Maximum Likelihood Estimation of Strong-Motion Attenuation Relationships

1991 ◽  
Vol 7 (2) ◽  
pp. 267-279 ◽  
Author(s):  
K. L. McLaughlin
Keyword(s):  
Maximum Likelihood ◽  
Strong Motion ◽  
Likelihood Estimation ◽  
Earthquake Ground Motion ◽  
Attenuation Relation ◽  
Ground Acceleration ◽  
Attenuation Relations ◽  
Attenuation Relationships ◽  
The Mean ◽  
Data Censoring

Strong-motion attenuation relations are commonly derived from earthquake ground motion collected on triggered recorders. Parametric attenuation relations are estimated from these data using standard least squares methods. The variance of ground acceleration is relatively large and for any given earthquake, there is a distance range for which only stations with larger than average amplitudes will trigger recording. Consequently observed accelerations at these distances are higher than the mean ground acceleration and a bias may be introduced into an attenuation relation regression by non-detection data censoring.

scholarly journals Variations between Foundation-Level and Free-Field Earthquake Ground Motions

2000 ◽  
Vol 16 (2) ◽  
pp. 511-532 ◽  
Author(s):  
Jonathan P. Stewart
Keyword(s):  
Free Field ◽  
Low Frequency ◽  
Strong Motion ◽  
Dimensionless Frequency ◽  
Spectral Acceleration ◽  
Ground Acceleration ◽  
Attenuation Relations ◽  
Ground Motion Selection ◽  
Motion Data ◽  
Embedded Foundations

Strong motion data from sites having both an instrumented structure and free-field accelerograph are compiled to evaluate the conditions for which foundation recordings provide a reasonably unbiased estimate of free-field motion with minimal uncertainty. Variations between foundation and free-field spectral acceleration are found to correlate well with dimensionless parameters that strongly influence kinematic and inertial soil-structure interaction phenomena such as embedement ratio, dimensionless frequency (i.e., product of radial frequency and foundation radius normalized by soil shear wave velocity), and ratio of structure-to-soil stiffness. Low frequency components of spectral acceleration recorded on shallowly embedded foundations are found to provide good estimates of free-field motion. In contrast, foundation-level peak ground acceleration (both horizontal and vertical) and maximum horizontal velocity, are found to be de-amplified. Implications for ground motion selection procedures employed in attenuation relations are discussed, and specific recommendations are made as to how these procedures could be improved.

scholarly journals Seismic Hazard of the Uttarakhand Himalaya, India, from Deterministic Modeling of Possible Rupture Planes in the Area

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Anand Joshi ◽  
Ashvini Kumar ◽  
Heriberta Castanos ◽  
Cinna Lomnitz
Keyword(s):  
Seismic Hazard ◽  
Peak Ground Acceleration ◽  
Strong Motion ◽  
Semiempirical Method ◽  
Empirical Method ◽  
Attenuation Relation ◽  
Ground Acceleration ◽  
Important Region ◽  
Semi Empirical ◽  
Uttarakhand Himalaya

This paper presents use of semiempirical method for seismic hazard zonation. The seismotectonically important region of Uttarakhand Himalaya has been considered in this work. Ruptures along the lineaments in the area identified from tectonic map are modeled deterministically using semi empirical approach given by Midorikawa (1993). This approach makes use of attenuation relation of peak ground acceleration for simulating strong ground motion at any site. Strong motion data collected over a span of three years in this region have been used to develop attenuation relation of peak ground acceleration of limited magnitude and distance applicability. The developed attenuation relation is used in the semi empirical method to predict peak ground acceleration from the modeled rupture planes in the area. A set of values of peak ground acceleration from possible ruptures in the area at the point of investigation is further used to compute probability of exceedance of peak ground acceleration of values 100 and 200 gals. The prepared map shows that regions like Tehri, Chamoli, Almora, Srinagar, Devprayag, Bageshwar, and Pauri fall in a zone of 10% probability of exceedence of peak ground acceleration of value 200 gals.

scholarly journals Uncertainties in attenuation relations for New Zealand seismic hazard analysis

1986 ◽  
Vol 19 (1) ◽  
pp. 28-39 ◽  
Author(s):  
G. H. McVerry
Keyword(s):  
New Zealand ◽  
Seismic Hazard ◽  
Hazard Analysis ◽  
Response Spectrum ◽  
Strong Motion ◽  
Seismic Hazard Analysis ◽  
Ground Acceleration ◽  
Attenuation Relations ◽  
Ground Shaking ◽  
Acceleration Data

Probabilistic techniques for seismic hazard analysis have
come into vogue in New Zealand for both the assessment of major projects and the development and review of seismic design codes. However, there are considerable uncertainties in the modelling
 of the strong-motion attenuation, which is necessarily based largely on overseas data. An excellent agreement is obtained between an average 5% damped response spectrum for New Zealand alluvial sites in the 20 to 59 km distance range and 5.4 to 6.0 magnitude class and that given by a Japanese model. Unfortunately, this corresponds to only about half the amplitude levels of 150 year spectra relevant to code design. The much more rapid decay
of ground shaking with distance in New Zealand has led to a considerable modification based on maximum ground acceleration
data from the Inangahua earthquake of the distance-dependence
of the Japanese response spectra model. Less scatter in New Zealand data has resulted in adopting a lower standard deviation for the attenuation model, which is important in reducing the considerable "probabilistic enhancement" of the hazard estimates. Regional differences in attenuation shown by intensities are difficult to resolve from the strong-motion acceleration data, apart from lower accelerations in Fiordland.

scholarly journals The Mw 7.2 Fiordland earthquake of August 21, 2003

2003 ◽  
Vol 36 (4) ◽  
pp. 233-248 ◽  
Author(s):  
Martin Reyners ◽  
Peter McGinty ◽  
Simon Cox ◽  
Ian Turnbull ◽  
Tim O'Neill ◽  
...  
Keyword(s):  
New Zealand ◽  
Ground Motions ◽  
Near Field ◽  
Strong Motion ◽  
Shallow Earthquake ◽  
Ground Acceleration ◽  
Attenuation Relationships ◽  
Steep Slopes ◽  
Epicentral Region ◽  
Shallow Part

The Mw 7.2 Fiordland earthquake of August 21 2003 was the largest shallow earthquake to occur in New Zealand for 35 years. Because of its location in an unpopulated area, it caused only minor damage to buildings, roads and infrastructure. It triggered numerous landslides on steep slopes in the epicentral region, where intensities reached MM9. Deployments of portable seismographs, strong motion recorders and GPS receivers in the epicentral region immediately after the event have established that the earthquake involved thrusting at the shallow part of the subduction interface between the Australian and Pacific plates. Recently installed strong motion recorders of the GeoNet network have ensured that the earthquake is New Zealand's best recorded subduction interface event. Microzonation effects are clear in some of the records. Current peak ground acceleration attenuation relationships for New Zealand subduction interface earthquakes underprediet the ground motions recorded during the earthquake, as was the case for previous large events in Fiordland in 1993 and 1989. The four portable strong motion recorders installed in the epicentral region have provided excellent near-field data on the larger aftershocks, with recorded peak ground accelerations ranging up to 0.28g from a nearby ML 6.1 event.

scholarly journals A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1394
Author(s):  
Mustapha Muhammad ◽  
Huda M. Alshanbari ◽  
Ayed R. A. Alanzi ◽  
Lixia Liu ◽  
Waqas Sami ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Weibull Model ◽  
Mean Square ◽  
Reliability Parameter ◽  
Coverage Probabilities ◽  
The Mean

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

SLAM++-A highly efficient and temporally scalable incremental SLAM framework

2017 ◽  
Vol 36 (2) ◽  
pp. 210-230 ◽  
Author(s):  
Viorela Ila ◽  
Lukas Polok ◽  
Marek Solony ◽  
Pavel Svoboda
Keyword(s):  
Computer Vision ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Likelihood Estimation ◽  
The State ◽  
Efficient Estimation ◽  
State Representation ◽  
The Mean

The most common way to deal with the uncertainty present in noisy sensorial perception and action is to model the problem with a probabilistic framework. Maximum likelihood estimation is a well-known estimation method used in many robotic and computer vision applications. Under Gaussian assumption, the maximum likelihood estimation converts to a nonlinear least squares problem. Efficient solutions to nonlinear least squares exist and they are based on iteratively solving sparse linear systems until convergence. In general, the existing solutions provide only an estimation of the mean state vector, the resulting covariance being computationally too expensive to recover. Nevertheless, in many simultaneous localization and mapping (SLAM) applications, knowing only the mean vector is not enough. Data association, obtaining reduced state representations, active decisions and next best view are only a few of the applications that require fast state covariance recovery. Furthermore, computer vision and robotic applications are in general performed online. In this case, the state is updated and recomputed every step and its size is continuously growing, therefore, the estimation process may become highly computationally demanding. This paper introduces a general framework for incremental maximum likelihood estimation called SLAM++, which fully benefits from the incremental nature of the online applications, and provides efficient estimation of both the mean and the covariance of the estimate. Based on that, we propose a strategy for maintaining a sparse and scalable state representation for large scale mapping, which uses information theory measures to integrate only informative and non-redundant contributions to the state representation. SLAM++ differs from existing implementations by performing all the matrix operations by blocks. This led to extremely fast matrix manipulation and arithmetic operations used in nonlinear least squares. Even though this paper tests SLAM++ efficiency on SLAM problems, its applicability remains general.

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