1. Wavefield Calibration Using Regional Network Data
R. B. Herrmann
Saint Louis University
C. J. Ammon
Pennsylvania State University

2. Questions What degree of calibration is required?
What can be done with a very good regional data set?
Crustal seismology is entering into a new age with the deployment of dense portable seismic arrays. The USArray effort of IRIS will entail the deployment of a large number of modern digital seismic instruments that will slowly cover the continental U.S. over a ten year period.
One type of crustal study that can be performed is related to learning enough to locate of earthquakes precisely. This requires good depth and origin time estimates as well as the determination of the epicentral coordinates. Surface-wave dispersion and receiver function studies may permit the determination of the crustal structure sufficiently well to accomplish this task.
We can begin to evaluate analysis techniques by processing data from a modern digital broadband seismic network, such as the one in Korea.

3. Joint Inversion
We will us the tool of joint inversion of surface wave dispersion and receiver functions to estimate the Earth model. The quantity S is to be minimized and in constructed to be a number in the range [0, 1] IF the data variances are known. The parameter ‘p’ selects between the importance of the receiver functions (p=0) and the surface-wave dispersion (p=1).
We have found the p=0.5 does not give equal weight to the two types of data. In addition the values of the sigma’s have a strong effect on the inversion.

4. Rayleigh Wave Sensitivity
It is useful to visualize the sensitivity of the data sets to perturbations in shear-wave velocity to be able to appreciate the limitations in an Earth model based on real data.
This figure shows the partial derivative with respect to shear-wave velocity of the Rayleigh wave phase velocity at periods of 10 and 40 seconds. Note that the partials are smooth, indicating that dispersion data from one mode of themselves will not require velocity discontinuities in the crust.

5. RFTN Partials
This figure shows the partial derivative of the receiver function with respect to a change in shear velocity in a layered model. The receiver function is at the bottom. The upper half of the model corresponds to the upper 50 km which happens to have uniform mantle-like velocity.
This figure indicates the following:
o Early parts of the receiver function are controlled by shallow structure.
o Later parts indicate a tradeoff between deeper and shallow structure.
RFTN

6. Postulated Advantages of Joint Inversion
Receiver function depends upon travel time and fine detail of structure related to conversions
Surface wave is smoothly affected by velocities So
Advantages of one overcome deficiencies of the other
Well this has to be tested.

7. Purpose of models
Assist location by correctly predicting first arrivals
Properly characterize dynamic wavefield to obtain quantitative estimates of source mechanism and strength
These are reasons for refining a local velocity model. My interests are directed toward the second task.

8. Receiver Function Sensitivity to Structure
Perturb simple crust/mantle model
Examine effect of gradient
Design model to have same vertical travel time
Before we start inverting real data, it is useful to study the effect of the crust-mantle transition on observed data. We will construct many models and compare the gravity signature, surface-wave dispersion and receiver functions.

9. Red = sharp / Blue = strong gradient
This is the model. Remember the colors. Blue represents a strong gradient and red a sharp discontinuity. The models were constructed so that vertical P-wave travel time from the base of the model to the surface is constant.
Red = sharp / Blue = strong gradient

10. Gravity Anomaly Imagine sampling different structures within a region
What would be seen in Bouguer anomaly
Lets now compare the gravity signature. We may be able to use this in the future to look at regional variations.

11. 180 mGal variation among models
This is the gravity field. Note that there is a 180 mGal variation between the models - a variation that can be observed.
180 mGal variation among models

12. Love
Rayleigh
This figure compares fundamental and first higher mode surface wave dispersion for Love and Rayleigh waves for the models. This study indicates that we need to have dispersion finely sampled in the period range of the fundamental mode to be able to distinguish among the models. There is greater sensitivity in the group velocities than in the phase velocities. The sensitivity of the first higher mode is not very useful since it is harder to observe.

13. Surface waves
Subtle differences in dispersion for fundamental mode in second period range
For surface waves to really contribute structure information, need dispersion for a fine grid of periods
Need short periods to focus on upper crust
This summarizes the usefulness of the surface waves.

14. Receiver Functions
Slides for different filter parameter - alpha =1.0 corresponds to a lowpass corner of about 1/3.14 Hz
Focus on effect of Moho transition on nature of P-wave receiver function
Now let’s look at the receiver functions.

15. The first bump does not change amplitude because it only depends on the free surface partition of incident P-wave amplitude into radial and vertical components. The upper 20 km of the models are the same.
When using PowerPoint it is useful to use the array keys to move forward and backward here to see the changes with the filter parameter.

16. An alpha=1. 0 corresponds to a lowpass filter at about 0. 3 Hz
An alpha=1.0 corresponds to a lowpass filter at about 0.3 Hz. Note that the
second bump (corresponding to the conversion of p to S at the Moho) is
sensitive to the nature of the transition. The arrivals at about 18 and 23 seconds arise from the first reflections of the free surface, which are then turned back to the surface. A gradient does not reflect signals well.
If we do not see these latter two bumps, the transition mus be a gradient.

17. This filter is a lowpass at about 1.0 Hz.

18. This is a lowpass at about 2 Hz.

19. Comments 1st peak controlled by shallow structure
Gradient indicated by absence of signal for high alpha, character by low alpha
Sharp moho is indicated by distinct bounce arrivals for all alpha, especially higher
Simultaneous fit to several alpha robust

20. KOREA Can GT5 be defined? Can Earth model be defined that can or
fit receiver function data
model regional waveforms or
Is the joint inversion model of any value?
GT5 means can the epicenter be determined to within 5.0 km.
We would like to address these questions with a data set from Korea.

21. This is the map of Korea Geology - note the very old rocks at many locations.
The surface geology in south Korea is essentially old, except for the southeast corner.

22. This is a Bouguer gravity map
This is a Bouguer gravity map. There is some correlation with the archaen terrains. The very negative anomalies near Manchuria are interesting - are these data good enough or is this related to volcanism due to subduction.

23. To provide incentive for this study, the focal mechanisms of this earthquake was determined using waveform inversion:
21 NOV 2001

24. 21 NOV 2001
WVFGRD
This is the focal mechanism

25. These are the fits of the observed (light gray) to predicted (black) waveforms
The observed and predicted data have been bandpassed using the sac command indicated.
bp c np 2

26. This shows how well the waveforms are fit using the CUS model in the 50 sec - 4 sec period range.
bp c np 2

27. This comparison of ground velocties is a test of the adequacy of a simple model of the crust to predict absplute ground motions at high frequencies.
bp c np 2

28. Excellent fit, even at high frequencies but
used Central US model - not model derived specifically or even valid for Korea so
perform joint inversion surface - wave/receiver function for a Korea model
However, the CUS model was used since the Green’s functions were pre-computed. We should really use a Korea specific model.

29. This figure shows the broadband stations of KMA and KIGAM which provide the receiver functions for the study.

30. Arranged by similarity in shape
Receiver functions
Two filter parameters
Stacked RFTN’s
Arranged by similarity in shape
Last 3 are from island stations
Similarity in RFTN’s -> similarity in structure
These are stacks of the individual receiver functions. Two filter settings were used. The number indicated the number of RFTN’s used to make the stack.

31. Phase velocity (Herrmann, 2001) - Group velocity (Stevens, 1999)
Here is the initial dispersion information. This corresponds from a few pahse velocity pooints from Herrmann (2001) and Stevens (2002) group velocity estimates.
SNU (InvSNU)
Phase velocity (Herrmann, 2001) - Group velocity (Stevens, 1999)

32. Stacked receiver function for alpha 1 and 2.5 25 stations
Dispersion Stevens (1999) and a few phase velocity points
joint96
same script (iterations controls ) for all
AK135 (modified)
This is what was done

33. This is the fit to the SNU RFTN data
This is the fit to the SNU RFTN data. The dispersion fit was indicate dint eh previous slide.
SNU (InvSNU)

34. Average of layer velocities, not slowness
All models
Average of layer velocities, not slowness
This is a superposition of all 25 models.

35. P-wave 1st Arrival Surface focus
This is the superposition of the predicted P-wave first arrival times for a surface focus event. Note the similarity.

36. Good fits to both data sets
Subtle differences in P-wave first arrival times
Models do not fit 21 NOV 01 earthquake data - surface wave arrival too late So
Augment with CUS dispersion
The lack of waveform fit to the data is a strong statement that the models are not correct. So

37. Lets force a fit by adding CUS model dispersion for periods less than 30 sec. The red curve is the prediction of the model at left.
SNU (nInvSNU)

38. Strong constraint on upper crust
The additional dispersion data does not permit much variability in the upper crust.

39. Fits using CUS dispersion
We can still fit the receiver functions (red - observed) (blue - predicted). We do not do well for the island stations of ULL SOG and SGP

40. P-wave 1st arrival surface focus
The predicted first arrival times change less too

41. SNU Model comparison
Red - first
Blue - CUS

42. Discussion RFTN need very good dispersion
Model requires independent test - waveform modeling?

43. New Dispersion Data Harvard group velocities Colorado group velocities
Phase velocities from Korea
Treat BB network as array
Optionally apply match filter
Apply McMechan and Yedlin p-tau implemented as sacpom96

44. 01 Jan 2001 Alaska Event - phase match output used from 10 stations
This is an example of applying sacpom96 to teleseismic data. The idea is to project the station data onto a great circle path and then perform a p-omega stack. Errors are introduced if the actual wave propagation path is not along the great circle. The bias is such that the estimates will be >= observed pahse velocity.
01 Jan 2001 Alaska Event - phase match output used from 10 stations

45. Red - Korea phase velocity
This is the new data set. The dispersion data set is domiinated by the new pahse velocity observtions. We aill have to down weight this later to add more influence to the group velocities.
Note that because of the very long periods observed, we will need a deeper starting model.
Also note that we need good dispersion values at periods less than 10 seconds, which can be obtained if we look at some regionmal events, e.g., < 20 degrees epicentral distance. To avoid multipathing effects, we should look for paths from the SW and NW quadrants.
Blue - Colorado
Green - Harvard
Orange - Stevens
Red - Korea phase velocity

46. Starting Model AK135 - depths > 50 km
Upper 50 km is a halfspace with velocity of z=50 km
Invert new dispersion
Use stacked RFTN’s
Use same script

47. Well we can fit the data. Not that the upper mantle changes
Well we can fit the data. Not that the upper mantle changes. Can we image the plate subducting beneath Korea?

48. This is the fit to the receiver functions.

49. Test Compare data, CUS and Korea model
Add modes to save time - so no P
Bandpass Hz

50. Traces are aligned at origin time.83 96 98
100
126
Red - observed
Green = CUS
Blue = Korea model
Note for speed in computation, model superposition was used to generate the KOREA synthetics, while wve-number integration was used with the CUS model.
Traces are aligned at origin time.
143

51. 143
148
163
191
200
Continued
Slight timing differences are seem, which are significant when applying waveform inversion techniques to get focal mechanisms for small earthquakes, for which there is little long period signal above noise.
208

52. Focal Mechanisms 21 NOV 2001 - waveform Mw=3.3
09 DEC surface-wave radiation pattern Mw=4.0
does not require precise location
does not require precise Earth model
does not require broadband signal
works with high noise

53. Rayleigh Wave
This shows the use of surface-wave radiation patterns to get the mechanisms of the 09 December 2000 earthquake.

54. Love Wave
Fortunately the mechanism was such that permitted us to observe the shape of the Love wave radiation pattern.

55. SEO spectra
This shows the fit tot he observed spectra at one station.

56. New Mechanisms
Since this presentation on April 25, 2003, the focal mechanism for the 09 Jan 2003 event has also been determined

57. KOREA Good data sets but little local activity
Waveforms exhibit distinct P and sP
together these are good depth indicators
Data are available to improve dispersion estimates
Some events may have good azimuthal distribution and stations to 200 km

58. Future work Continued interaction with SNU and KMRI on
Ground motion scaling with distance
Location
Source mechanisms
Seismic Hazard maps

59. Organize and dig into data sets
Get more data, especially events within 20 degrees away in NW and SE sector from Korea
Why? Get shorter period dispersion
Digital data available from KMA website (if one reads Korean)

60. to study Teleseismic P-wave residuals 1 Hz dispersion for upper 1 km
What is high frequency phase attenuation

61. Questions What degree of calibration is required?
What can be done with a very good regional data set?

62. and Computer Programs in Seismology
no major release - bug fixes
Simple command line programs for location
sacloc *.sac
eqlocate

63. ELOCATE sac2eloc *.sac elocate -DEPTH -10 -M 7 -BATCH
Error Ellipse X= km Y= km Theta = deg
RMS Error : sec
Travel_Time_Table: CUS
Latitude : N km
Longitude : E km
Depth : km
Epoch Time : sec
Event Time : sec