Free field ground motions at various depths derived from actual seismograph records by using elastodynamic infinite elements
This paper presents a method for the analysis of free field ground motions at various depths from actual seismograph records. The proposed method replaces the propagating rupture on the fault surface by a fictitious focal point and a seismograph station in the vicinity of the given soil site. A fictitious focal point and seismograph station scheme is used to calibrate the free field ground motion of the soil site. The harmonic vibration analysis of the half space, which elastodynamic infinite elements are adopted in the far field and finite elements in the near field, yields the Fourier transform of any constituent wave in terms of the amplitude of the forces applied at the focal point, thus in terms of the Fourier transforms of the accelerations in three orthogonal directions recorded at a seismograph station. If a seismograph station is in the far field (as it is usually), the recorded values there can be transformed into the values at the infinite element node by means of appropriate shape functions. The results can be more refined in case of the availability of simultaneous records at more seismograph stations. In case of N stations, we assume N fictitious focal points, and solve a set of 3N simultaneous equations of 3N forces, three orthogonal forces at each focal point. Naturally, only the results by the present method were exact at the calibrated points, and should be accurate in-between and near those points. The accelerations at the points near seismograph stations at various depths can also be obtained. An appropriate inverse Fourier transform algorithm will properly yields all results as time functions.
free field seismograph infinite element finite element focal point exponential integral