Inversion of phase times for hypocenters and shallow crustal velocities, Mojave Desert, California

abstract Phase times for an ensemble of 20 aftershocks of the June 1, 1975, Galway Lake earthquake were inverted to determine hypocenters and local velocity structure simultaneously. A maximum likelihood formulation of linear, least-squares inversion was used so that the data were weighted according to their estimated variances. A trade-off parameter controlled the relative importance of the RMS error and the amount by which the model changed at each iteration. Individual aftershocks must be selected so that a wide variety of travel paths are represented. Initial trials disclosed that careful constraints are necessary for allowed changes in station delays. Fixed velocity boundaries, based on a priori information, were used for each of several starting models, and only layer velocities were allowed to vary. Each of the trials indicated that shallow crustal velocities in the vincinity of Galway Lake are somewhat lower than those of the usual velocity models. The velocities are not strongly constrained by this data set, but the results are consistent with a subsequent, detailed refraction survey by other workers. Mapping the travel-time surface in time-depth-distance space helps clarify the limitations inherent in a given problem.

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Particle swarm optimization of 2D magnetotelluric data

Geophysics ◽

10.1190/geo2018-0166.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. E125-E141 ◽

Cited By ~ 7

Author(s):

Francesca Pace ◽

Alessandro Santilano ◽

Alberto Godio

Keyword(s):

Inverse Problem ◽

Particle Swarm Optimization ◽

A Priori ◽

Particle Swarm ◽

Stability And Convergence ◽

Real Field ◽

A Priori Information ◽

Data Set ◽

Swarm Optimization ◽

Priori Information

We implement the particle swarm optimization (PSO) algorithm for the two-dimensional (2D) magnetotelluric (MT) inverse problem. We first validate PSO on two synthetic models of different complexity and then apply it to an MT benchmark for real-field data, the COPROD2 data set (Canada). We pay particular attention to the selection of the PSO input parameters to properly address the complexity of the 2D MT inverse problem. We enhance the stability and convergence of the solution of the geophysical problem by applying the hierarchical PSO with time-varying acceleration coefficients (HPSO-TVAC). Moreover, we parallelize the code to reduce the computation time because PSO is a computationally demanding global search algorithm. The inverse problem was solved for the synthetic data both by giving a priori information at the beginning and by using a random initialization. The a priori information was given to a small number of particles as the initial position within the search space of solutions, so that the swarming behavior was only slightly influenced. We have demonstrated that there is no need for the a priori initialization to obtain robust 2D models because the results are largely comparable with the results from randomly initialized PSO. The optimization of the COPROD2 data set provides a resistivity model of the earth in line with results from previous interpretations. Our results suggest that the 2D MT inverse problem can be successfully addressed by means of computational swarm intelligence.

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A COMBINATION SCHEME FOR FUZZY CLUSTERING

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001402002052 ◽

2002 ◽

Vol 16 (07) ◽

pp. 901-912 ◽

Cited By ~ 52

Author(s):

EVGENIA DIMITRIADOU ◽

ANDREAS WEINGESSEL ◽

KURT HORNIK

Keyword(s):

A Priori ◽

Fuzzy Cluster ◽

A Priori Information ◽

Cluster Validity ◽

Data Set ◽

Cluster Algorithms ◽

Combination Scheme ◽

Priori Information ◽

Theoretical Considerations ◽

Structurally Stable

In this paper we present a voting scheme for fuzzy cluster algorithms. This voting method allows us to combine several runs of cluster algorithms resulting in a common partition. This helps us to tackle the problem of choosing the appropriate clustering method for a data set where we have no a priori information about it. We mathematically derive the algorithm from theoretical considerations. Experiments show that the voting algorithm finds structurally stable results. Several cluster validity indexes show the improvement of the voting result in comparison to simple fuzzy voting.

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A method to derive the Site Atmospheric State Best Estimate (SASBE) of ozone profiles from radiosonde and passive microwave data

Atmospheric Measurement Techniques Discussions ◽

10.5194/amtd-8-3399-2015 ◽

2015 ◽

Vol 8 (3) ◽

pp. 3399-3422 ◽

Cited By ~ 4

Author(s):

E. Maillard Barras ◽

A. Haefele ◽

R. Stübi ◽

D. Ruffieux

Keyword(s):

Brightness Temperature ◽

A Priori ◽

A Priori Information ◽

Data Set ◽

Ozone Data ◽

Best Estimate ◽

Vertical Range ◽

Ozone Profile ◽

Atmospheric State ◽

Priori Information

Abstract. We present a method to derive the site atmospheric state best estimate (SASBE) of the ozone profile combining brightness temperature spectra around the 142 GHz absorption line of ozone measured by the microwave radiometer SOMORA and ozone profiles measured by the radiosonde (RS). The SASBE ozone profile is obtained using the radiosonde ozone profile as a priori information in an optimal estimation retrieval of the SOMORA radiometer. The resulting ozone profile ranges from ground up to 65 km altitude and makes optimal use of the available information at each altitude. The high vertical resolution of the radiosonde profile can be conserved and the uncertainty of the SASBE is well defined at each altitude. A SASBE ozone profile dataset has been generated for Payerne, Switzerland, with a temporal resolution of 3 profiles a week for the time period ranging from 2011 to 2013. The relative difference of the SASBE ozone profiles to the AURA/MLS ozone profiles lies between −3 to 6% over the vertical range of 20–65 km. Above 20 km, the agreement between the SASBE and AURA/MLS ozone profiles is better than the agreement between the operational SOMORA ozone data set and AURA/MLS. Below 20 km the SASBE ozone data are identical to the radiosonde measurements. The same method has been applied to ECWMF-ERA interim ozone profiles and SOMORA data to generate a SASBE dataset with a time resolution of 4 profiles per day. These SASBE ozone profiles agree between −4 and +8% with AURA/MLS. The improved agreement of the SASBE datasets with AURA/MLS above 20 km demonstrates the benefit of better a priori information in the retrieval of ozone from brightness temperature data.

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Structurally tailored 3D anisotropic controlled-source electromagnetic resistivity inversion with cross-gradient criterion and simultaneous model calibration

Geophysics ◽

10.1190/geo2018-0639.1 ◽

2019 ◽

Vol 84 (6) ◽

pp. E387-E402 ◽

Cited By ~ 2

Author(s):

Max A. Meju ◽

Randall L. Mackie ◽

Federico Miorelli ◽

Ahmad Shahir Saleh ◽

Roger V. Miller

Keyword(s):

Field Data ◽

A Priori ◽

Calibration Data ◽

A Priori Information ◽

Data Set ◽

Low Contrast ◽

Controlled Source ◽

Low Resistivity ◽

Band Limited ◽

Priori Information

Geologic interpretation of 3D anisotropic resistivity models from conventional marine controlled-source electromagnetic (CSEM) data inversion faces difficulties in low-resistivity contrast sediments and structurally complex environments that typify the new frontiers for hydrocarbon exploration. Currently, the typically reconstructed horizontal resistivity [Formula: see text] and vertical resistivity [Formula: see text] models often have conflicting depth structures that are difficult to explain in terms of subsurface geology, and the resulting resistivities may not be close to the true formation resistivities required for estimating reservoir parameters. We have investigated the concept that an objective geologically oriented or structurally tailored inversion can be achieved by requiring that the cross-product of the gradient of horizontal resistivity and the gradient of the vertical resistivity is equal to zero at significant geologic boundaries. We incorporate this boundary-shape criterion in our 3D inverse problem formulations, implemented within nonlinear model-space and conjugate-gradient contexts, for cases in which a priori calibration data from wells and/or seismically derived subsurface boundaries are available and for cases in which these are lacking. The resulting fit-for-purpose solutions serve to better analyze the peculiarity of a given data set. We applied these algorithms to synthetic and field CSEM data sets representing a fold-thrust environment with low-resistivity and low-contrast sediments. The resulting [Formula: see text] and [Formula: see text] models from cross-gradient joint inversion of synthetic data of appropriate frequency bandwidth without a priori information are structurally similar and consistent with the test models, whereas those from the inversions of band-limited field data are consistent with the available seismic and resistivity well-log data. This particular approach will thus be useful for lithologic correlation in frontier regions with limited a priori information using broadband CSEM data. For these band-limited field data, we found that the anisotropic bulk resistivities of the low-contrast sediments are better determined by incorporating a priori calibration data from triaxial resistivity logs and seismic horizons.

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Reconstruction of borehole radar images by a modified f–k migration

Geophysical Journal International ◽

10.1093/gji/ggaa094 ◽

2020 ◽

Vol 221 (3) ◽

pp. 1626-1634

Author(s):

Jianjian Huo ◽

Binzhong Zhou ◽

Qing Zhao ◽

Iain M Mason

Keyword(s):

Final Section ◽

Early Stage ◽

A Priori ◽

A Priori Information ◽

Data Set ◽

Radar Images ◽

Imaging Tool ◽

Bedding Planes ◽

Borehole Radar ◽

Priori Information

SUMMARY Borehole radar (BHR) is an effective imaging tool. It can be used to detect and map faults, fractures, folds, domes, partings and mine workings. Most BHRs have azimuthally omnidirectional radiation patterns. The echoes sensed by such BHRs may come from any direction. Considering a radar in a straight borehole that passes through a stack of flat reflection planes, V-shaped events or crosses appear on the time section. One of the arms of each cross is a real image while the other is an ambiguity of known origin. Directional ambiguities such as these obstruct efforts to interpret the data. In this paper, we address this difficulty by using a modified f–k migration algorithm to translate crosses into lines on the final section that are consistent with a priori information about for example bedding. Compared with conventional strategies, for example migration + f–k dip filter, this approach integrates the two separated processes into one and is straightforward, computationally effective and simple to implement. The method is demonstrated using a synthetic model and a real BHR field data set. It allows the interpreter to use a priori information about fault swarms or plausible bedding planes at an early stage. The reconstructed BHR image helps the search for geological anomalies such as fractures, partings, domes and rolls that could be a hazard for mining.

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Unbiased Least-Squares Modelling

Mathematics ◽

10.3390/math8060982 ◽

2020 ◽

Vol 8 (6) ◽

pp. 982

Author(s):

Marta Gatto ◽

Fabio Marcuzzi

Keyword(s):

Parameter Estimation ◽

Least Squares ◽

A Priori ◽

Numerical Results ◽

General Linear ◽

A Priori Information ◽

Linear Least Squares ◽

Parameter Estimation Problem ◽

Essential Properties ◽

Priori Information

In this paper we analyze the bias in a general linear least-squares parameter estimation problem, when it is caused by deterministic variables that have not been included in the model. We propose a method to substantially reduce this bias, under the hypothesis that some a-priori information on the magnitude of the modelled and unmodelled components of the model is known. We call this method Unbiased Least-Squares (ULS) parameter estimation and present here its essential properties and some numerical results on an applied example.

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3-D inversion of magnetic data

Geophysics ◽

10.1190/1.1443968 ◽

1996 ◽

Vol 61 (2) ◽

pp. 394-408 ◽

Cited By ~ 542

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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