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Least-squares linear regression is so popular that it is sometimes applied without checking whether its basic requirements are satisfied. In particular, in studying earthquake phenomena, the conditions (a) that the uncertainty on the independent variable is at least one order of magnitude smaller than the one on the dependent variable, (b) that both data and uncertainties are normally distributed and (c) that residuals are constant are at times disregarded. This may easily lead to wrong results. As an alternative to least squares, when the ratio between errors on the independent and the dependent variable can be estimated, orthogonal regression can be applied. We test the performance of orthogonal regression in its general form against Gaussian and non-Gaussian data and error distributions and compare it with standard least-square regression. General orthogonal regression is found to be superior or equal to the standard least squares in all the cases investigated and its use is recommended. We also compare the performance of orthogonal regression versus standard regression when, as often happens in the literature, the ratio between errors on the independent and the dependent variables cannot be estimated and is arbitrarily set to 1. We apply these results to magnitude scale conversion, which is a common problem in seismology, with important implications in seismic hazard evaluation, and analyse it through specific tests. Our analysis concludes that the commonly used standard regression may induce systematic errors in magnitude conversion as high as 0.3-0.4, and, even more importantly, this can introduce apparent catalogue incompleteness, as well as a heavy bias in estimates of the slope of the frequency-magnitude distributions. All this can be avoided by using the general orthogonal regression in magnitude conversions.

In a number of practical cases, a typical one being the investigation of the subsoil properties below roads or foundations, one faces the problem of measuring the elastic properties of a geological layer (here called 'hidden layer') underlying a more compact and rigid surface layer. In such cases, the effectiveness of common surface seismic methods is poor for different reasons, but mostly linked to the reflection--transmission properties of the waves at a stiff-to-soft interface. Borehole methods are more efficient, but expensive and only provide vertical information at certain points. Attempts carried out in the past to characterize the hidden layer properties through surface seismic techniques consisted in placing the seismic source on the surface alongside, but off the stiff artificial layer (road or foundation). An alternative approach is presented based on placing the seismic source just below the stiff artificial layer. In cases where soil improvement--compaction are carried out through injection of expanding resins, then the hidden layer can be easily reached via the injecting tools and in some cases (e.g., urban settings characterized by laterally continuous artificial layers or roads constructed on embankments) this can be the only viable option. The results obtained from this approach using a number of practical cases where roads affected by differential sinking have later been compacted will be presented. The average soil improvement that can be achieved with the specific kind of expanding resin used in this study is then quantified. Key words: surface wave methods, soil improvement, resin injection. Dans un certain nombre de cas pratiques, parmi lesquels figure typiquement l'etude des proprietes du sous-sol des routes ou des fondations, on est confronte au probleme de la mesure des proprietes elastiques d'une couche geologique (nommee ici << couche cachee >>) situee sous une couche de surface plus compacte et plus rigide. Dans de tels cas, l'efficacite des methodes sismiques de surface traditionnelles est limitee pour differentes raisons et principalement liee aux proprietes de reflexion-transmission des ondes a l'interface d'une couche rigide et d'une couche molle. Les methodes consistant a creuser un trou de sonde sont plus efficaces mais plus cheres et ne fournissent que des donnees verticales en quelques points precis. Les tentatives entreprises dans le passe pour caracteriser les proprietes de la couche cachee a l'aide de techniques sismiques de surface consistaient a placer la source sismique sur la surface le long et en retrait de la couche artificielle rigide (route ou fondation). Une autre approche est presentee qui consiste a positionner la source sismique juste en dessous de la couche artificielle rigide. Dans les cas ou des operations d'amelioration-compactage du sol sont realisees par injection de resines expansibles, la couche cachee est facilement accessible fi l'aide d'outils d'injection et, dans certains cas (p. ex. configuration urbaine caracterisee par des couches artificielles continues laterales ou routes construites sur des remblais), il s'agit de la seule solution viable disponible. Les resultats obtenus a partir de cette approche et a l'aide de differents cas pratiques, dans lesquels les routes touchees par un affaissement differentiel ont ete compactees par la suite, seront presentes. L'amelioration globale du sol, amelioration realisee au moyen du type b specifique de resine expansible utilise dans la presente etude sera ensuite mesuree. [Traduit par la Redaction] Mots-cles: methodes des ondes de surface, amelioration du sol, injection de resine., Introduction In practical applications of civil engineering one of the main interests is in measuring the elastic parameters of the subsoil. In this work, the focus of attention is on [...]

Sediment-filled basins are of interest both in exploration geophysics and in earthquake seismology in assessing their potential to amplify ground shaking. By means of numerical models, we present a number of dimensionless ratios between the main resonance frequencies that can be measured on the top of the basins and their geometry and mechanical properties, under the hypothesis of rigid bedrock. These resonance frequency ratios depend largely on the aspect ratio of the basins, whereas the mechanical properties of the sediments (specifically, the Poisson's coefficient) do not substantially affect the horizontal resonance frequency ratios. We discuss whether the modal frequencies measured on real basins can be used to extract information about the basins themselves and whether the theoretical expected modal sequence can be used to design experimental surveys aimed at assessing the dynamic behavior of basins. [ABSTRACT FROM AUTHOR]

Site response is a critical consideration when assessing earthquake hazards. Site characterization is key to understanding site effects as influenced by seismic site conditions of the local geology. Thus, a number of geophysical site characterization methods were developed to meet the demand for accurate and cost-effective results. As a consequence, a number of studies have been administered periodically as blind trials to evaluate the state-of-practice on-site characterization. We present results from the Consortium of Organizations for Strong Motion Observation Systems (COSMOS) blind trials, which used data recorded from surface-based microtremor array methods (MAM) at four sites where geomorphic conditions vary from deep alluvial basins to an alpine valley. Thirty-four invited analysts participated. Data were incrementally released to 17 available analysts who participated in all four phases: (1) two-station arrays, (2) sparse triangular arrays, (3) complex nested triangular or circular arrays, and (4) all available geological control site information including drill hole data. Another set of 17 analysts provided results from two sites and two phases only. Although data from one site consisted of recordings from three-component sensors, the other three sites consisted of data recorded only by vertical-component sensors. The sites cover a range of noise source distributions, ranging from one site with a highly directional microtremor wave field to others with omni-directional (azimuthally distributed) wave fields. We review results from different processing techniques (e.g., beam-forming, spatial autocorrelation, cross-correlation, or seismic interferometry) applied by the analysts and compare the effectiveness between the differing wave field distributions. We define the M index as a quality index based on estimates of the time-averaged shear-wave velocity of the upper 10 (VS10), 30 (VS30), 100 (VS100), and 300 (VS300) meters and show its usefulness in quantitative comparisons of VS profiles from multiple analysts. Our findings are expected to aid in building an evidence-based consensus on preferred cost-effective arrays and processing methodology for future studies of seismic site effects. [ABSTRACT FROM AUTHOR]