(s):  
B. Funke ◽  
T. von Clarmann
Keyword(s):  
Maximum Likelihood ◽  
A Priori ◽  
Mean Value ◽  
Natural Variability ◽  
High Signal ◽  
Method Of Averaging ◽  
Signal To Noise ◽  
Mixing Ratios ◽  
Priori Information ◽  
The One

Abstract. Calculation of mean trace gas contributions from profiles obtained by retrievals of the logarithm of the abundance rather than retrievals of the abundance itself are prone to biases. By means of a system simulator, biases of linear versus logarithmic averaging were evaluated for both maximum likelihood and maximum a priori retrievals, for various signal to noise ratios and atmospheric variabilities. These biases can easily reach several ten percent. As a rule of thumb we found for maximum likelihood retrievals that linear averaging better represents the true mean value in cases of large local natural variability and high signal to noise ratios, while for small local natural variability logarithmic averaging often is superior. In the case of maximum a posteriori retrievals, the mean is dominated by the a priori information used in the retrievals and the method of averaging is of minor concern. For larger natural variabilities, the appropriateness of the one or the other method of averaging depends on the particular case because the various biasing mechanisms partly compensate in a hardly predictable manner. This complication arises mainly because of the fact that in logarithmic retrievals the weight of the prior information depends on abundance of the gas itself. No simple rule was found on which kind of averaging is superior, and instead of suggesting simple recipes we cannot do much more than to create awareness of the traps related with averaging of mixing ratios obtained from logarithmic retrievals.

scholarly journals On Sequencing a Protein with Nanopores, tRNAs, and RNAs with Matching Terminal Codons

2019 ◽  
Author(s):  
G Sampath
Keyword(s):  
De Novo ◽  
A Priori ◽  
Protein Molecule ◽  
Electrolytic Cell ◽  
A Priori Information ◽  
Unfolded Protein ◽  
In Trans ◽  
Priori Information ◽  
The One ◽  
A Current

A method for sequencing a protein from a codon sequence is proposed. An unfolded protein molecule is threaded through a nano-sized pore in an electrolytic cell carboxyl end first and held with a voltage such that only the first residue is exposed in the trans chamber of the cell. A tRNA molecule in trans with matching anticodon for the residue binds itself to the latter in the presence of suitable catalysts. It is then cleaved and transferred to an extended electrolytic cell with N pores, 40 ≤ N ≤ 61, in N individual cis chambers and a single trans chamber. Each pore holds an RNA molecule ending in a unique codon that is held exposed in the trans chamber. In the presence of suitable catalysts the anticodon in the transferred tRNA binds with the codon of a matching RNA molecule. By reversing the voltages in the extended cell every RNA molecule except the one to which the transferred tRNA is bound retracts into its cis chamber, this identifies the residue unambiguously. The detected residue in the first cell is cleaved and the process repeated. Unlike in other nanopore-based methods, it suffices to detect the occurrence of a current blockade without having to measure the pore current precisely. A simplified but more time-consuming version that uses only the first cell is also described. In either case no a priori information about the protein is needed so de novo sequencing is possible. A feasibility analysis of the proposed scheme is presented.

Global nonlinear inversion of transient EM data from conducting surroundings using a free‐space plate model

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 783-790 ◽  
Author(s):  
Shashi P. Sharma ◽  
Pertti Kaikkonen
Keyword(s):  
Free Space ◽  
Synthetic Data ◽  
Electromagnetic Response ◽  
Model Parameters ◽  
Nonlinear Inversion ◽  
Conductive Plate ◽  
Transient Electromagnetic ◽  
Conducting Body ◽  
Geological Conditions ◽  
Very Fast Simulated Annealing

A platelike conducting body in free space is used as a model to invert transient electromagnetic data using the very fast simulated annealing procedure as a global optimization tool. When the host rock conductivity is non‐zero, acceptable fits between the observed and computed responses are difficult to obtain. In general, the conducting body is assigned a lower conductance, larger dimensions (strike length and depth extent) and a smaller depth than the true values. We approximate the response of a conducting host to yield reliable estimates of model parameters as well as a good fit between the observed and computed responses. Our procedure is based on the assumption that the observed electromagnetic response is the sum of the response due to the conductive target and the response due to conducting surroundings (host and overburden). It is also assumed that the host response is laterally invariant, implying a layered earth and fixed source‐receiver geometry. The validity of the superposition assumption is tested against the full solution for a conductive plate in a finite conducting host. The efficacy of our approach is demonstrated using noise‐free and noisy synthetic data and two field examples measured in different geological conditions.

A STOPPING RULE FOR THE CONJUGATE GRADIENT REGULARIZATION METHOD APPLIED TO INVERSE PROBLEMS IN ACOUSTICS

2006 ◽  
Vol 14 (04) ◽  
pp. 397-414 ◽  
Author(s):  
THOMAS DELILLO ◽  
TOMASZ HRYCAK
Keyword(s):  
Conjugate Gradient ◽  
A Priori ◽  
A Priori Information ◽  
Parameter Choice ◽  
Regularization Algorithm ◽  
Lanczos Process ◽  
Choice Strategy ◽  
Priori Information ◽  
The One ◽  
Parameter Choice Strategy

We present a novel parameter choice strategy for the conjugate gradient regularization algorithm which does not assume a priori information about the magnitude of the measurement error. Our approach is to regularize within the Krylov subspaces associated with the normal equations. We implement conjugate gradient via the Lanczos bidiagonalization process with reorthogonalization, and then we construct regularized solutions using the SVD of a bidiagonal projection constructed by the Lanczos process. We compare our method with the one proposed by Hanke and Raus and illustrate its performance with numerical experiments, including detection of acoustic boundary vibrations.

Layered and laterally constrained 2D inversion of resistivity data

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 752-761 ◽  
Author(s):  
Esben Auken ◽  
Anders Vest Christiansen
Keyword(s):  
A Priori ◽  
Sedimentary Environment ◽  
Model Parameters ◽  
Inversion Result ◽  
2D Inversion ◽  
Resistivity Data ◽  
Geological Information ◽  
Priori Information ◽  
Smooth Transitions ◽  
Structure Inversion

In a sedimentary environment, quasi‐layered models often can represent the actual geology more accurately than smooth minimum‐structure models. We present a 2D inversion scheme with lateral constraints and sharp boundaries (LCI) for continuous resistivity data. All data and models are inverted as one system, producing layered solutions with laterally smooth transitions. The models are regularized through lateral constraints that tie interface depths or thicknesses and resistivities of adjacent layers. A priori information, used to resolve ambiguities and to add, for example, geological information, can be added at any point of the profile and migrates through the lateral constraints to parameters at adjacent sites. Similarly, information from areas with well‐resolved parameters migrates through the constraints to help resolve areas with poorly constrained parameters. The estimated model is complemented by a full sensitivity analysis of the model parameters supporting quantitative evaluation of the inversion result. A simple synthetic model proves the need for a quasi‐layered, 2D inversion when compared with a traditional 2D minimum‐structure inversion. A 2D minimum‐structure inversion produces models with spatially smooth resistivity transitions, making identification of layer boundaries difficult. A continuous vertical electrical sounding field example from Sweden with a depression in the depth to bedrock supports the conclusions drawn from the synthetic example. A till layer on top of the bedrock, hidden in the traditional inversion result, is identified using the 2D LCI scheme. Furthermore, the depth to the bedrock surface is easily identified for most of the profile with the 2D LCI model, which is not the case with the model from the traditional minimum‐structure inversion.

BAYESIAN METHODS IN THE EVALUATION OF SCATTERING DATA

2006 ◽  
Vol 15 (02) ◽  
pp. 354-361
Author(s):  
H. J. KRAPPE
Keyword(s):  
Elastic Scattering ◽  
Bayesian Methods ◽  
Optical Model ◽  
A Priori ◽  
Scattering Data ◽  
Model Parameters ◽  
A Priori Information ◽  
Model Independent ◽  
Priori Information

It is shown how a priori information can be introduced in an optimal way to extract optical-model parameters in a model-independent way from incomplete elastic scattering data.

scholarly journals Modeling induced polarization effects in helicopter time domain electromagnetic data: Synthetic case studies

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. E31-E50 ◽  
Author(s):  
Andrea Viezzoli ◽  
Vladislav Kaminski ◽  
Gianluca Fiandaca
Keyword(s):  
Time Domain ◽  
A Priori ◽  
Induced Polarization ◽  
Earth Model ◽  
Model Parameters ◽  
Model Approximation ◽  
Generic Models ◽  
Time Domain Electromagnetic ◽  
Airborne Electromagnetic ◽  
Priori Information

We have developed a synthetic multiparametric modeling and inversion exercise undertaken to study the robustness of inverting airborne time-domain electromagnetic (TDEM) data to extract Cole-Cole parameters. The following issues were addressed: nonuniqueness, ill posedness, dependency on manual processing and the effect of constraints, and a priori information. We have used a 1D layered earth model approximation and lateral constraints. Synthetic simulations were performed for several models and the corresponding Cole-Cole parameters. The possibility to recover these models by means of laterally constrained multiparametric inversion was evaluated, including recovery of chargeability distributions from shallow and deep targets based on analysis of induced polarization (IP) effects, simulated in airborne TDEM data. Different scenarios were studied, including chargeable targets associated with the conductive and resistive environments. In particular, four generic models were considered for the exercise: a sulfide model, a kimberlite model, and two generic models focusing on the depth of investigation. Our study indicated that, in cases when relaxation time ([Formula: see text]) values are in the range to which the airborne electromagnetic is most sensitive (e.g., approximately 1 ms), it is possible to recover deep chargeable targets (to depths more than 130 m) in association with high electrical conductivity and in resistive environments. Furthermore, it was found that the recovery of a deep conductor, masked by a shallower chargeable target, became possible only when full Cole-Cole modeling was used in the inversion. Lateral constraints improved the recoverability of model parameters. Finally, modeling IP effects increased the accuracy of recovered electrical resistivity models.

scholarly journals Aircraft Turbine Engine Automatic Control Based on Adaptive Dynamic Models

2020 ◽  
Vol 2020 (4) ◽  
pp. 61-70
Author(s):  
Sergiy Yepifanov
Keyword(s):  
Automatic Control ◽  
Thermodynamic Model ◽  
Dynamic Models ◽  
A Priori ◽  
Static Model ◽  
Measuring System ◽  
Model Parameters ◽  
A Priori Information ◽  
Static Models ◽  
Priori Information

AbstractOne of the most perspective development directions of the aircraft engine is the application of adaptive digital automatic control systems (ACS). The significant element of the adaptation is the correction of mathematical models of both engine and its executive, measuring devices. These models help to solve tasks of control and are a combination of static models and dynamic models, as static models describe relations between parameters at steady-state modes, and dynamic ones characterize deviations of the parameters from static values.The work considers problems of the models’ correction using parametric identification methods. It is shown that the main problem of the precise engine simulation is the correction of the static model. A robust procedure that is based on a wide application of a priori information about performances of the engine and its measuring system is proposed for this purpose. One of many variants of this procedure provides an application of the non-linear thermodynamic model of the working process and estimation of individual corrections to the engine components’ characteristics with further substitution of the thermodynamic model by approximating on-board static model. Physically grounded estimates are obtained based on a priori information setting about the estimated parameters and engine performances, using fuzzy sets.Executive devices (actuators) and the most inertial temperature sensors require correction to their dynamic models. Researches showed, in case that the data for identification are collected during regular operation of ACS, the estimates of dynamic model parameters can be strongly correlated that reasons inadmissible errors.The reason is inside the substantial limitations on transients’ intensity that contain regular algorithms of acceleration/deceleration control. Therefore, test actions on the engine are required. Their character and minimum composition are determined using the derived relations between errors in model coefficients, measurement process, and control action parameters.

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