1. Three-dimensional velocity models and probabilistic earthquake location
Title
Stephan Husen
Institute of Geophysics, ETH Zurich, Switzerland,
with contributions from
Anthony Lomax
Scientific Software, Mouans-Sartoux, France,
Edi Kissling
Institute of Geophysics, ETH Zurich, Switzerland

2. Linearized earthquake location
Introduction
Linearized earthquake location
linearized earthquake
location
Traditional earthquake location
linearized methods (HYPO71, HYPOELLIPSE, HYPOINVERSE,..)
3D Velocity Model
1-D velocity models (plus station delays)
Probabilistic Earthquake
Location
error bars or error ellipses (linear)
Location Examples
efficient
Introduction: What is been used currently in routine earthquake location. Why? Limitations.
…. but linearized methods and 1-D velocity models are only approximations!
Conclusions

3. what do we need Introduction How can we improve the situation?
improvement
How can we improve the situation?
3D Velocity Model
3-D velocity models (Local earthquake tomography, controlled-source experiment)
Probabilistic Earthquake
Location
Non-linear earthquake location (NonLinLoc)
Location Examples
Conclusions

4. Example mine blast Introduction Mine Blast - True location is known
relocation mine blast
Mine Blast - True location is known
3D Velocity Model
Probabilistic Earthquake
Location
Location Examples
True location
True location
Introduction: What is been used currently in routine earthquake location. Why? Limitations.
Non-linear solution (3D)
Linear solution (1D)
Linear solution (1D)
Conclusions

5. Data quality 3D Velocity Model Introduction Probabilistic Earthquake
earthquake data in Switzerland
Probabilistic Earthquake
Location
Location Examples
Describe process of creating a 3-D velocity model for Switzerland. First, local earthquake data. Only highest quality could be used since data is picked by many different people. Earthquakes are well distributed within the crust; lower crust is only poorly sampled.
729 earthquakes with 10,044 P-observations
Conclusions
only highest quality data (impulsive onsets)

6. Moho topography 3D Velocity Model Introduction
Probabilistic Earthquake
Location
Location Examples
Numerous wide-angle and reflection profiles were conducted in Switzerland to determine the crustal structure. Pn and PmP phases(red lines) were used to develop a 3-D model of Moho topography beneath Switzerland. Data was weighted by their quality. Surfaces were interpolated by requiring the smoothest topography possible to fit the data.
Waldhauser et al., 1998
3-D Moho topography beneath Switzerland as determined by controlled-source seismology data
Conclusions

7. Min. 1D model 3D Velocity Model Introduction Subset of 200 earthquakes
Simultaneous inversion for 1D velocity models, hypocenter locations, and station delays
Probabilistic Earthquake
Location
Location Examples
Describe process of creating a 3-D velocity model for Switzerland. First, local earthquake data. Only highest quality could be used since data is picked by many different people. Earthquakes are well distributed within the crust; lower crust is only poorly sampled.
Software VELEST
Initial models
Final models
Conclusions

8. LET model 3D Velocity Model Introduction Probabilistic Earthquake
local earthquake
tomography
Probabilistic Earthquake
Location
Lower crust / Moho is not well resolved
crust is well resolved
Location Examples
Final P-wave model determined by earthquake data shows good resolution in the crust. Figure shows two vertical cross sections through the model. Dashed line denotes approximate position of Moho. We see significant velocity variations. However, lower crust / Moho is not well resolved. Moho topography beneath Switzerland is important because we often observe Pn at large distances.
3-D P-wave velocity model determined by local earthquake data
Conclusions
Software SIMULPS14

9. CSS model 3D Velocity Model Introduction Probabilistic Earthquake
controlled-source data
Probabilistic Earthquake
Location
Location Examples
Controlled-source data was converted into a 3-D P-wave velocity model. No lateral velocity variations in the crust but precise information on Moho topography and sedimentary basins
Conclusions
3-D P-wave velocity model determined by controlled-source seismology (CSS) data

10. Final model 3D Velocity Model Introduction Probabilistic Earthquake
final (combined) model
Probabilistic Earthquake
Location
Location Examples
Lower crust / Moho is controlled by CSS data
crust is controlled by earthquake data
CSS model used as initial model for local earthquake tomography. In areas of good resolution model shows velocities determined by earthquake data. In areas of low resolution, model stays close to the CSS model. Thus, reliable crustal velocities, Moho topography, and velocities in major sedimentary basins.
Conclusions
Final 3D P-wave velocity model determined by earthquake data and controlled-source data

11. NonLinLoc Tarantola and Valette (1982)
Introduction
NonLinLoc
Tarantola and Valette (1982)
3D Velocity Model
Posteriori Probability Density Function (x) (PDF):
(x) = K(x)*exp[-1/2misfitL2(x)]
Probabilistic Earthquake Location
relies on known a priori information (x) on model parameters and on observations.
software NonLinLoc
PDF is computed using global sampling techniques - grid search or Oct-Tree importance sampling.
Location Examples
Probabilistic earthquake locations is based on formulation of the probabilistic formulation of inversion by Tarantola and Valette (1982). For the earthquake location problem the solution is given by the PDF. The PDF relies on probability density functions to express our knowledge about model parameters and observations including errors. Errors need to be Gaussian. The PDF is the full, non-linear solution to the earthquake location problem and includes complete location uncertainties, which can be non-linear. Approach has been coded into software package NonLinLoc by Anthony. Available on the internet.
PDF gives complete location uncertainties.
Conclusions
Software NonLinLoc:

12. Global sampling methods
Introduction
Global sampling methods
Grid-Search
3D Velocity Model
Probabilistic Earthquake Location
Grid-Search
Location Examples
How can we compute the PDF? Two approaches: grid-search and global sampling methods. Grid-search computes PDF at every point in the grid. Series of nested grid with decreasing sampling interval and size of the grid. Grid-search gives complete PDF but is inefficient and computationally intensive, thus slow.
complete mapping
Conclusions
inefficient and slow

13. Global sampling methods
Introduction
Global sampling methods
Grid-Search
Oct-Tree sampling
3D Velocity Model
Probabilistic Earthquake Location
Grid-Search vs.
Oct-Tree sampling
Location Examples
Second approach: Oct-Tree importance sampling. Sample only those areas densely where PDF shows strong topography, i.e. close to minima. Final number of cells is given by user. Very efficient since not the entire PDF is sampled, thus fast. But Oct-Tree does not give complete information on PDF. Multiple minima, however, are detected. Oct-Tree is very appropriate for routine earthquake location.
complete mapping
importance sampling
Conclusions
inefficient and slow
efficient and fast

14. Location uncertainties
Introduction
Location uncertainties
Grid-search
Oct-Tree importance sampling
3D Velocity Model
Probabilistic Earthquake Location
solution and location uncertainties
Location Examples
Representation of location uncertainties. Grid-search: confidence contours -> complete. Oct-Tree: scatter clouds obtained by drawing samples from the PDF proportional the probability -> discrete, not complete. NonLinLoc also computes traditional 68% error ellipsoid and Gaussian expectation hypocenter.
confidence contours
scatter clouds
Conclusions
maximum likelihood hypocenter location
68% confidence ellipsoid

15. Example 1 Location Examples Introduction 3D Velocity Model
: N E 4.1km
3D Velocity Model
Nobs: 8
RMS: 0.04 s
GAP: 193
Dmin: 1.9 km
Probabilistic Earthquake Location
Difference:
dx: 1.0 km
dy: 5.2 km
dz: 0.1 km
Location Examples
In the following examples of earthquake locations obtained with NonLinLoc using the 3-D velocity model presented before. Maximum likelihood location is at intersection of green lines; SED routine location (linear) is at intersection of black lines. Difference denote distance between non-linear and linear (SED) earthquake locations. This is an example of highly non-linear location uncertainties, which cannot represented by error ellipsoid. Although both locations are close, error given by SED is way too small and does not reflect the true errors. In addition, standard parameters such as RMS, GAP, nobs, Dmin do not indicate the poor location quality.
non-linear uncertainties
SED error:
ERRH: 1.9 km
ERRZ: 2.6 km
Non-linear(3D)
Conclusions
Linear(1D)

16. Example 2 Location Examples Introduction 3D Velocity Model
: N E -0.9 km
3D Velocity Model
Nobs: 8
RMS: 0.14 s
GAP: 164
Dmin: 16.9 km
Probabilistic Earthquake Location
Difference:
dx: 2.5 km
dy: 3.0 km
dz: 15.7 km
Location Examples
This is an example of a well defined hypocenter location with a single minima. However, focal depth shows large errors because no observation within focal depth distance. SED located the event much deeper. In addition, error estimates (shown by blue crosses) are too small such that a seismologist would interpret the earthquake to be within the crust. In fact, it is likely that the event is located in the upper crust.
no control on focal depth
Non-linear(3D)
SED error:
ERRH: 2.2 km
ERRZ: 2.6 km
Linear(1D)
Conclusions

17. Mine Blast Location Examples Introduction 3D Velocity Model
: N E 4.1km
3D Velocity Model
Nobs: 26(8)
RMS: 0.26(0.03) s
GAP: 73
Dmin: 22.8 km
Probabilistic Earthquake Location
Difference:
dx: 1.0 km
dy: 5.2 km
dz: 0.1 km
Location Examples
true location
Relocation of mine blasts or shots from refraction experiments provide important information on absolute location errors. So far, location uncertainties were only relative since we cannot quantify the error of our velocity model. This is an example of a well recorded mine blast. However, only epicenter is well constrained since no station was nearby. Epicenter locations of SED and our are close to the true location. SED used only 8 observations since observations at distances > 80 km often show Pn as first arrival, which is poorly modeled with a 1-D velocity model. Using our 3-D velocity model we can use all phases. Focal depth estimates are too deep for both locations. However, true location is within our location uncertainties that are large. SED error is again much smaller. Based on the SED location, one would interpret this event to be an earthquake within the crust.
mine blast
SED error:
ERRH: 0.7 km
ERRZ: 2.0 km
Conclusions

18. Conclusions Conclusions Conclusions Introduction 3D Velocity Model
combination of local earthquake data and controlled-source data provides reliable 3-D velocity models
Probabilistic Earthquake Location
probabilistic earthquake location combined with global sampling algorithms is efficient and reliable
location uncertainties obtained by probabilistic earthquake location prove to be much more reliable, important for planetary data sets with few instruments
Location Examples
Conclusions

19. Conclusions Outlook Conclusions Introduction
application and tuning of existing geophysical methods to planetary data sets (real and synthetic) considering their peculiarities, i.e. small number of receivers
3D Velocity Model
Probabilistic Earthquake Location
Location Examples
Conclusions