California Institute of Technology – Seismological Laboratory GE 162 Introduction to Seismology Lecture notes Jean Paul (Pablo) Ampuero – [email protected] Winter 2013 - 2016 GE 162 Introduction to Seismology Winter 2013 - 2016 Contents 1 Overview and 1D wave equation .......................................................................................................... 5 1.1 Overview, etc ................................................................................................................................ 5 1.2 Longitudinal waves in a rod: derivation of the wave equation .................................................... 5 1.2.1 Description of the problem and kinematics.......................................................................... 5 1.2.2 Dynamics ............................................................................................................................... 6 1.2.3 Rheology ............................................................................................................................... 6 1.2.4 The 1D wave equation .......................................................................................................... 6 2 1D wave equation: solution and main properties ................................................................................ 8 2.1 General solution ............................................................................................................................ 8 2.2 Reflection at one end .................................................................................................................... 8 2.3 Fourier transform .......................................................................................................................... 9 2.4 Harmonic waves ............................................................................................................................ 9 3 Energy, reflection/transmission, normal modes ............................................................................... 11 3.1 Impedance .................................................................................................................................. 11 3.2 Energy considerations for harmonic waves ................................................................................ 11 3.3 Reflection and transmission at a material interface ................................................................... 11 3.4 Normal modes of a finite elastic rod ........................................................................................... 12 3.5 Duality between modes and propagating waves........................................................................ 13 4 Green’s function. Waves in heterogeneous media. ........................................................................... 14 4.1 Linear invariant systems, Green’s functions, convolution .......................................................... 14 4.2 Green’s function for the 1D wave equation ............................................................................... 14 4.3 Waves in heterogeneous medium (WKBJ approximation) ......................................................... 15 5 The 3D elastic wave equation ............................................................................................................. 16 5.1 Strain ........................................................................................................................................... 16 5.2 Stress ........................................................................................................................................... 16 5.3 Momentum equation .................................................................................................................. 16 5.4 Elasticity ...................................................................................................................................... 16 5.5 The seismic wave equation ......................................................................................................... 17 5.6 It’s a perturbative equation ........................................................................................................ 17 5.7 P and S waves examples ............................................................................................................. 17 5.8 General decomposition into P and S waves ................................................................................ 18 1 GE 162 Introduction to Seismology Winter 2013 - 2016 5.9 Polarization of body waves ......................................................................................................... 18 5.10 Usual characteristics of body waves ........................................................................................... 19 6 Body waves ......................................................................................................................................... 20 6.1 Spherical waves, far-field, near-field .......................................................................................... 20 6.2 Ray theory: eikonal equation, ray tracing ................................................................................... 20 6.3 Rays in depth-dependent media, Snell’s law, refraction ............................................................ 21 7 More on body waves .......................................................................................................................... 22 7.1 Layer over half-space: head waves ............................................................................................. 22 7.2 A steep transition zone ............................................................................................................... 23 7.3 A low velocity zone ..................................................................................................................... 23 7.4 Wave amplitude along a ray ....................................................................................................... 25 7.5 Ray parameter in spherically symmetric Earth ........................................................................... 25 7.6 Body waves in the Earth .............................................................................................................. 25 8 Surface waves I: Love waves ............................................................................................................... 30 8.1 Separation between SH and P-SV waves .................................................................................... 30 8.2 SH reflection and transmission coefficients at a material interface ........................................... 30 8.3 Love waves .................................................................................................................................. 32 8.4 Dispersion relation ...................................................................................................................... 32 8.5 Phase and group velocities ......................................................................................................... 34 8.6 Airy phase .................................................................................................................................... 35 9 Surface waves II: Rayleigh waves ........................................................................................................ 36 9.1 Rayleigh waves ............................................................................................................................ 36 9.2 Surface waves in a heterogeneous Earth .................................................................................... 38 9.3 Implications for tsunami waves .................................................................................................. 39 10 Normal modes of the Earth ............................................................................................................ 40 11 Attenuation and scattering ............................................................................................................. 47 11.1 Attenuation of normal modes .................................................................................................... 47 11.2 A damped oscillator .................................................................................................................... 48 11.3 A propagating wave .................................................................................................................... 48 12 Scattering ........................................................................................................................................ 50 13 Seismic sources. .............................................................................................................................. 55 13.1 Kinematic vs dynamic description of earthquake sources ......................................................... 55 2 GE 162 Introduction to Seismology Winter 2013 - 2016 13.2 Stress glut and equivalent body force ........................................................................................ 55 13.3 Equivalent body force representation of fault slip ..................................................................... 55 13.4 Moment tensor ........................................................................................................................... 56 13.5 Seismic moment and moment magnitude ................................................................................