Estimation of density, magnetization, and depth to source: A nonlinear and noniterative 3-D potential‐field method

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 814-830 ◽  
Author(s):  
Maurizio Fedi
Keyword(s):  
A Priori ◽  
Real Data ◽  
Field Method ◽  
Magnetic Data ◽  
System Of Equations ◽  
Source Depth ◽  
A Priori Information ◽  
Magnetization Direction ◽  
Priori Information ◽  
Magnetic Case

The depth to the top, or bottom, and the density of a 3-D homogeneous source can be estimated from its gravity or magnetic anomalies by using a priori information on the maximum and minimum source depths. For the magnetic case, the magnetization direction is assumed to be constant and known. The source is assumed to be within a layer of known depth to the top h and thickness t. A depth model, satisfying both the data and the a priori information is found, together with its associated density/magnetization contrast. The methodology first derives, from the measured data, a set of apparent densities [Formula: see text] (or magnetizations), which do not depend on the layer parameters h and t, but only on source thickness. A nonlinear system of equations based on [Formula: see text], with source thicknesses as unknowns, is constructed. To simplify the solution, a more practical system of equations is formed. Each equation depends on only one value of thickness. Solving for the thicknesses, taking into account the above a priori information, the source depth to the top (or to the bottom) is determined uniquely. Finally, the depth solutions allow a unit‐density gravity model to be computed, which is compared to the observed gravity to determine the density contrast. A similar procedure can be used for magnetic data. Tests on synthetic anomalies and on real data demonstrate the good performance of this method.

A new potential field shape descriptor using continuous wavelet transforms

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. G81-G92
Author(s):  
P. Cavalier ◽  
D. W. O’Hagan
Keyword(s):  
Potential Field ◽  
Wavelet Transforms ◽  
A Priori ◽  
Shape Descriptor ◽  
Continuous Wavelet ◽  
Source Depth ◽  
A Priori Information ◽  
Field Source ◽  
Continuous Wavelet Transforms ◽  
Priori Information

Potential field characterization aims at determining source depths, inclination, and type, preferably without a priori information. For ideal sources, the type is often defined from the field’s degree of homogeneity, derived from its expression in the space domain. We have developed a new shape descriptor for potential field source functions, stemming from spectral-domain parameters, which manifest clearly when using continuous wavelet transforms (CWTs). We generalize the use of the maximum wavelet coefficient points in the CWT diagram for the analysis of all types of potential fields (gravity, magnetic, and self-potential). We interpret the CWT diagram as a similarity diagram between the wavelet and the analyzed signal, which has fewer limitations than its interpretation as a weighted and upward-continued field projection. We develop new formulas for magnetic source depth prediction, as well as for effective inclination estimation, using various kinds of wavelets. We found that the potential field source functions exhibit precise behaviors in the CWT analysis that can be predicted using a single parameter [Formula: see text], which is related to their Fourier transforms. This parameter being scale and rotation-invariant can be used as a source-body shape descriptor similar to the commonly used structural index (SI). An advantage of the new descriptor is an increased level of discrimination between sources because it takes different values to describe the horizontal or the vertical cylinder structures. Our approach is illustrated on synthetic examples and real data. The method can be applied directly with the native form of the CWT without scaling factor modification, negative plane diagram extension, or downward plotting. This framework offers an alternative to existing wavelet-like projection methods or other classic deconvolution techniques relying on SI for determining the source depth, dip, and type without a priori information, with an increased level of differentiation between source structures thanks to the new shape descriptor.

scholarly journals Unconstrained, robust Kalman filtering for GNSS troposphere tomography

2013 ◽  
Vol 6 (5) ◽  
pp. 9133-9162 ◽  
Author(s):  
W. Rohm ◽  
K. Zhang ◽  
J. Bosy
Keyword(s):  
Water Vapour ◽  
Kalman Filtering ◽  
Weather Prediction ◽  
A Priori ◽  
Real Data ◽  
Reference Station ◽  
A Priori Information ◽  
Dependent Observations ◽  
Integrated Water Vapour ◽  
Priori Information

Abstract. The mesoscale variability of water vapour (WV) in the troposphere is a highly complex phenomenon and modeling and monitoring the WV distribution is a very important but challenging task. Any observation technique that can reliably provide WV distribution is essential for both monitoring and predicting weather. GNSS tomography technique is a powerful tool that builds upon the critical ground-based GNSS infrastructure – Continuous Operating Reference Station (CORS) networks and can be used to sense the amount of WV. Previous research suggests that 3-D WV field from GNSS tomography has an uncertainty of 1 hPa. However all the models used in GNSS tomography heavily rely on a priori information and constraints from non-GNSS measurements. In this study, 3-D GNSS tomography models are investigated based on an unconstrained approach with limited a priori information. A case study is designed and the results show that unconstrained solutions are feasible by using a robust Kalman filtering technique and effective removal of linearly dependent observations and parameters. Discrepancies between reference wet refractivity data derived from the Australian Numerical Weather Prediction (NWP) model (i.e. ACCESS) and the GNSS tomography model using both simulated and real data are 4.2 ppm (mm km−1) and 6.5 ppm (mm km−1), respectively, which are essentially in the same order of accuracy. Therefore the accuracy of the integrated values should not be worse than 0.06 m in terms of zenith wet delay and the integrated water vapour is a fifth of this value which is roughly 10 mm.

scholarly journals An Algorithm for Estimating Fixed Points of Dynamical Systems from Time Series

1998 ◽  
Vol 08 (11) ◽  
pp. 2203-2213 ◽  
Author(s):  
Luis A. Aguirre ◽  
Álvaro V. P. Souza
Keyword(s):  
Time Series ◽  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Prior Knowledge ◽  
A Priori ◽  
Real Data ◽  
A Priori Information ◽  
Chua's Circuit ◽  
Priori Information

This paper presents an algorithm for estimating fixed points of dynamical systems from time series. In some cases the new procedure can accurately estimate fixed points of which there is very little information in the data. Another advantage is that, although no prior knowledge is assumed, the new algorithm permits the user to employ a priori information about the system such as symmetry and the existence of a trivial fixed point. The new algorithm is tested on the Lorenz and Rössler systems and on real data taken from Chua's circuit.

scholarly journals Limited constraint, robust Kalman filtering for GNSS troposphere tomography

2014 ◽  
Vol 7 (5) ◽  
pp. 1475-1486 ◽  
Author(s):  
W. Rohm ◽  
K. Zhang ◽  
J. Bosy
Keyword(s):  
Kalman Filtering ◽  
Weather Prediction ◽  
A Priori ◽  
Real Data ◽  
Satellite System ◽  
Reference Station ◽  
A Priori Information ◽  
Dependent Observations ◽  
Priori Information ◽  
Nwp Model

Abstract. The mesoscale variability of water vapour (WV) in the troposphere is a highly complex phenomenon and modelling and monitoring the WV distribution is a very important but challenging task. Any observation technique that can reliably provide WV distribution is essential for both monitoring and predicting weather. The global navigation satellite system (GNSS) tomography technique is a powerful tool that builds upon the critical ground-based GNSS infrastructure (e.g. Continuous Operating Reference Station – CORS – networks) that can be used to sense the amount of WV. Previous research shows that the 3-D WV field from GNSS tomography has an uncertainty of 1 hPa. However, all the models used in GNSS tomography heavily rely on a priori information and constraints from non-GNSS measurements. In this study, 3-D GNSS tomography models are investigated based on a limited constrained approach – i.e. horizontal and vertical correlations between voxels were not introduced, instead various a priori information were added into the system. A case study is designed and the results show that proposed solutions are feasible by using a robust Kalman filtering technique and effective removal of linearly dependent observations and parameters. Discrepancies between reference wet refractivity data derived from the Australian Numerical Weather Prediction (NWP) model (ACCESS) and the GNSS tomography model using both simulated and real data are 4.2 ppm (mm km−1) and 6.2 ppm (mm km−1), respectively, which are essentially in the same order of accuracy.

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.

Interpretation of magnetic data using an enhanced local wavenumber (ELW) method

Geophysics ◽  
2005 ◽  
Vol 70 (2) ◽  
pp. L7-L12 ◽  
Author(s):  
Ahmed Salem ◽  
Dhananjay Ravat ◽  
Richard Smith ◽  
Keisuke Ushijima
Keyword(s):  
Linear Equation ◽  
Random Noise ◽  
A Priori ◽  
Magnetic Data ◽  
Model Parameters ◽  
A Priori Information ◽  
Location Parameters ◽  
Local Wavenumber ◽  
Priori Information ◽  
Theoretical Simulations

This paper presents an enhancement of the local-wavenumber method (named ELW for “enhanced local wavenumber”) for interpretation of profile magnetic data. This method uses the traditional and phase-rotated local wavenumbers to produce a linear equation as a function of the model parameters. The equation can be solved to determine the horizontal location and depth of a 2D magnetic body without specifying a priori information about the nature of the sources. Using the obtained source-location parameters, the nature of the source can then be inferred. The method was tested using theoretical simulations with random noise over a dike body. It was able to provide both the location and an index characterizing the nature of the source body. The practical utility of the method is demonstrated using field examples over dikelike bodies from Canada and Egypt.

3-D inversion of magnetic data

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 394-408 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Objective Function ◽  
A Priori ◽  
Magnetic Data ◽  
A Priori Information ◽  
Data Set ◽  
Earth Models ◽  
Priori Information ◽  
Model Region ◽  
D Model ◽  
Physical Realizability

We present a method for inverting surface magnetic data to recover 3-D susceptibility models. To allow the maximum flexibility for the model to represent geologically realistic structures, we discretize the 3-D model region into a set of rectangular cells, each having a constant susceptibility. The number of cells is generally far greater than the number of the data available, and thus we solve an underdetermined problem. Solutions are obtained by minimizing a global objective function composed of the model objective function and data misfit. The algorithm can incorporate a priori information into the model objective function by using one or more appropriate weighting functions. The model for inversion can be either susceptibility or its logarithm. If susceptibility is chosen, a positivity constraint is imposed to reduce the nonuniqueness and to maintain physical realizability. Our algorithm assumes that there is no remanent magnetization and that the magnetic data are produced by induced magnetization only. All minimizations are carried out with a subspace approach where only a small number of search vectors is used at each iteration. This obviates the need to solve a large system of equations directly, and hence earth models with many cells can be solved on a deskside workstation. The algorithm is tested on synthetic examples and on a field data set.

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