Removing Love waves from shallow seismic SH-wave data

Geophysical exploration measurements are used to obtain an image of the geological structures of the subsurface, as detailed as possible. To this end, a wavefield is generated by a seismic source. This wavefield propagates through the subsurface, and will partly reflect on boundaries between layers with contrasting properties, and it will partly propagate further into the subsurface. De wavefields that have propagated back to the surface are measured with receivers. When this experiment is repeated several times on different locations, the measured data can be used to obtain the desired image. There are two kinds of seismic waves that can propagate through the subsurface. The ones that are generally used are the pressure waves, or P-waves, where the movement of the particles is parallel to the propagation direction of the wave. The other ones are the shear waves, or S-waves, where the movement of the particles is perpendicular to the propagation direction of the wave. When the particle movement is horizontally polarized (perpendicular to the plane of propagation), this wave type is often decoupled, or in other words, it propagates independently of other wave types. These waves are also called SH-waves. The surface of the Earth behaves as a perfect reflector for SH-waves. This means that all SH-waves that reach the surface will be completely reflected back into the subsurface. When the top layer of the subsurface is thin (smaller than the wavelength of the SH-wave), and when this top layer has a lower wave velocity than deeper layers, then the presence of the surface leads to a kind of surface waves, which were first described by A.E. H. Love, and are therefore called 'Love waves'. Love wave characteristics are: their group velocity is almost equal to the shear wave velocity; since they propagate solely along the surface, they attenuate slowly and are thus often stronger than reflected waves; and they are dispersive. The presence of Love waves deteriorates the quality of the final picture (or seismogram), because they obscure the desired reflections. Existing techniques to remove Love waves from seismic data often perform insufficient, or require certain knowledge about the subsurface. This knowledge is generally not available. Therefore, the ideal method should be one where the measured data alone is sufficient to separate the Love waves from the desired reflection information. The method we describe in this thesis uses the Betti-Rayleigh reciprocity theorem for elastic media. Reciprocity is a mathematical tool to relate two different states to each other. Here, one state is the actual situation, where the medium is bounded by a stress-free surface. The other state is an ideal situation, where there is no surface, and the top layer is extended to infinity. When there is no surface, there are also no surface waves. By applying the reciprocity theorem, we derive an integral equation, from which the Love wave free wavefield can be solved as a function of the data that do contain these surface waves. Other input parameters are the (shear-) wave velocity and the mass density of the top layer, and the source wavelet. When the data are discrete, the integral equation becomes a matrix equation. This can be solved using conventional numerical methods, such as matrix inversion. When the medium is horizontally layered (a so called 1-D medium), the kernel of the matrix equation becomes diagonal in the wave-number domain. Then the matrix equation reduces to a scalar expression. We tested the method on several synthetic datasets. In all cases, the Love waves were completely removed. Even other noise in the form of scattered Love waves was removed, in the cases where it was present. The method also had no problems when the input parameters were chosen wrongly. And when distortions were introduced into the data (distortions like random noise, or the effects of anelastic attenuation), the method still performed well. To test the method on field data, we performed a seismic experiment on the site of the Sofia tunnel (before it was drilled) near Hendrik Ido Ambacht in the Netherlands. The dataset that was the result seemed all right at first. Strong Love waves were indeed present in the data. However, we could not succeed in removing these Love waves with the method. Even worse, the method added noise to the data, to such an extent, that it completely obscured the original data. Although we searched extensively for possible reasons, we were not able to find the exact cause of the bad results. In the final chapter, we made a start to remove the surface waves from coupled P- and SV-wave systems, using the same method as we did for SH-waves. Because P- and SV-waves are coupled, the resulting equations are also coupled. This means that we need all possible source and receiver combinations to remove the surface waves. But it appeared that the equations could be solved independently with regard to the source direction. We validated the theory with an example where we removed the Rayleigh wave from the response of a homogeneous