Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Seismology Lecture 3 EPS 122 –Spring 2017 Thursday 02/23/2017 Instructor: Barbara Romanowicz Equation of motion (Isotropic, homogeneous medium, 1D) ∂2 u ∂2 u ρ 2 = (λ + 2µ ) 2 + f ∂t ∂x Medium described by : (ρ,λ,µ) or (ρ ,α ,β) P waves – velocity: λ + 2µ VP = α = ρ S waves - velocity µ VS = ρ Polarisation of P and S waves S waves are shear waves No volume change, shear and rotaIon P waves and S waves have different velociIes Vs < Vp P waves are compressional waves cause volume change – compression And rarefacIon No rotaIon Similar to sound waves in air Ref: Stein and Wysession Rotation of coordinate system • Instruments are generally oriented (Z, N, E) • Ray path is in the vertical plane containing the source and the receiver • In the horizontal plane tangent to the earth’s surface at the location of the station, we want to rotate the coordinate system from (N,E) to (L,T) where: – L is for “longitudinal” – indicating the sourcestation great circle direction – T is transverse: 90 degrees from L (conventionally counted counterclockwise) Shallow earthquake From Stein and Wysession, 2003 ALPHABET SOUP FOR SEISMIC WAVES core mantle Reflected waves on the CMB and the ICB SS P S Surface waves Shallow earthquake From Stein and Wysession, 2003 Surface waves • Two types – Rayleigh waves (R) – Love waves (G) Appear on different seismometer components Surface waves • The amplitude of surface waves decays with depth and depends on the ratio of the depth to the wavelength. – => longer period (i.e. longer wavelength) surface waves tell us more about deeper parts of the mantle – => shorter period surface waves are appropriate for studying the shallow parts (crust, uppermost mantle) • Surface waves are primarily sensitive to shear wave velocity • They are dispersive (velocity depends on period) – Generally longer period waves arrive first Mongolia earthquake recorded in Japan Surface wave dispersion • Group velocity (U) – km/s – Velocity of travel of energy at a particular frequency • Phase velocity (C) - km/s – Velocity of travel of a particular phase (peak or trough) • Consider the sum of two harmonic waves with slightly different angular frequencies and wavenumbers: u(x, t) = cos(ω1t − k1 x) + cos(ω 2 t − k2 x) with : ω1 = ω + δω1;ω 2 = ω − δω ; δω << ω k1 = k + δ k;k2 = k − δ k;k << k • We obtain: u(x, t) = 2 cos(ω t − kx)cos(δω ⋅ t − δ k ⋅ x) u(x, t) = 2 cos(ω t − kx)cos(δω t − δ kx) carrier Envelope travels at group velocity: dω U= dk Carrier travels at phase velocity: C= ω k Lower frequency smaller wavenumber: varies more slowly in Ime and space: envelope RelaIon between group and phase velocity: U= dω dk => ω C= k U =C+k dC dC = C +ω dk dω (layer over half-‐space)