Surface-Wave Dispersion
In this tutorial, we demonstrate the application of BayesBay to a common problem in seismology: inferring the subsurface shear-velocity structure from observations of surface-wave group or phase velocity.
Background
Surface waves are seismic waves generated by earthquakes and seismic ambient noise that travel along the surface of our planet. Two distinct types of surface waves are observed: Rayleigh waves, characterized by an elliptical particle motion in the vertical plane containing the direction of propagation, and Love waves, which are horizontally polarized and move perpendicular to the direction of propagation.
When propagating through a vertically heterogeneous medium like the solid Earth, surface waves exhibit dispersive properties. This means that different surface-wave frequencies travel at different speeds because they sample different depth ranges — and thus different elastic properties — of the Earth’s interior. The frequency-dependent group or phase velocity of a surface wave, typically referred to as dispersion curve, varies as a function of subsusurface density (\(\rho\)), shear velocity (\(V_S\)), and compressional velocity (\(V_P\)), with the sensitivity to \(V_S\) being significantly larger compared to the other two. This makes surface waves widely employed in the tomographic imaging of the \(V_S\) structure as a function of depth, at both crustal and lithospheric/upper-mantle scale.
The problem of finding the subsurface model, \(\mathbf{m}\), that best explains an observed dispersion curve, \(\mathbf{d}_{obs}\), is inherently nonlinear and non-unique, meaning that distinct predictions \(\mathbf{d}_{pred} = g(\mathbf{m})\) can similarly fit the observed data. Addressing this geophysical inverse problem typically requires discretizing the Earth’s interior into a series of layers atop a homogeneous half-space, with each layer characterized by its thickness, \(V_S\), \(V_P\), and \(\rho\). In the following examples, this is achieved via the Voronoi tessellation provided by the bayesbay.discretization.Voronoi1D class, allowing the number of stratified model layers to be treated as an unknown, to be inferred from the data.
This tutorial comprises: