Department of Geology, University of Oslo,
P.O. Box 1046, Blindern, 0316 Oslo, Norway.
Email:
valerie.maupin@geologi.uio.no
poster/oral: oral
| For seismologists, the ultimate goal of modelling wave propagation is to understand seismological data and to prepare for their inversion in terms of Earth structure. In this talk, I will focus on the different methods we have to model surface waves at relatively short periods, for which the free oscillation formalism is not well adapted, and show how they can be used to interpret and invert data. Surface wave propagation in laterally homogeneous structures has been well understood for several decades, at least in isotropic structures, where they propagate as independent Love and Rayleigh modes. Therefore, most current efforts are devoted to modelling the waves in laterally heterogeneous structures. In structures with smoothly varying properties, modes still propagate independently of each other, but adapt to the changing structure by deforming their displacement with depth, and by following frequency-dependent rays along the surface of the Earth. Therefore, they arrive at the stations in directions which do not necessarily coincide with the great-circle direction. This deviation leads to an apparent polarisation anomaly which at first-order depends on the transverse gradient of velocity between the source and the station, and which can be exploited to supplement classical phase information in surface wave tomography. The heterogeneities also contribute to focusing and defocusing of the wavefield. When the structure varies more sharply, the modes do not only deform, but they also get coupled to each other and can be partly reflected. The coupling is proportional to the horizontal gradients of velocity in the structure. The expression for the mode coupling has been derived in 2, 2.5 and 3-D. In 3-D, this is probably the most efficient and general method we have to model surface wave propagation, but as far as I know, no practical implementation of the equations has been done in 3-D models. As an example of application in 2.5-D, I will show how local mode coupling can be used to model velocity and polarisation of Rayleigh waves trapped along a structure similar to the Hawaiian chain. Another class of methods is based on defining a reference structure and using the modes calculated in that structure as a basis for representing the wavefield in the heterogeneous structure. Heterogeneities, which can be isotropic or anisotropic, act as secondary sources which scatter energy away from the initial propagation direction and lead to mode coupling. Methods with varying degrees of scattering have been devised. I will show applications of this class of methods in 3D structures containing anisotropy, with special emphasis on the polarisation pattern that the anisotropy can yield. Although less effective than the local mode coupling methods, these reference mode methods are better suited to devise inverse methods, and have been used in particular to improve current methods of surface wave tomography. In conclusion, I will present some of the challenges that I think we are now facing concerning surface wave propagation. First of all, I think that we need to incorporate the results of the modelling into data analysis and inversion tools. In particular, we need to devise strategies to sort out or to take into account simultaneously the effect of heterogeneities and anisotropy on the wavefield, and in particular on its polarisation. In order to interpret the wealth of data we have at periods shorter than 40s, we will need to develop inverse methods which can tackle the non-linear behaviour of these waves when they propagate in the very heterogeneous upper part of the Earth. |