An Introduction to Surface Wave Analysis Michael E. Pasyanos - IRIS

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Phase Velocity Measurements Single station (event-station) • Need to know the source phase ϕ 0 , 2π indeterminacy Mechanism and depth needed to determine source phase ϕ 0 . Unwrapping the phase by working from long periods. u(x, t) = 1 π AMPLITUDE ∞ ∫ 0 PHASE & ω û(ω, x)× cos ωt − c(ω) x + φ (ω) ) ( 0 + dω ' * φ(ω) = φ 0 (ω)− ωx 1 + 2πN + ωt c(ω) ψ 1 (ω) = ωt 1 + φ o (ω)− ωx 1 c(ω) + 2πN
Phase Velocity Measurements Two-station method (event-event) • Source phase ϕ 0 cancels • Still have 2π indeterminacy ψ 1 (ω)− ψ 2 (ω) = ω(t 1 − t 2 )− c(ω) = ω c(ω) (x − x 1 2 )+ 2πM x 1 − x 2 (t 1 − t 2 )+ T[M − (1/ 2π)(ψ 1 (ω)− ψ 2 (ω))] Two-plane method (Forsyth, 1998) § uses the sum of two plane waves, each with initially unknown amplitude, initial phase, and propagation direction to represent the nonplanar incoming wavefield, i.e., a total of six parameters to describe the incoming wavefield. U(ω) = A 1 (ω) exp(-iφ 1 ) + A 2 (ω) exp(-iφ 2 ) φ 1 = φ 1 0 + ω[r cos(ψ - θ 1 ) - x]/c(ω) + ω(τ-τ 0 ) φ 2 = φ 2 0 + ω[r cos(ψ - θ 2 ) - x]/c(ω) + ω(τ-τ 0 )
Page 1 and 2: An Introduction to Surface Wave Ana
Page 3 and 4: Section 1 - Background on Surface W
Page 5 and 6: Group Velocity vs. Phase Velocity S
Page 7 and 8: Rayleigh Waves Designated LR = “L
Page 9 and 10: Rayleigh Waves vs. Love Waves Unrot
Page 11 and 12: Higher Modes Higher mode exist, but
Page 13 and 14: Dispersion Variations: Crustal Thic
Page 15 and 16: Sensitivity kernels Sensitivity ker
Page 17 and 18: Applications Joint inversion of sur
Page 19 and 20: Recent Tectonic History of Middle E
Page 21 and 22: Surface Wave Results for the Middle
Page 23 and 24: Section 2 - Surface Wave Analysis -
Page 25 and 26: Multiple-Filter Analysis PGSWMFA =
Page 27 and 28: Ambient Noise Analysis Has the pote
Page 29: Consistency between group and phase
Page 33 and 34: Seismic Tomography - Importance of
Page 35 and 36: Getting from dispersion maps and di
Page 37 and 38: Inversion vs. grid search The inver
Page 39 and 40: Results can be combined to produce
Page 41 and 42: Tradeoffs among various parameters
Page 43 and 44: One approach employed in Pasyanos a
Page 45 and 46: Summary § § § § § The analysis
Page 47 and 48: Surface Wave Model - Coverage Paths
Page 49 and 50: Examples get_dispersion 23.522499 4
Page 51 and 52: Tools Comparing between dispersion
Page 53 and 54: Introduction Crustal models like CR
Page 55 and 56: Parameterization Lateral Parameteri
Page 57 and 58: Varying the starting model After cr
Page 59 and 60: We assemble the results to construc
Page 61 and 62: High-resolution regional results fo
Page 63 and 64: Depth slices through the model 50 k
Page 65 and 66: High-resolution regional results fo
Page 67 and 68: The resulting model recovers the di

An Introduction to Surface Wave Analysis Michael E. Pasyanos - IRIS

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