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.

“Unexpected” shear‐wave behavior

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1879-1883 ◽  
Author(s):  
Steve Horne ◽  
Colin MacBeth ◽  
Enru Liu
Keyword(s):  
Shear Wave ◽  
Symmetry Axis ◽  
A Priori ◽  
Transversely Isotropic ◽  
Seismic Profile ◽  
Test Facility ◽  
A Priori Information ◽  
Fracture Systems ◽  
Geological Information ◽  
Priori Information

In a previous study, we inverted shear‐wave birefringence observations from an azimuthal vertical seismic profile (VSP) experiment conducted at the Conoco Borehole Test Facility, Oklahoma (Horne and MacBeth, 1994; Horne, 1995). Our results indicate that the observations can be interpreted in terms of two distinctly different transversely isotropic (TI) models (Figure 1). The first model predicts the symmetry axis to be at N165°E and dipping 10° to the northwest. This orientation coincides with geological information relating to the fracture system that strikes between N50°E and N75°E (Queen and Rizer, 1990). Thus, this first model is consistent with a priori information, so that a possible source of the anisotropy can be identified. However, the second model derived from the inversion results suggests the symmetry axis to be at N200°E and dipping 30° to the southwest. If we interpret this result in terms of an equivalent medium resulting from aligned cracks or fractures, then this inferred crack‐fracture strike would lie in a direction conflicting with the a priori measurements. The bimodal nature of this solution can be readily understood if we examine the shear‐wave behavior for the different models shown in Figure 2. In this plot, the symmetry axis is chosen to be the [Formula: see text]. If we consider the near‐vertical propagation directions that are typically measured in VSP experiments, it can be seen that the qS1 polarizations lie either perpendicular (model 1) or parallel (model 2) to the symmetry axis. Since these polarizations are usually interpreted in terms of aligned crack‐fracture systems, the inferred strike would lie in the [Formula: see text] plane for model 1 and the [Formula: see text] plane for model 2. This interpretation is completely incorrect for model 2, since this inferred alignment is actually orthogonal to the alignment implied by the symmetry of the TI system. This situation represents a worrying aspect to the interpretation of shear‐wave surveys used to characterize crack‐fracture systems. The question that we address is whether anisotropic materials that possess properties similar to those of model 2 can be constructed from equivalent media resulting from cracks or fractures. We also consider other sources of anisotropy that may lead to this behavior.

Should blood transport kinetics be modeled in metabolic processes?

1984 ◽  
Vol 247 (5) ◽  
pp. R895-R900
Author(s):  
G. Belforte ◽  
B. Bona ◽  
G. Molino
Keyword(s):  
A Priori ◽  
Model Parameters ◽  
Physiological System ◽  
A Priori Information ◽  
Design Task ◽  
Single Compartment ◽  
Priori Information ◽  
Blood Transport ◽  
Insight Into ◽  
Drug Kinetics

We analyze the interaction between blood transport phenomena and uptake processes when drug kinetics are studied with compartmental models. Relevant advantages in the physiological interpretation of the model parameters are obtained when blood transport is explicitly included in the model. This is done by aggregating into a single compartment all the blood spaces where no exchange with extravascular spaces takes place and separating into different blood compartments those spaces where some uptake and/or return occurs. The proposed strategy extensively uses all available a priori information about the physiological system, instead of considering only the information available in the measurements. This modeling approach has three main advantages: it provides greater insight into the identified quantities; it allows the introduction of quantitative a priori information; and it facilitates the experiment design task.

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.

A constrained global inversion method using an overparameterized scheme: Application to poststack seismic data

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 613-626 ◽  
Author(s):  
Xin‐Quan Ma
Keyword(s):  
Simulated Annealing ◽  
Seismic Data ◽  
A Priori ◽  
Constant Thickness ◽  
Inversion Method ◽  
Model Parameters ◽  
A Priori Information ◽  
Initial Model ◽  
Seismic Waveform ◽  
Priori Information

A global optimization algorithm using simulated annealing has advantages over local optimization approaches in that it can escape from being trapped in local minima and it does not require a good initial model and function derivatives to find a global minimum. It is therefore more attractive and suitable for seismic waveform inversion. I adopt an improved version of a simulated annealing algorithm to invert simultaneously for acoustic impedance and layer interfaces from poststack seismic data. The earth’s subsurface is overparameterized by a series of microlayers with constant thickness in two‐way traveltime. The algorithm is constrained using the low‐frequency impedance trend and has been made computationally more efficient using this a priori information as an initial model. A search bound of each parameter, derived directly from the a priori information, reduces the nonuniqueness problem. Application of this technique to synthetic and field data examples helps one recover the true model parameters and reveals good continuity of estimated impedance across a seismic section. This approach has the capability of revealing the high‐resolution detail needed for reservoir characterization when a reliable migrated image is available with good well ties.

Improvements to elastic full-waveform inversion using cross-gradient constraints

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. R105-R115 ◽  
Author(s):  
Edgar Manukyan ◽  
Hansruedi Maurer ◽  
André Nuber
Keyword(s):  
Field Data ◽  
A Priori ◽  
Waveform Inversion ◽  
Structural Similarity ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
A Priori Information ◽  
Individual Parameter ◽  
Full Waveform ◽  
Priori Information

Seismic full-waveform inversion (FWI) is potentially a powerful method for obtaining high-resolution subsurface images, but the results are often distorted by nonlinear effects and parameter trade-offs. Such distortions can be particularly severe in the case of multiparameter FWI, such as elastic FWI, in which inversion is performed simultaneously for P- and S-wave velocities and density. The problem can be alleviated by adding constraints in the form of plausible a priori information. A usually well-justified constraint includes the structural similarity of different model parameters; i.e., an anomalous body likely exhibits variations in all elastic properties, although their magnitudes may be different. To consider such types of a priori information, we have developed a structurally constrained elastic FWI, which is based on minimization of the cross products of gradients of different model parameters. Our synthetic 2D experiments show that structurally constrained FWI can significantly improve model reconstruction. It is also demonstrated that our approach still leads to improved results, even when the structural similarity between the individual parameter types is not exactly met. Inversions of field data show that in comparison to conventional FWI, structurally constrained FWI is able to match the field data equally well while requiring less structural complexity of the subsurface.

scholarly journals Interpretation of Magnetic Anomalies over 2D Fault and Sheet-Type Mineralized Structures Using Very Fast Simulated Annealing Global Optimization: An Understanding of Uncertainty and Geological Implications

Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 6) ◽  
Author(s):  
Arkoprovo Biswas ◽  
Khushwant Rao
Keyword(s):  
A Priori ◽  
Theoretical Models ◽  
Magnetic Anomalies ◽  
Type Structure ◽  
Equivalent Model ◽  
Magnetic Data ◽  
Model Parameters ◽  
A Priori Information ◽  
Wide Range ◽  
Priori Information

Abstract Identification of intraterrane dislocation zones and associated mineralized bodies is of immense importance in exploration geophysics. Understanding such structures from geophysical anomalies is challenging and cumbersome. In the present study, we present a fast and competent algorithm for interpreting magnetic anomalies from such dislocation and mineralized zones. Such dislocation and mineralized zones are well explained from 2D fault and sheet-type structures. The different parameters from 2D fault and sheet-type structures such as the intensity of magnetization (k), depth to the top (z1), depth to the bottom (z2), origin location (x0), and dip angle (θ) of the fault and sheet from magnetic anomalies are interpreted. The interpretation suggests that there is uncertainty in defining the model parameters z1 and z2 for the 2D inclined fault; k, z1, and z2 for the 2D vertical fault and finite sheet-type structure; and k and z for the infinite sheet-type structure. Here, it shows a wide range of solutions depicting an equivalent model with smaller misfits. However, the final interpreted mean model is close to the actual model with the least uncertainty. Histograms and crossplots for 2D fault and sheet-type structures also reveal the same. The present algorithm is demonstrated with four theoretical models, including the effect of noises. Furthermore, the investigation of magnetic data was also applied from three field examples from intraterrane dislocation zones (Australia), deep-seated dislocation zones (India) as a 2D fault plane, and mineralized zones (Canada) as sheet-type structures. The final estimated model parameters are in good agreement with the earlier methods applied for these field examples with a priori information wherever available in the literature. However, the present method can simultaneously interpret all model parameters without a priori information.

scholarly journals Exponential Modelling for Mutual-Cohering of Subband Radar Data

2005 ◽  
Vol 3 ◽  
pp. 199-204
Author(s):  
U. Siart ◽  
S. Tejero ◽  
J. Detlefsen
Keyword(s):  
A Priori ◽  
Full Range ◽  
Super Resolution ◽  
Radar Data ◽  
Exponential Model ◽  
Model Parameters ◽  
Mutual Coherence ◽  
Frequency Bands ◽  
Priori Information ◽  
Signal Modelling

Abstract. Increasing resolution and accuracy is an important issue in almost any type of radar sensor application. However, both resolution and accuracy are strongly related to the available signal bandwidth and energy that can be used. Nowadays, often several sensors operating in different frequency bands become available on a sensor platform. It is an attractive goal to use the potential of advanced signal modelling and optimization procedures by making proper use of information stemming from different frequency bands at the RF signal level. An important prerequisite for optimal use of signal energy is coherence between all contributing sensors. Coherent multi-sensor platforms are greatly expensive and are thus not available in general. This paper presents an approach for accurately estimating object radar responses using subband measurements at different RF frequencies. An exponential model approach allows to compensate for the lack of mutual coherence between independently operating sensors. Mutual coherence is recovered from the a-priori information that both sensors have common scattering centers in view. Minimizing the total squared deviation between measured data and a full-range exponential signal model leads to more accurate pole angles and pole magnitudes compared to single-band optimization. The model parameters (range and magnitude of point scatterers) after this full-range optimization process are also more accurate than the parameters obtained from a commonly used super-resolution procedure (root-MUSIC) applied to the non-coherent subband data.

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