We introduce a new method to determine the magnitude of complete- ness Mc and its uncertainty. Our method models the entire magnitude range (EMR method) consisting of the self-similar complete part of the frequency-magnitude dis- tribution and the incomplete portion, thus providing a comprehensive seismicity model. We compare the EMR method with three existing techniques, finding that EMR shows a superior performance when applied to synthetic test cases or real data from regional and global earthquake catalogues. This method, however, is also the most computationally intensive. Accurate knowledge of Mc is essential for many seismicity-based studies, and particularly for mapping out seismicity parameters such as the b-value of the Gutenberg-Richter relationship. By explicitly computing the uncertainties in Mc using a bootstrap approach, we show that uncertainties inb-values are larger than traditionally assumed, especially when considering small sample sizes. As examples, we investigated temporal variations of Mc for the 1992 Landers aftershock sequence and found that it was underestimated on average by 0.2 with former techniques. Mapping Mc on a global scale, Mc reveals considerable spatial variations for the Harvard Centroid Moment Tensor (CMT) (5.3 Mc 6.0) and the International Seismological Centre (ISC) catalogue (4.3 Mc 5.0).

Assessing the Quality of Earthquake Catalogues: Estimating the Magnitude of Completeness and Its Uncertainty

The nature of noise wavefield and its applications for site effects studies A literature review

http://home.ustc.edu.cn/~ly2014/Advances_in_Geosciences/Reading%20materials%20for%20Week%202/Group6-Characterisation%20of%20the%20Basel%201%20enhanced%20geothermal%20system.pdf

Characterisation of the Basel 1 enhanced geothermal system

Models capable of estimating losses in future earthquakes are of fundamental importance for emergency planners and for the insurance and reinsurance industries. One of the main ingredients in a loss model is an accurate, transparent and conceptually sound algorithm to assess the seismic vulnerability of the building stock and indeed many tools and methodologies have been proposed over the past 30 years for this purpose. This paper takes a look at some of the most significant contributions in the field of vulnerability assessment and identifies the key advantages and disadvantages of these procedures in order to distinguish the main characteristics of an ideal methodology.

/pdf/development-of-seismic-vulnerability-assessment-1xbax4ru36.pdf

Development of seismic vulnerability assessment methodologies over the past 30 years

SUMMARY Ambient vibration techniques such as the H/V method may have the potential to significantly contribute to site effect evaluation, particularly in urban areas. Previous studies interpret the so-called Nakamura’s technique in relation to the ellipticity ratio of Rayleigh waves, which, for a high enough impedance contrast, exhibits a pronounced peak close to the fundamental S-wave resonance frequency. Within the European SESAME project (Site EffectS assessment using AMbient Excitations) this interpretation has been tested through noise numerical simulation under well-controlled conditions in terms of source type and distribution and propagation structure. We will present simulations for a simple realistic site (one sedimentary layer over bedrock) characterized by a rather high impedance contrast and low quality factor. Careful H/V and array analysis on these noise synthetics allow an in-depth investigation of the link between H/V ratio peaks and the noise wavefield composition for the soil model considered here: (1) when sources are near (4 to 50 times the layer thickness) and surficial, H/V curves exhibit one single peak, while the array analysis shows that the wavefield is dominated by Rayleigh waves; (2) when sources are distant (more than 50 times the layer thickness) and located inside the sedimentary layer, two peaks show up on the H/V curve, while the array analysis indicates both Rayleigh waves and strong S head waves; the first peak is due to both fundamental Rayleigh waves and resonance of head S waves, the second is only due to the resonance of head S waves; (3) when sources are deep (located inside the bedrock), whatever their distance, H/V ratio exhibit peaks at the fundamental and harmonic resonance frequencies, while array analyses indicate only non-dispersive body waves; the H/V is thus simply due to multiple reflections of S waves within the layer. Therefore, considering that experimental H/V ratio (i.e. derived from actual noise measured in the field) exhibit in most cases only one peak, we conclude that H/V ratio is (1) mainly controlled by local surface sources, (2) mainly due to the ellipticity of the fundamental Rayleigh waves. Then the amplitude of H/V peak is not able to give a good estimate of site amplification factor.

https://hal-insu.archives-ouvertes.fr/insu-00265520/document

H/V ratio: a tool for site effects evaluation. Results from 1-D noise simulations

SUMMARY The mode summation method and a finite difference technique are applied to investigate the spectral ratio between the horizontal and vertical components (H/V ratio) of ambient vibrations and to explore the variation of the resonance frequency and the amplitude and shape of polarization as a function of the structure and the source positions. Layered structural models are used by assuming a large number of sources distributed around a receiver, with shallow source depths that are randomly assigned. We identify stable parts of the H/V ratios that are independent of the source distance and are dominated by the ellipticity of the fundamental-mode Rayleigh wave in the frequency band between the fundamental frequency of resonance of the unconsolidated sediments and the first minimum of the average H/V ratio. The ellipticity in this frequency band is determined by the layering of the sediments. The numerical simulations are compared with observations at a site where the thickness and velocity structure of the unconsolidated sediments are known from S-wave and surface wave measurements. Two methods are applied to compute the H/V ratio, the classical method in the frequency domain and a method based on frequency–time analysis that allows us to locate P–SV wavelets in the time-series. The main problem in comparing synthetics with observations is the contribution of SH waves in the observed H/V ratios. We propose a method to minimize these effects and the effects of the superposition of different incoming P–SV waves. An inversion scheme is applied to the stable parts of the observed H/V ratio, based on a genetic algorithm, to retrieve the S-wave velocity structure from a single ambient vibration record.

/pdf/a-theoretical-investigation-of-average-h-v-ratios-3llf9yz4ok.pdf

A theoretical investigation of average H/V ratios

H/V spectral ratios from microtremors areused to retrieve the S-velocity structurefrom a single ambient vibration record, byusing its relation to the ellipticity ofthe fundamental mode Rayleigh wave and theamplitude of observed H/V ratio.Constraints are needed in order to restrictthe possible range of solutions, and theinversion is applied to sites where thethickness of the unconsolidated sedimentsis approximately known from boreholeinformation. Within the uncertainty, theinverted structures agree well with theresults from other S-wave measuringtechniques such as downhole and cross-holemeasurements, and the analysis of ambientvibrations measured on an array.The influence of the inversion uncertaintyon site-amplification estimates forearthquakes is then investigated. For allinverted models, site response is computedfor a large number of events, which allowsto define the uncertainty by the aprioriunknown source position and mechanism of afuture earthquake. In most cases thevariability between the results obtainedfor the different models is much smallerthan the variability introduced by theunknown source position. The accuracy withwhich S-wave velocity structures can beretrieved from observed H/V ratios istherefore sufficient for an application ofthe method in seismic hazard analysis for aspecific site.

/pdf/inversion-of-local-s-wave-velocity-structures-from-average-h-qaufrepbze.pdf

Inversion of local S-wave velocity structures from average H/V ratios, and their use for the estimation of site-effects

Earthquakes in Switzerland and Surrounding Regions During 1999

Earthquake scenarios for the city of Basel

SUMMARY The S-wave velocity is a very important factor in local hazard assessment. Direct measurement with conventional methods is very costly and therefore inexpensive and efficient methods are needed to make local hazard assessment more feasible. Techniques based on the analysis of recordings of ambient vibrations from small-scale arrays of sensors have become popular recently. One technique that is favoured by several research groups is the extraction of the dispersion curve by estimation of the f ‐k spectrum and its inversion for the S-wave velocity structure. This paper presents the results from an application based on high-resolution beamforming applied to the vertical component of the measurements. Synthetic ambient vibrations generated with a 2-D finite-difference code are used to illustrate and test the application. By superposition of random signals it is shown that the dispersion curve can be extracted even if 60 per cent of the wavefield consists of spatially uncorrelated signals. The errors in the phase velocities amount to less than 10 per cent. The dispersion curve can be extracted from the fundamental frequency of resonance upwards. Data from two real measurements are presented—from one site close to a city and another site within an industrial complex. The inverted S-wave velocity structures agree with reference data for the sites. The rule of thumb for the resolution of the method is confirmed.

/pdf/array-measurements-of-s-wave-velocities-from-ambient-1d2ifgwhze.pdf

Fortunat Kind

Papers

A theoretical investigation of average H/V ratios

Inversion of local S-wave velocity structures from average H/V ratios, and their use for the estimation of site-effects

Earthquakes in Switzerland and Surrounding Regions During 1999

Earthquake scenarios for the city of Basel

Array measurements of S‐wave velocities from ambient vibrations