Source investigation of a small event using empirical Green's functions and simulated annealing

We propose a two-step inversion of three-component seismograms that (1) recovers the far-field source time function at each station and (2) estimates the distribution of co-seismic slip on the fault plane for small earthquakes (magnitude 3 to 4). The empirical Green's function (EGF) method consists of finding a small earthquake located near the one we wish to study and then performing a deconvolution to remove the path, site, and instrumental effects from the main-event signal.
The deconvolution between the two earthquakes is an unstable procedure: we have therefore developed a simulated annealing technique to recover a stable and positive source time function (STF) in the time domain at each station with an estimation of uncertainties. Given a good azimuthal coverage, we can obtain information on the directivity effect as well as on the rupture process. We propose an inversion method by simulated annealing using the STF to recover the distribution of slip on the fault plane with a constant rupture-velocity model. This method permits estimation of physical quantities on the fault plane, as well as possible identification of the real fault plane.
We apply this two-step procedure for an event of magnitude 3 recorded in the Gulf of Corinth in August 1991. A nearby event of magnitude 2 provides us with empirical Green's functions for each station. We estimate an active fault area of 0.02 to 0.15 km² and deduce a stress-drop value of 1 to 30 bar and an average slip of 0.1 to 1.6 cm. The selected fault of the main event is in good agreement with the existence of a detachment surface inferred from the tectonics of this half-graben.     

Recent Advances in Prediction and Processing of Strong Ground Motions

We present an overview of our recent results on utilizing small earthquakes in the earthquake engineering practice. Site-specific ground motion time-histories of large earthquakes can be successfully simulated using recordings of small earthquakes which are often referred to as 'empirical Green's functions' in seismology. Another important practical problem is whether and how these observations can be used in seismic risk studies which are based on empirical attenuation relations for ground motion parameters. We study a possibility of extrapolating attenuation relations for small earthquakes, to larger magnitudes using the data from the Garner Valley downhole array in Southern California. Finally we introduce efficient ground motion processing techniques in frequency- and time-domains and apply them to site response estimation.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Determination of S-wave velocity structure using microtremors and spac method applied in Thessaloniki (Greece)

Array measurements of microtremors at 16 sites in the city of Thessaloniki were performed to estimate the V_s velocity of soil formations for site effect analysis. The spatial autocorrelation method was used to determine phase velocity dispersion curves in the frequency range from 0.8–1.5 to 6–7 Hz. A Rayleigh wave inversion technique (stochastic method) was subsequently applied to determine the Vs profiles at all the examined sites. The determination of V_s profiles reached a depth of 320 m. Comparisons with V_s values from cross-hole tests at the same sites proved the reliability of the SPAC method. The accuracy of the V_s profiles, the ability to reach large penetration depths in densely populated urban areas and its low cost compared to conventional geophysical prospecting, make Mictrotremor Exploration Method very attractive and useful for microzonation and site effects studies. An example of its application for the site characterization in Thessaloniki is presented herein.     

Centrifuge modelling of the influence of crustal fabrics on the development of transfer zones: insights into the mechanics of continental rifting architecture

Centrifuge analogue experiments are used to model the reactivation of pre-existing crustal fabrics during extension. The models reproduced a weakness zone in the lower crust whose geometry was varied in order to investigate its role in controlling the architecture of rift segments and related transfer zones. The typical rift system geometry was characterised by two offset rift segments connected by a major transfer zone in which boundary faults were oblique to the extension vector and displayed a significant transcurrent component of movement. The transfer zone was also characterised by cross-basin faults with both trend and strike-slip component of movement opposite to that displayed by the master faults. Typically, different structural patterns were obtained by changing the offset angle φ between the rift segments, supporting that the structural pattern at transfer zones is strongly influenced by the orientation of pre-existing discontinuities with respect to the stretching vector. In the models, the aspect ratio (ratio of length vs. width) of the transfer zone shows a positive correlation with the offset angle (i.e., the more the inherited fabric is parallel to the extension direction, the longer and narrower the transfer zones). In case of staircase offset of the rift segments (φ=90°), the structural pattern was characterised by two isolated rift depressions linked by a narrow transfer zone in which border faults with alternating polarity overlapped. Prominent rise of the ductile lower crust was also observed at the transfer zone. Many of these geometrical features display striking similarities with natural rift systems. The results of the current experiments provide useful insights into the mechanics of continental rift architecture, supporting that rift propagation, width and along-axis segmentation may be strongly controlled by the reactivation of pre-existing pervasive crustal fabrics.     

Curve-Fitting Schemes for Fragmentation Data

Fragmentation measurements in the form of sieve passing and mass fraction data were used to test the capability of three different distributions to fit the observed data over a wide range in fragment size and mass. These distributions were based on Rosin-Rammler, lognormal and simple sigmoidal (S-shaped) functions, having 2 input parameters for the single-component versions and 5 input parameters for the two-component versions. Provided convergence was achieved in the non-linear curve-fitting technique, the two-component versions always provided superior fits to the observed data. However, these versions were very sensitive to variations in the values chosen for the input parameters. In this particular regard, the two-component sigmoidal function was the most robust. The present results also show that the two-component lognormal function provided the best fit to the fragmentation data in a general sense, and the two-component Rosin-Rammler function provided the worst fit. However, there was not a significant difference between any of the three methods.     

Lake-Sediment Records of Recent Environmental Change on Svalbard: Results of Diatom Analysis

Surface sediments from 23 lakes on Svalbard were analysed for diatoms. About 182 taxa were found but samples generally have a low richness, with the majority of sites dominated by benthic genera such as Fragilaria, Navicula, and Achnanthes. Centric Cyclotella species occur at only three sites. Modern relationships between diatom abundance and water chemistry and other environmental variables were explored numerically and a preliminary transfer function for pH was developed. Lakes fell into three groups on the basis of their diatom assemblages: (1) high pH, high cation, high conductivity sites characterised by Amphora libyca, (2) shallow sites with relatively high nutrient values characterised by Fragilaria species, and (3) more acid and dilute sites with high amounts of snow cover in the catchments characterised by small Achnanthes species and Navicula digitulus. Five sediment cores representing the recent past were also analysed for diatoms. Three shallow sites were dominated by Fragilaria species throughout the period represented by the cores and no shifts in inferred pH were found. At two deeper sites (Arresjøen, Birgervatnet) major assemblage shifts are found which are unrelated to independent evidence for atmospheric contamination. Early (ca. 1200 AD) changes found at both sites are possibly related to the onset of the ‘Little Ice Age’. Later changes are neither synchronous nor similar in nature and might be best explained as individual responses to the recovery from the ‘Little Ice Age’ and subsequent climatic warming.