Abstract Large number of earthquakes have epicenters in offshore areas and their effects are a matter of great concern. This paper applies, for two dimensional problems, the Indirect Boundary Element Method to calculate the seismic pressure profile with the water depth due to the incidence of P- and SV-waves on the seabed, which can be characterized using the soil properties. Moreover, seismic amplifications of the seabed are highlighted. Our formulation can be considered as a numerical implementation of the Huygens’ Principle in which the diffracted waves are constructed at the boundary from which they are radiated. Thus mathematically, it is fully equivalent to the classical Somigliana’s representation theorem. Numerical results show the importance of knowing the properties of the marine soil because the pressure profile has an enormous dependence with respect to them. In some cases, pressure amplifications of six times between extreme values of soil materials can be expected. In addition, results from a layered numerical model evince that large seismic amplifications may be found, they can reach values up to 15.57 and 18.36 times the incident P- and SV-waves, respectively.

Resumen Un gran número de sismos tienen epicentros en áreas fuera de la costa y sus efectos son preocupantes. Este artículo aplica, para problemas bidimensionales, el Método Indirecto de Elementos Frontera para calcular el perfil de presiones sísmicas, en toda la profundidad del agua, debida a la incidencia de ondas P y SV sobre un fondo marino, el cual se caracteriza por su relación de Poisson. Se hace énfasis también en las amplificaciones del fondo marino. Nuestra formulación puede ser considerada como una implementación numérica del Principio de Huygens, en el cual las ondas difractadas son construidas desde las fronteras desde las cuales son radiadas. Esto es equivalente al teorema de representación de Somigliana. Los resultados numéricos muestran la importancia de las propiedades del suelo marino debido a que el perfil de presiones muestra mucha dependencia respecto a ellas. En algunos casos, las amplificaciones de las presiones son seis veces entre valores extremos del suelo. Se incluyen también, resultados de modelos con estratos y se evidencia que las amplificaciones sísmicas que pueden alcanzarse se encuentran entre 15.57 y 18.36 veces la onda incidente P y SV, respectivamente.

Abstract The purpose of this study is to obtain numerical estimations of seismic pressures in offshore areas considering the effect of seabed configurations and soil materials. To this end, the Boundary Element Method is used to irradiate waves, so that force densities can be obtained for each boundary element. From this hypothesis, Huygens´ Principle is implemented since the diffracted waves are constructed at the boundary from which they are radiated. Application of boundary conditions allows us to determine a system of integral equations of Fredholm type of second kind and zero order. Various models were analyzed, the first one is used to validate the proposed formulation. Other models of ideal seabed configurations are developed to estimate the seismic pressure profiles at several locations. The influence of P- and SV-wave incidence was also highlighted. In general terms, it was found that soil materials with high wave propagation velocities generate low pressure fields. The difference between the maximum pressure values obtained for a soil material with shear wave velocity of β = 3000 m/s is approximately 9 times lower than those obtained for a material with β = 90 m/s, for the P-wave incidence, and 2.5 times for the case of SV-waves. These results are relevant because the seabed material has direct implications on the field pressure obtained. A relevant finding is that the highest seismic wave pressure due to an offshore earthquake is almost always located at the seafloor.

Abstract Scattering and diffraction of P and SV waves caused by parallel oriented cracks located near to a free surface are investigated in this work. The Indirect Boundary Element Method (IBEM) was applied for studying the wave propagation phenomena in a half-plane model that contain the cracks. Various incidence angles of P and SV waves are considered. Sometime before it has been reported that a near free-surface crack generates scattered surface waves whose amplitude spectra show conspicuous resonance peaks. Such effect has been attributed to local resonances originated in a virtual layer between the shallowest crack and the free surface. For our case of two parallel crack system, where cracks are located at different depths, the amplitude spectra show additional peaks, which can be associated with the presence of the second crack. Given similar sizes between these two cracks, the characteristic resonance frequency observed at the free surface corresponds mainly to the equivalent layer formed by the shallowest crack and the free surface. However, when the deepest crack becomes sufficiently large with respect to the shallow crack, two resonance characteristic frequency peaks appear in the measured spectra at the free surface. Some examples including a three crack system are also illustrated in our work. The identification and characterization of the seismic response for the scattered field generated by the second and third crack has been an intricate task and, the time domain interpretation of traces becomes quite complicated. The results in this paper have been validated against some other reported from classic papers. In order to show the seismic response and multiple scattering effects due to the presence of systems of cracks, calculations in frequency and time domain are provided.

Resumen En este trabajo se investiga la difracción y dispersión de ondas P y SV por la presencia de grietas orientadas paralelamente localizadas cerca de una superficie libre. Se utiliza el Método Indirecto de Elementos de Frontera (IBEM) para estudiar el fenómeno de propagación de onda en un modelo con semi-espacio plano que contiene grietas. Se consideran varios ángulos de incidencia de ondas P y SV. Ya antes ha sido reportado en la literatura especializada que una grieta cercana a la superficie libre genera ondas superficiales difractadas cuyos espectros de amplitudes muestran picos de resonancia muy pronunciados. Tal efecto ha sido atribuido a resonancias locales de un estrato virtual entre la cara superior de la grieta y la superficie libre. Para nuestro caso de dos grietas paralelas cercanas a la superficie libre, los espectros de amplitudes muestran picos adicionales que pueden asociarse con la presencia de la segunda grieta. Si las grietas son de tamaño similar, la frecuencia característica de resonancia medida en la superficie libre corresponde principalmente al estrato equivalente formado por la grieta más somera y la superficie libre. Sin embargo, cuando la grieta más profunda llega a ser suficientemente larga con respecto a la grieta más somera, aparecen dos picos de frecuencias características de resonancias en los espectros medidos en la superficie. Nuestro trabajo también muestra ejemplos con sistemas de tres grietas. Esto ha resultado en una tarea intrincada, sobre todo en la identificación y caracterización de la respuesta sísmica del campo difractado generado por la segunda y tercera grietas y por su parte, la interpretación en el dominio del tiempo de las trazas obtenidas se vuelve bastante complicada. Los resultados en este trabajo han sido validados contra otros reportados en artículos clásicos. Con objeto de ilustrar la respuesta sísmica y los efectos de difracción múltiple debido a la presencia de sistemas de grietas, se proveen cálculos en el dominio del tiempo y la frecuencia.