Coupling spectral elements and modes in a spherical Earth: an extension to the ‘sandwich’ case

Abstract

S U M M A R YWe present an extension to the coupling scheme of the spectral element method (SEM) with a normal-mode solution in spherical geometry. This extension allows us to consider a thin spherical shell of spectral elements between two modal solutions above and below. The SEM is based on a high-order variational formulation in space and a second-order explicit scheme in time. It combines the geometrical flexibility of the classical finite-element method with the exponential convergence rate associated with spectral techniques. In the inner sphere and outer shell, the solution is sought in terms of a modal solution in the frequency domain after expansion on the spherical harmonics basis. The SEM has been shown to obtain excellent accuracy in solving the wave equation in complex media but is still numerically expensive for the whole Earth for high-frequency simulations. On the other hand, modal solutions are well known and numerically cheap in spherically symmetric models. By combining these two methods we take advantage of both, allowing high-frequency simulations in global Earth models with 3-D structure in a limited depth range. Within the spectral element method, the coupling is introduced via a dynamic interface operator, a Dirichlet-to-Neumann operator which can be explicitly constructed in the frequency and generalized spherical harmonics domain using modal solutions in the inner sphere and outer shell. The presence of the source and receivers in the top modal solution shell requires some special treatment. The accuracy of the method is checked against the mode summation method in simple spherically symmetric models and shows very good agreement for all type of waves, including diffracted waves travelling on the coupling boundary. A first simulation in a 3-D D -layer model based on the tomographic model SAW24b16 is presented up to a corner frequency of 1/12 s. The comparison with data shows surprisingly good results for the 3-D model even when the observed waveform amplitudes differ significantly from those predicted in the spherically symmetric reference model (PREM).

Seismic imaging of the laterally varying D″ region beneath the Cocos Plate

“…Hybrid approaches, where full 3‐D geometries can be implemented in a subset of the globe (e.g. the coupled mode and spectral element approach, Capdeville et al 2003), are promising for computing synthetics with shorter dominant periods using fully 3‐D model geometries in the region of interest. A recent application by Toh et al (2005) modelled the lowermost 370 km of the mantle in 3‐D, pushing the calculations to dominant periods of 8 s. In order to attain shorter dominant periods we use the axisymmetric spherical Earth finite difference method (SHaxi) (based on Igel & Weber 1995, 1996; and extended in Jahnke et al 2006) and explore laterally varying D″ structure beneath the Cocos Plate guided by recent data analyses.…”

The limits of ray theory when measuring shear wave splitting in the lowermost mantle withScSwaves

“…Chen & Tromp (2007) studied splitting in body waves from upper mantle anisotropy, but not the more complicated case of core reflections and D ′′ anisotropy. Cottaar & Romanowicz (2013) did not address comparisons between forward methods, but used finite-frequency, three-dimensional (3D) calculations (Capdeville et al 2003) to model splitting in D ′′ , though in S diff waves. Similarly, Komatitsch et al (2010b) also examined S diff , concluding, like Maupin (1994), before, that isotropic velocity variations in D ′′ can lead to apparent splitting; neither case again addressed ScS waves.…”

Seismic Constraints on a Double‐Layered Asymmetric Whole‐Mantle Plume Beneath Hawai‘i

“…The Monterey Ocean Bottom Broadband (MOBB) seismic station is located 40 km offshore in the Monterey Bay, CA, at a water depth of ~1,000 m (Romanowicz et al, 2003;2006) However, the usage of MOBB seismic data for purposes such as regional moment tensor (MT) determination has been greatly restricted due to severe noise from seafloor deformation forced by ocean infragravity (IG) waves� Given the water depth at MOBB, the IG-induced noise on the vertical component seismogram peaks in 20-200s (Dolenc et al, 2005), which overlaps with the band (10-100 s) for regional MT analysis� Fortunately, MOBB contains a Differential Pressure Gauge (DPG) which provides continuous water pressure recordings at a sufficiently high sampling rate (1 sps)� It has been noticed that a strong correlation exists between seafloor vertical ground motion and pressure in the IG band (Dolenc et al, 2005)� A transfer function (TF) between the two components can therefore be defined and utilized to remove the IG noise from vertical component seismogram (Webb and Crawford, 1999;Crawford and Webb, 2000;Crawford et al, 2006;Dolenc et al, 2007)� If the TF is time invariant, then it can be pre-computed and used in a real-time fashion for noise removal� Following Webb and Crawford (1999), the transfer function T(ω) can be expressed as…”