Slip heterogeneity, body-wave spectra, and directivity of earthquake ruptures

We present a broadband kinematic model based on a self-similar k-square distribution of the coseismic slip, with an instantaneous rise-time and a constant rupture velocity. The phase of the slip spectrum at high wave number is random. This model generates an ?-squared body-wave radiation, and a particular directivity factor C2d scaling the amplitude of the body-wave spectra, where Cd is the standard directivity factor. Considering the source models with a propagating pulse and a finite rise-time, we assume that within the slipping band, the rupture has some random character, with small scale rupture in various directions. With such a model, the pulse cannot be resolved, and the directivity factor is still C2d at low frequency; at periods shorter than the rise-time, however, the directivity effect drops to much smaller rms values. This frequency dependent directivity effect, which is expected to be the strongest for sites located in the direction of rupture, was evidenced for the Landers 1992 earthquake, leading to a 2 to 3 s rise-time of the slip pulse. This kinematic model can be used with more refined theoretical Green's functions, including near-field terms and surface waves, or with empirical Green's functions, for generating realistic broadband records in the vicinity of moderate to large earthquakes, in a frequency range relevant for engineering applications (0 Hz to about 20 Hz).

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Spin-wave spectra and Green's functions in two-sublattice spiral magnets

Theoretical and Mathematical Physics ◽

10.1007/bf01016125 ◽

1991 ◽

Vol 87 (2) ◽

pp. 526-532

Author(s):

M. Yu. Kovalevskii ◽

A. A. Rozhkov

Keyword(s):

Spin Wave ◽

Green's Functions ◽

Green’S Functions ◽

Wave Spectra

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High-frequency global wavefields for local 3D structures by wavefield injection and extrapolation

Geophysical Journal International ◽

10.1093/gji/ggaa563 ◽

2020 ◽

Author(s):

Marta Pienkowska ◽

Vadim Monteiller ◽

Tarje Nissen-Meyer

Keyword(s):

Wave Propagation ◽

Large Scale ◽

Green's Functions ◽

Green’S Functions ◽

Body Wave ◽

Computational Cost ◽

Spectral Element ◽

Earth Model ◽

Local Domain ◽

Global Database

Summary Earth structure is multiscale, and seismology remains the primary means of deciphering signatures from small structures over large distances. To enable this at the highest resolution, we present a flexible injection and extrapolation type hybrid framework that couples wavefields from a precomputed global database of accurate Green's functions for 1-D models with a local three dimensional (3-D) method of choice (e.g. a spectral element or a finite difference solver). The interface allows to embed a full 3-D domain in a spherically symmetric Earth model, tackling large-scale wave propagation with focus on localized heterogeneous complex structures. Thanks to reasonable computational costs (10k CPU hours) and storage requirements (a few TB for 1 Hz waveforms) of databases of global Green’s functions, the method provides coupling of 3-D wavefields that can reach the highest observable body-wave frequencies in the 1-4 Hz range. The framework is highly flexible and adaptable; alterations in source properties (radiation patterns, source-time function), in the source-receiver geometry, and in local domain dimensions and location can be introduced without re-running the global simulation. The once-and-for-all database approach reduces the overall computational cost by a factor of 5,000-100,000 relative to a full 3-D run, provided that the local domain is of the order of tens of wavelengths in size. In this paper we present the details of the method and its implementation, show benchmarks with a 3-D spectral-element solver, discuss its setup-dependent performance, and explore possible wave-propagation applications.

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