Osculation of surface waves

• Applicant: Dr. Thomas Forbriger
• Subject Area: Geophysics
• Term: from 2014 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 259997182

Seismic surface waves in structures with depth dependent properties are dispersive. This means that their propagation velocity depends on frequency. In this case several eigen-solutions (modes, overtones with different eigen-function) to the boundary value problem exist, which differ in propagation velocity. The relation between propagation velocity and frequency is commonly expressed in terms of so-called dispersion curves. In some cases, which are not yet understood, different modes appear degenerate. This means, that overtones with different physical properties exist at the same eigen-value (wave-number at given frequency). Closer investigation of such phenomena reveals that modes usually are not degenerate exactly, their dispersion curves only come very close to each other. In recorded field data they thus become indistinguishable. Different terms are used in literature for this phenomenon. In the current proposal we use the most often used term 'osculation', although we do not address osculations in the strict mathematical sense. Recent investigations show osculations surprisingly often in shallow seismic field data. A possible cause might be strong material contrasts which are typical for the shallow subsurface. The cause, however, is not yet fully understood. Nevertheless, specific properties of the subsurface structure are responsible for the appearance of osculations. Such, from an osculation in recorded data this specific property of the structure under investigation could be inferred. A prerequisite for practical application hence is a deeper understanding of the nature of osculation phenomena.In the current project we aim to investigate the mathematical nature of the boundary value problem which controls the propagation of Rayleigh waves. If we succeed in understanding the mathematical causes for the existence of osculation points, we aim to make the link to the corresponding physical properties of the material in a second step. I expect that the such gained understanding will become a valuable tool in the inversion of shallow seismic Rayleigh waves, for example in civil engineering applications.

• DFG Programme: Research Grants