Geology 5640/6640 Introduction to Seismology 25 Mar 2015 © A.R. Lowry 2015 Last time: Normal Modes Normal modes are used for source modeling and estimation of global structure (including PREM) —> Include toroidal (SH excitation by Love waves) and spheroidal (P-SV excitation by Rayleigh waves) modes, each mode has different period… —> Used to verify earlier inferences of solid inner core —> Normal mode analysis was the quickest to show that moment release in Sumatra-Andaman event was M w ~ 9.3 (~10x more energy than body/surface wave estimates and much earlier than geodetic estimates) Read for Wed 25 Mar: S&W (§3.1–3.3)

Slichter mode (triplet) (pointed out in 1961) : 1 S 1 Translation of the solid inner core in the liquid outer core ( 1 S 1, period ~ 4-8 h) Controlled by the density jump between the inner and outer core, and the Archimedean force of the fluid core

Core modes Oscillations in the fluid outer core (periods in the tidal band (?) Information on the stratification of the outer core

Normal Modes From Tohoku-Oki: Spectrum for the superconducting gravimeter at Membach (courtesy Michel van Camp, ROB)

Normal Modes From Tohoku-Oki:

Refraction Seismology: For applications in the near- surface, we commonly think of the medium as approximately layered, and use travel-times of reflected and refracted arrivals from an active source to describe the thicknesses, velocity properties, and geometry of the layers. Shown are for a single horizontal layer.

An Aside on Travel-Times: As we’ve discussed previously, travel-time is a skeletal representation of the first moment in time at which a seismic phase arrives. If one were to do it by hand, you might pick that moment as something like the arrow at left (but given that the arrival is superposed on perturbations in the background noise, there’s some uncertainty or “slop” in making that pick!) More often in the digital era, picks are made using cross- correlation matching, in which amplitudes are compared to a synthetic or an observed arrival at another location. By shifting the reference arrival in time and multiplying to see which time shift produces the maximum similarity, arrival times can be very accurately determined. Always remember though that amplitudes and phase also contain info about the medium… which travel-times ignore! t

Another Aside: Forward vs Inverse Modeling Most often in seismology, we seek to use data to determine something about Earth structure or the seismic source. This is inverse modeling. Forward modeling would be the opposite problem in which we already know the source properties and Earth structure and we want to predict travel-times or seismograms. However, we must first derive the forward model in order to use it in the inverse model!