Complete synthetic seismograms up to 2 Hz for transversely isotropic spherically symmetric media
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Abstract:
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.Keywords:
Seismogram
Transverse isotropy
Earth structure
Transverse isotropy
Elasticity
Axis of symmetry
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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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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.
Seismogram
Earth structure
Mode (computer interface)
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The present work proposes an approach to adapt existing isotropic models to transversely isotropic materials. The main idea is to introduce equivalence relations between the real material and a fictitious isotropic one on which one can take all the advantages of the well-established isotropic theory. Two applications of this approach are presented here: a failure criterion and a damage model that takes into account the load-induced anisotropy. In both cases, theoretical predictions are in agreement with the experimental data. In the present paper, the developed approach is applied to sedimentary rock materials; nevertheless, it can be generalized to any material that exhibits transverse isotropy. Copyright © 2015 John Wiley & Sons, Ltd.
Transverse isotropy
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Abstract Any technique for synthesizing seismograms in an isotropic model, having continuous variation of velocities with depth, can be easily adapted to the synthesis of seismograms in a transversely isotropic model. The only changes necessary are modifications in the calculation of turning radii and delay times τ( p ) and substitutions of functions that depend on ray parameter in the reflection transmission coefficients. An example synthesis of S waves interacting with a transversely isotropic D ″ layer illustrates an alternative hypothesis for explaining differences in the arrival time of ScSH versus ScSV at distances greater than 75°.
Transverse isotropy
Seismogram
Reflection
Arrival time
Earth model
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