EPS207 Laboratory in Observational Seismology

Class Meetings Friday morning from 9am-12noon Room: 365 McCone

Course Objectives Review and learn common methods for seismogram synthesis. Learn techniques of waveform modeling. Learn to recognize source and propagation components of observed waveforms. Develop waveform modeling projects which can be used to build Senior Honors, Masters and Ph.D. theses.

Class Structure Student presented literature review. Student presented computer exercises Final term research project (started about mid-term, and counting for the entire course grade) Example Term Paper

U(t)=S(t)*[g(t)*a(t)]*I(t) Linear Filter Theory U(t)=S(t)*[g(t)*a(t)]*I(t) U(t)=S(t)*G(t)*I(t) U(w)=S(w)G(w)I(w)

Instruments Modern broadband system

Sources Finite-Source Magnitude Point-Source

Approximations of the Representation Theorem Spatial point-source Spatial and temporal point-source M has units of moment. i and j refer to directions of forces and derivatives. i.e. they define couples

Whole Space Half Space Rewriting Linear Equation

Three Fundamental Fault Synthetics Sum to produce any arbitrary mechanism

There are 5 independent scaling coefficients (A) The A coefficients are functions of station azimuth, strike, dip and rake.

Approximations of the Representation Theorem Spatial point-source Spatial and temporal point-source M has units of moment. i and j refer to directions of forces and derivatives. i.e. they define couples

Parkfield Moment Tensor MHC ISA MHC ISA

What can we estimate from these waveforms?

AMP=5 CM DURATION=4 SEC

Ahyi Kim’s Parkfield Source Model Mo=1.1e+25 dyne cm MW=6.0

You Will Model This Record

Example of Northridge Modeling

How are Green’s Functions Computed? General Equation of Motion Assume Isotropy Vector Wave Equation

Finite-Differences

How are Green’s Functions Computed? General Equation of Motion Assume Isotropy Vector Wave Equation

Helmholtz Decomposition 1 2 f, , c, are scalar displacement potential functions. Application of the above relationships to the vector wave equation results in three separated scalar wave equations for P, SV and SH waves

Substitution of 2 into 1

S-waves SV waves SH waves

P-waves P waves

How is vector motion found? Why go to such trouble? Solutions to scalar wave equations are simpler. What has been assumed? Homogeneous media leading to 1D boundary value problems How is vector motion found? Solve each scalar wave equation separately and then combine using Helmholtz equation

Green’s Function Solution

First Assignment Read selected papers on Generalized Ray Theory (paper 2) Perform Computer exercises Lab 0 and Lab 0.1 Come prepared to discuss the papers Come prepared to discuss the computer exercises If possible bring your laptops to class so we can have “online” class discussions