3-D linearized scattering of surface waves and a formalism for surface wave holography

Summary. Scattering of surface waves by lateral heterogeneities is analysed in the Born approximation. It is assumed that the background medium is either laterally homogeneous, or smoothly varying in the horizontal direction. A dyadic representation of the Green's function simplifies the theory tremendously. Several examples of the theory are presented. The scattering and mode conversion coefficients are shown for scattering of surface waves by the root of an Alpine-like crustal structure. Furthermore a 'great circle theorem'in a plane geometry is derived. A new proof of Snell's law is given for surface wave scattering by a quarter-space. It is shown how a stationary phase approximation can be used to simplify the Fourier synthesis of the scattered wave in the time domain. Finally a procedure is suggested to do 'surface wave holography'.     

Anelasticity of the Crust and Upper Mantle of South America From the Inversion of Observed Surface Wave Attenuation

Fundamental-mode Rayleigh and Love waves generated by several earthquakes situated along great-circle paths between pairs of seismograph stations have been analysed to obtain coefficients of attenuation, group velocities, phase velocities, and specific quality factors in the period range 18–80s in two regions of the South American continent. One set of paths crosses the shield region which lies on the eastern coast and another set traverses the mountainous region inland. the average attenuation coefficient values are clearly higher in the tectonically active western region throughout the entire period range than in the eastern or shield region.
Inversion of the attenuation data yielded shear wave internal friction ( Q ^-1_β) models as a function of depth in the crust and upper mantle in both regions. A low- Q zone below the lithosphere is prominent in both regions. the results show that substantial variations of Q _β occur in the two regions of South America. the Q_β values were found to be inversely related to the heat flow values or to the temperature.     

Source tomography by simulated annealing using broad-band surface waves and geodetic data: application to the Mw= 8.1 Chile 1995 event

We invert surface-wave and geodetic data for the spatio-temporal complexity of slip during the M _w =8.1 Chile 1995 event by simulated annealing. This quasi-global inversion method allows for a wide exploration of model space, and retains the non-linearity of the source tomography problem. Complex source spectra are obtained from 5 to 45 mHz from first- and second-orbit fundamental-mode Rayleigh waves using an empirical Green's function cross-correlation technique. Coseismic displacement vectors were measured at 10 GPS sites near Antofagasta. They are part of a French-Chilean experiment which monitors the Northern Chile seismic gap. The spectra, together with the geodetic data, are inverted for the moment distribution on a 2-D dipping fault, under the physical constraints of slip positivity and causality. Marginal a posteriori distributions of the model parameters are obtained from several independently inverted solutions. In general, features of the slip model are well resolved. Data are well fitted by a purely unilateral southward rupture with a nearly uniform velocity around 2.5–3.0 km s⁻¹, and a total duration of 65 s. Several regions of moment release were imaged, one near the hypocentre, a major one 80 km south of it and a minor one 160 km south of it. The major patch of moment release seemed to have propagated to relatively shallow depths near the trench, 100 km SSW of the epicentre. The region of major slip is located updip of the 1987, M _w =7.5 earthquake, suggesting a causal relationship. Most of the slip occurred updip of the hypocentre (36 km), but the entire coupled plate interface (20–40 km) ruptured during the Chile 1995 event.     

Effects of slight anisotropy on surface waves

We present a complete ray theory for the calculation of surface-wave observables from anisotropic phase-velocity maps. Starting with the surface-wave dispersion relation in an anisotropic earth model, we derive practical dynamical ray-tracing equations. These equations allow calculation of the observables phase, arrival-angle and amplitude in a ray theoretical framework. Using perturbation theory, we also obtain approximate expressions for these observables. We assess the accuracy of the first-order approximations by using both theories to make predictions on a sample anisotropic phase-velocity map. A comparison of the two methods illustrates the size and type of errors which are introduced by perturbation theory. Perturbation theory phase and arrival-angle predictions agree well with the exact calculation, but amplitude predictions are poor. Many previous studies have modelled surface-wave propagation using only isotropic structure, not allowing for anisotropy. We present hypothetical examples to simulate isotropic modelling of surface waves which pass through anisotropic material. Synthetic data sets of phase and arrival angle are produced by ray tracing with exact ray theory on anisotropic phase-velocity maps. The isotropic models obtained by inverting synthetic anisotropic phase data sets produce deceptively high variance reductions because the effects of anisotropy are mapped into short-wavelength isotropic structure. Inversion of synthetic arrival-angle data sets for isotropic models results in poor variance reductions and poor recovery of the isotropic part of the anisotropic input map. Therefore, successful anisotropic phase-velocity inversions of real data require the inclusion of both phase and arrival-angle measurements.     

The crustal structure beneath the northwest fjords, Iceland, from receiver functions and surface waves

Five broad-band seismic stations were operated in the northwest fjords area of Iceland from 1996 to 1998 as part of the Iceland Hotspot project. The structures of the upper 35  km or so beneath these stations were determined by the modelling and joint inversion of receiver functions and regional surface wave phase velocities. More than 40 teleseismic events and a few regional events containing high-quality surface wave trains were used. Although the middle period passband of the seismograms is corrupted by oceanic microseismic noise, which hinders the interpretation of structural details, the inversions reveal the overall features. Many profiles obtained exhibit large velocity gradients in the upper 5  km or so, smaller zero gradients below this, and, at ~23  km depth, a zone 2–4  km thick with higher velocity gradients. The two shallower intervals are fairly consistent with the 'upper' and 'lower' crust, defined by Flovenz (1980 ). The deep zone of enhanced velocity gradient seems to correspond to the sharp reflector first reported by Bjarnason et al . (1993 ) and identified by them as the 'Moho'. However, this type of structure is not ubiquitous beneath the northwest fjords area. The distinctiveness of the three intervals is variable, and in some cases a structure with velocity gradient increasing smoothly with depth is observed. We term these two end-members structures of the first and second types respectively. Structures of the second type correlate with older areas. Substantial variation in fundamental structure is to be expected in Iceland because of the great geological heterogeneity there.