Introduction to Seismology Geology 5640/6640 Introduction to Seismology 29 Mar 2017 Last time: Finished Up Normal Modes • Normal modes have potentially infinite numbers of frequencies for differing harmonics; we observe many of these up to l ~ 30. These give information about Earth structure and properties; source size/location. Refraction Seismic For a layer-over-halfspace with source/receiver at the surface, can have three body wave arrivals: a direct wave, reflected wave and refracted wave • These are modeled as travel-times (time from source to initial deflection of the seismogram) Read for Fri 29 Mar: S&W 119-157 (§3.1–3.3) © A.R. Lowry 2017

The layer-over-halfspace here has three different possible raypaths from source to receiver: • The direct wave: t = x/v0 (a line with slope 1/v0) • The reflected wave: (a hyperbolic; asymptotic to the direct wave) • The head wave: (a line with slope 1/v1 and intercept depends on h0, v1, v0)

Given a known source and observations of travel-times at several different distances, we can get velocities from the slopes of the direct and head-wave arrivals on a time-vs-distance plot… And then thickness from the intercept of the head wave. Refraction = equation of a line: with slope m: and intercept b:

Example of crustal-scale seismic refraction: Note that research seismologists often plot arrivals with “reduced velocity”, so that some chosen velocity would appear as a horizontal line on the time-distance plot. v = 4 km/s v = 6 km/s v = 8 km/s

Modern research seismic data tend to be a little more densely sampled so may look less linear… But large-scale (crustal) seismic reflection/refraction studies like this one are getting increasingly rare, as they are incredibly expensive and we now find that we can get more bang for the buck from passive array studies.

A very useful principle to bear in mind as you think about these approaches is the Principle of Reciprocity: If you switch positions of a source and receiver, you’ll get the same ray-paths and travel-times, regardless of the medium.

Refraction Examples: two layers over a halfspace For multiple layers, slope is still 1/v in the medium… Intercept depends on thickness and velocity in each of the overlying layers as:

Refraction Examples: A low-velocity zone A low-velocity layer will not return energy to the surface so is “invisible” to the refraction method… It’s presence won’t affect estimates of velocity in the layers below, but it will affect all estimates of thickness for deeper layers.

Refraction Examples: A blind zone This can be overcome if the arrival is recognized. The problem is that it will never be a first-arrival, so must be picked later in the wave train where it gets a bit dodgy…

dip, so it’s important to reverse the profile… Then More generally we expect that layers may have some slight dip, so it’s important to reverse the profile… Then a

To get structure from more realistic data sets we usually use more flexible (& more complicated) equations…

These results from Meltzer et al. (BSSA, 1987) were obtained using a ray-tracing approach. Many studies from the past two decades use Colin Zelt’s RayInvr inversion codes (a shareware package)…