Introduction to Seismology Geology 5640/6640 Introduction to Seismology 24 Mar 2017 Last time: Surface Waves • Dispersive waves have both group velocity U (velocity of the envelope or “beat”) and phase velocity c (velocity of individual peaks) where Note in this animation, as in surface waves, c > U! • Can measure group frequency from separation of individual and velocity as distance over time of group arrival from origin • Or more accurately by separating frequencies in Fourier domain • Can get phase velocity by differencing phase at pairs of sites (Here red = c; green = U) Read for Mon 27 Mar: S&W 119-157 (§3.1–3.3) © A.R. Lowry 2017

Normal Modes Note: These slides borrow heavily from a presentation by Michel van Camp, ROB… Gravimeters for seismological broadband monitoring: Earth’s free oscillations Michel Van Camp Royal Observatory of Belgium

What is a free oscillation? x Fundamental L 1st Harmonic 2nd Harmonic 3rd Harmonic etc. Free oscillation = stationary wave Interference of two counter propagating waves (see e.g. http://www2.biglobe.ne.jp/~norimari/science/JavaEd/e-wave4.html)

Seismic normal modes  Periods < 54 min, amplitudes < 1 mm (Duck from Théocrite, © J.-L. & P. Coudray) Few minutes after the earthquake Constructive interferences  free oscillations (or stationary waves) Few hours after the earthquake (0S20)  Periods < 54 min, amplitudes < 1 mm  Observable months after great earthquakes (e.g. Sumatra, Dec 2004 took about 5 months to decay)

Travelling surface waves This record section plot displays vertical displacements of the Earth's surface recorded by seismometers plotted with time (since the earthquake initiation) on the horizontal axis, and vertical displacements of the Earth on the vertical axis (note the 1 cm scale bar at the bottom for scale). The traces are arranged by distance from the epicenter in degrees. The earliest, lower amplitude, signal is that of the compressional (P) wave, which takes about 22 minutes to reach the other side of the planet (the antipode). The largest amplitude signals are seismic surface waves that reach the antipode after about 100 minutes. The surface waves can be clearly seen to reinforce near the antipode (with the closest seismic stations in Ecuador), and to subsequently circle the planet to return to the epicentral region after about 200 minutes. A major aftershock (magnitude 7.1) can be seen at the closest stations starting just after the 200 minute mark (note the relative size of this aftershock, which would be considered a major earthquake under ordinary circumstances, compared to the mainshock). Richard Aster, New Mexico Institute of Mining and Technology Rick Aster, Colorado State University http://www.iris.iris.edu/sumatra/

Historic  First theories: • First mathematical formulations for a steel sphere: Lamb, 1882: 78 min • Love, 1911 : Earth  steel sphere + gravitation: eigen period = 60 minutes  First Observations: • Potsdam, 1889: first teleseism (Japan): waves can travel the whole Earth. • Isabella (California) 1952 : Kamchatka earthquake (Mw=9.0). Attempt to identify a « mode » of 57 minutes. Wrong but reawake interest. • Isabella (California) 22 may 1960: Chile earthquake (Mw = 9.5): numerous modes are identified • Alaska 1964 earthquake (Mw = 9.2) • Columbia 1970: deep earthquake (650 km): overtones  IDA Network

On the sphere… n = radial order n = 0 : fundamental Vibrating string: On the sphere: Radial eigenfunction Surface eigenfunction n = radial order n = 0 : fundamental n > 0 : overtones l, m = surface orders l = angular order -l < m < l = azimuthal order

Why study normal modes? Almn are the excitation amplitudes, analogous to An in the 1D (string) example… So from measurements of u one can get information about the source (provided the eigenfrequencies lmn are known!) Conversely, given a source function Almn and known lmn, one can predict u… The modes form the basis vectors to describe displacements if one wants to model synthetic seismograms. The frequencies lmn depend on density, shear modulus, and compressibility modulus of the Earth… so are used to get Earth structure. 8

Recall PREM is derived from normal modes!