Resumen de Some new theoretical considerations about the ellipticity of Rayleigh waves in the light of site-effect studies in Israel and Mexico

Peter G. Malischewsky, Y. Zaslavsky, M. Gorstein, V. Pinsky, T. T. Tran, F. Scherbaum, H. Flores Estrella

• español

  La amplificación del movimiento del terreno, como resultado de la presencia de suelos blandos, es un fenómeno común en áreas urbanas y bien identificado como un factor que incrementa el daño y el número de pérdidas humanas. Por otro lado, para el análisis de la amenaza sísmica, el estudio de la elipticidad de las ondas de Rayleigh se ha hecho más popular en el contexto del uso de registros de vibraciones ambientales, además, los resultados pueden ser usados en la inversión de la estructura de velocidades. Los efectos de sitio normalmente pueden ser modelados a partir de un perfil de velocidades simple, dado el alto contraste de impedancias en la estructura somera del subsuelo. Por lo tanto, el análisis y el entendimiento de las implicaciones de un modelo tan simple como una capa sobre un semiespacio (LOH, por sus siglas en inglés) son de suma importancia, no sólo teórica sino también práctica. Adicionalmente, para registros de vibraciones ambientales todavía no se cuenta con un modelo teórico que explique de manera satisfactoria los resultados de los cocientes espectrales H/V; un punto de inicio sobre la elipticidad de las ondas Rayleigh es la fórmula exacta propuesta por Malischewsky y Scherbaum (2004). Es possible mostrar que un modelo tan simple como LOH puede producir una gran variedad de curvas H/V-versus-frecuencia y mostramos como ejemplo las curvas H/V con más de un máximo para los casos de Israel y de México. Este fenómeno se atribuye a la contribución de capas adicionales, esto es, que el primer máximo se asocia con la frecuencia de resonancia de la primera capa y los máximos secundarios se asocian con las frecuencias de resonancia de capas más profundas. Demostramos que con un modelo LOH obtenemos dos máximos, para ciertos valores del módulo de Poisson. Sin embargo, este modelo simple no puede explicar las curvas experimentales consideradas, para las que posiblemente se requieran perfiles de velocidades más complejos y modos de propagación superiores. Estas consideraciones pueden implicar restricciones para los valores del módulo de Poisson, que normalmente no se toman en consideración. En conclusión, estas investigaciones analíticas y semi-analíticas son indispensables para un mejor entendimiento del comportamiento de la elipticidad de las ondas de Rayleigh en su uso para estudios de efectos de sitio.

• English

  It is well-known that ground motion amplification due to soft soils, common in urban areas, is a major contributor to increasing damage and number of causalities. Indirectly, the study of Rayleigh-wave ellipticities has recently gained considerable popularity in the context of studying ambient seismic vibrations for seismic hazard analysis. The output can be integrated into the inversion process for the velocity structure. Due to the strong impedance contrast in the shallow subsurface structure, local site effects are often fairly well predicted by simple models. Therefore, a thorough theoretical understanding of even a single layer over half-space (LOH) is not only of theoretical but also of considerable practical interest. Adding to this argument is the fact that an accepted theoretical model for the interpretation of H/V-measurements from ambient vibrations, still has to be developed. A useful starting point for the theoretical investigation of the ellipticity of Rayleigh waves is the exact formula derived by Malischewsky and Scherbaum (2004). It can be shown, that already the simple LOH model is able to produce a great variety of H/V-versus-frequency curves with different character. We cite observations 141 142 Geofis. Int. 49 (3), 2010 Introduction It is well-known that the ellipticity of Rayleigh waves is important in applying the popular H/V method for the estimation of local site effects and the characterization of shallow site structure. H/V spectral ratios of ambient vibrations are increasingly used in investigations of local site amplifications during strong earthquakes, as ambient noise is often dominated by Rayleigh waves (Scherbaum et al., 2003; Bard, 1998). It can be even said that the H/V spectral ratio technique, originally introduced by Nogoshi and Igarashi (1971), also known as Nakamura’s method (Nakamura, 1989; 2009), has become the primary tool of choice in many of the ambient noise related studies (see e.

  g., Muciarelli et al., 2009).

  However, the fundamentals of the H/V technique are controversial [the history and different opinions are discussed e. g., by Bonnefoy-Claudet et al. (2006) and Petrosino (2006)]. These different opinions even refer to the term H/V technique itself. The spectral ratio H/V is usually taken from ambient noise but sometimes also from earthquakes [see e. g., Zschau and Parolai (2004) or Flores Estrella (2009)] or artificial explosions. Following Chávez-García (2009), microtremors can be explored in two directions: estimation of a local transfer function and estimation of the subsoil structure and from there obtain site effects by modelling. He points out that the use of H/V spectral ratio of microtremors to estimate a local transfer function has a weaker physical basis than spectral ratios relative to the reference site. Nevertheless, it has been successful to estimate site effects. This success has been explained by the assumption that microtremors consist of body waves [see e. g., Nakamura (1989)] contrary to the observation in the papers by Bard (1998) and Scherbaum et al. (2003) cited above. On the other from Israel and Mexico as an example of H/V-curves with more than one maximum. This phenomenon is usually contributed to additional layers, where the first maximum is connected with the shear-resonance frequency of the first layer and the secondary maximum with a resonance frequency of a deeper layer. We demonstrate that already the simple LOH model yields two peaks in a certain range of Poisson ratios. However this simple model cannot explain the experimental curves under consideration, where more complex models and higher modes are necessary. These considerations can yield constraints for Poisson ratios which are otherwise less controlled. In conclusion, such theoretical investigations of analytical or half-analytical character are necessary for a better understanding of the behaviour of the ellipticity of Rayleigh waves and its use for site effect studies.