Complete synthetic seismograms based on a spherical self-gravitating Earth model with an atmosphere–ocean–mantle–core structure
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Abstract:
A hybrid method is proposed to calculate complete synthetic seismograms based on a spherically symmetric and self-gravitating Earth with a multilayered structure of atmosphere, ocean, mantle, liquid core and solid core. For large wavelengths, a numerical scheme is used to solve the geodynamic boundary-value problem without any approximation on the deformation and gravity coupling. With decreasing wavelength, the gravity effect on the deformation becomes negligible and the analytical propagator scheme can be used. Many useful approaches are used to overcome the numerical problems that may arise in both analytical and numerical schemes. Some of these approaches have been established in the seismological community and the others are developed for the first time. Based on the stable and efficient hybrid algorithm, an all-in-one code QSSP is implemented to cover the complete spectrum of seismological interests. The performance of the code is demonstrated by various tests including the curvature effect on teleseismic body and surface waves, the appearance of multiple reflected, teleseismic core phases, the gravity effect on long period surface waves and free oscillations, the simulation of near-field displacement seismograms with the static offset, the coupling of tsunami and infrasound waves, and free oscillations of the solid Earth, the atmosphere and the ocean. QSSP is open source software that can be used as a stand-alone FORTRAN code or may be applied in combination with a Python toolbox to calculate and handle Green's function databases for efficient coding of source inversion problems.Keywords:
Seismogram
Earth structure
Seismogram
Earth structure
Centroid
Moment tensor
Synthetic seismogram
Synthetic data
Seismic moment
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SUMMARY We investigate the impact of unmodelled 3-D structural heterogeneity on inverted W-phase source parameters. We generate a large data set of synthetic seismograms accounting for the Earths 3-D structure for 250 earthquakes globally distributed. The W-phase algorithm is then used to invert for earthquake CMT parameters, assuming a spherical Earth model. The impact of lateral heterogeneity is assessed by comparing inverted source parameters with those used to compute the 3-D synthetics. Results show that the 3-D structure mainly affects centroid location while the effect on the other source parameters remains small. Centroid mislocations present clear geographical patterns. In particular, W-phase solutions for earthquakes in South America are on average biased 17 km to the east of the actual centroid locations. This effect is significantly reduced using an azimuthally well balanced distribution of seismological stations. Source parameters are generally more impacted by mantle heterogeneity while the scalar moment of shallow earthquakes seems to be mainly impacted by the crustal structure. Shallow earthquakes present a variability of Mrθ and Mrϕ moment tensor elements, resulting both from the small amplitude and a larger uncertainty of the associated Green’s functions.
Seismogram
Centroid
Earth structure
Moment tensor
Seismic moment
Earth model
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Seismogram
Earth structure
Moment tensor
Point source
Seismic moment
Synthetic seismogram
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Using Gilbert & Dziewonski's retrieved structural parameters, Earth model 1066A, their Qμ(r) model, and the moment rate tensor for the Colombian earthquake of 1970 July 31, we produce 75 theoretical seismograms in epicentral co-ordinates by superimposing all the normal modes (1105 modes) within a period range from 100·1 to 963·8 s. The computed seismograms are compared with the respective observed ones. Such a comparison is possible not only because all the modes in the frequency range are taken into account in the computation, but also because we have a realistic kinematic source mechanism at our disposal. A qualitative, though far from exact, reproduction of actual seismograms was successfully effected, indicating the moment rate tensor represents a reasonable source model for the Colombian earthquake. In particular, on the average we are able to reproduce the observed amplitudes to within 30 per cent. Among surface and body-wave phases identified, multiple S-waves can be identified up to 21 S at almost 8 h after the origin time on both the observed and computed co-latitudinal record sections.
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Moment tensor
Earth structure
Seismic moment
Focal mechanism
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We performed an investigation of the large scale seismic wave speeds and density structure of the Earth’s mantle using free oscillations. Seismic free oscillations, or normal modes, are convenient for analysing low-frequency seismograms in a hetero- geneous Earth. To use these, we must address how to calculate exact seismograms using normal modes, and how to formulate the inverse problem to infer Earth’s 3D structure. The most important findings of this research are: • In order for seismograms to be theoretically exact, full mode coupling calcula- tions must involve an infinite set of modes. In practice, only a finite subset of modes can be used, introducing an error into the seismograms. We found that coupling modes 1-2 mHz above the highest frequency of interest is essential for having sufficiently accurate signals to infer density. • Observations of free oscillations provide important constraints on the heteroge- neous structure of the Earth. This inference problem has usually been addressed by the measurement and interpretation of splitting functions. These can be seen as secondary data extracted from low frequency seismograms. The measurement step necessitates the calculation of synthetic seismograms, but current imple- mentations rely on approximations referred to as self- or group-coupling and do not use fully accurate seismograms. We therefore investigated whether a systematic error might be present in currently published splitting functions. As is well known, the density signal is weak in low-frequency seismograms. Our results suggest this signal is of similar magnitude to the realistic uncertainties associated with currently published splitting functions. Thus, great care must be taken in any attempt to robustly infer details of Earth’s density structure using current splitting functions. • We investigated the problem of inferring density using currently published split- ting functions with properly calibrated uncertainties together with a novel prob- abilistic inversion technique, Hamiltonian Monte Carlo. Models are strongly dependent on damping. We found that shear wave speed models are statisti- cally significant in terms of misfit change, while density and compressional wave speeds are not. Therefore any interpretation of Earth’s mantle density based on splitting functions might be inaccurate. • A promising approach is the direct spectral inversion, which uses spectra di- rectly without the need of splitting functions. We found that misfit changes corresponding to the inferred models are statistically significant even for den- sity and compressional wave speed, but depend on a good starting model. We only used group coupling and relatively low frequency spectra for computa- tional reasons. Full coupling together with high frequencies might solve this long-lasting problem to infer density contrasts in the Earth’s mantle.
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Earth structure
Mode (computer interface)
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Seismological data used by Shearer (1990, 1991) to infer the existence of a seismic discontinuity at 520 km depth are compared with complete long‐period body wave seismograms calculated for the International Association of Seismology and Physics of the Earth's Interior 1991 (Iaspei91) Earth model. The Iaspei91 model does not contain a seismic discontinuity at or near 520 km depth. The observed P and SH multiples caused by topside reflections and SS precursors caused by underside reflections from the 410‐km and 660‐km discontinuities are well reproduced by the synthetic stacks. The synthetics exhibit clear “phase extrema” between these reflections that correlate well with similar features in the observed waveform stacks. Shearer interpreted these “phase extrema” as separate reflections from a seismic discontinuity at 520 km depth. Cross‐correlation analysis of synthetic seismograms gives an apparent discontinuity depth of about 520 km for P and SH multiples as well as SS precursors. Similarly, amplitude analysis of synthetic upper mantle reflections is in reasonable agreement with the observations reported by Shearer (1991). The phase extrema seen in the synthetics are the result of an extended, multicycle wavelet which is composed of depth phases and other structural phases such as reverberations from the crustal layer, convolved with the instrument response of long‐period stations of the Global Seismograph Network. The comparison of observational data, presented by Shearer (1990, 1991), with the synthetic seismogram stacks of this paper shows that the claim of good seismological evidence for a 520‐km seismic discontinuity as a global feature is not compelling.
Seismogram
Classification of discontinuities
Discontinuity (linguistics)
Synthetic seismogram
Earth structure
Seismometer
Core–mantle boundary
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Seismogram
Synthetic seismogram
Seismometer
Earth structure
Earth model
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During the last four years of U.S. research into theoretical seismology, effective techniques of computing synthetic seismograms have come into quite general use. Good agreement between a synthetic record and an instrumental record of ground motion (the raw data of seismology) implies a good understanding of the seismic source; of Earth structure; and of the theory of wave propagation relevant to the frequency content of the data. At periods T greater than about twenty seconds, there is now in general terms a fairly complete understanding of all the details in a seismogram, provided one ignores the (usually) minor effects of lateral variation of Earth structure. For 2 < T < 20 seconds, only limited portions of a seismogram (e.g., 15 seconds following a P‐arrival) may be fully understood, the limitations coming from noises in the data due to lateral scattering, and also from our ignorance of the source, of fine‐scale vertical Earth structure, and attenuation. At periods less than about two seconds, the understanding of seismograms is usually limited only to time windows within which identifiable pulses arrive. At these short periods, our knowledge of Earth structure is inadequate; scattering effects are stronger, but are poorly understood except for some progress in the context of seismic reflection prospecting within crustal layers.
Seismogram
Earth structure
Reflection
Synthetic seismogram
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We use the direct solution method (DSM) with optimally accurate numerical operators to calculate complete (including both body and surface waves) three-component synthetic seismograms for transversely isotropic (TI), spherically symmetric media, up to 2 Hz. We present examples of calculations for both deep (600 km) and shallow (5 km) sources. Such synthetics should be useful in forward and inverse studies of earth structure. In order to make these calculations accurately and efficiently the vertical grid spacing, maximum angular order, and cut-off depth must be carefully and systematically chosen.
Seismogram
Transverse isotropy
Earth structure
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