1. EPS207 Laboratory in Observational Seismology

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

3. 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.

4. 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

5. 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)

6. Instruments
Modern broadband system

7. Sources
Finite-Source
Magnitude
Point-Source

8. 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

10. Whole Space
Half Space
Rewriting
Linear Equation

12. Three Fundamental Fault Synthetics
Sum to produce any arbitrary mechanism

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

14. 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

16. Parkfield Moment Tensor
MHC
ISA
MHC
ISA

17. What can we estimate from these waveforms?

18. AMP=5 CM
DURATION=4 SEC

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

21. You Will Model This Record

22. Example of Northridge Modeling

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

24. Finite-Differences

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

26. Helmholtz Decomposition1 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

27. Substitution of 2 into 1

28. S-waves
SV waves
SH waves

29. P-waves
P waves

30. 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

31. Green’s Function Solution

35. 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