GOCAD ENSG Conference
3D Modeling of Natural Objects : A Challenge for the 2000's
4 - 5 June 1998
Modeling Fault Surfaces from Earthquake Hypocenters with gOcad
Sara Carena (1)
(1) Princeton 3D Structure Project
Geosciences Dept., Princeton University, Princeton, NJ 08540, U.S.A.
Email: firstname.lastname@example.org - Phone: (609) 258 1515
Until recently only limited 3D imaging and model-building tools have been available to seismologists to get a true 3D view of the distribution of earthquakes on a fault surface, even though this can be a great help in understanding and modeling earthquake processes.
In the past year, Van Dusen  and Zimmer  explored the use of gOcad in modeling fault surfaces from earthquake hypocenter locations. Their work shows that gOcad can indeed be suitable for this purpose, but there are also some specific difficulties building fault-surface models from earthquakes. The main problem is the difficulty of creating branching surfaces from a set of points, whereas real faults often show splays. Another problem is the large random errors in earthquake locations which can result in the formation of many geologically unrealistic "bumps" on the model fault surface.
Methods and Results
In order to find the best procedure to model fault surfaces in 3D from earthquake data, I repeated the procedures of both Van Dusen and Zimmer, comparing the results. I generated fault surfaces using approximately 8000 aftershocks of the Loma Prieta earthquake located by Dietz and Ellsworth . I discarded all earthquakes with either vertical or horizontal errors equal or larger than 5.0 km, then applied a clustering code by Jones and Stewart  on the remaining points. This code moves the aftershock hypocenters with respect to one another on the basis of their error ellipsoids, and the result is a tighter clustering of the hypocenters. Less scattering in the point set means fewer bumps on the final surface. As far as branching surfaces are concerned, splitting the original data set in as many subsets as the number of different surfaces  seems to give good results, though the techniques for rejoining the surfaces need some improvement (holes or overlaps can form along the suture). After creating and rejoining all branches, I computed errors, with respect to the original point set, on the fault surfaces. High-error areas generally indicate complex structures that were not adequately resolved (like splays or en echelon faults), thus I used them as a guide to get better fitting surfaces.
Of course, simply creating a surface from earthquake locations is only the first step towards modeling fault surfaces. I included then other data in the model as properties, either stored directly in the original point set (like magnitude and origin time of each earthquake), or projected onto the surface generated from it (like slip associated with the main shock).
As far as the slip is concerned, I projected data coming from three different models onto the fault surface. All three models represent the fault surface as a plane roughly parallel to the northern part of the real fault. Berozas model  has by far the greatest number of data, and gives therefore the most detailed results when projected onto the surface. Beroza already noticed that areas of high slip usually have fewer aftershocks. Gocad allows a far clearer view of the distribution of slip compared to the aftershocks pattern, because there is no need to project aftershocks on a plane, but rather the slip data are projected onto a more realistic fault plane.
Figure 1:slip amplitude from  compared to the aftershocks pattern.
With gOcad it was possible to determine a fairly realistic overall shape for a fault using earthquake hypocenters, though there are still some problems with the details of the fault surface. Gocad allows to store, manipulate and visualize in 3D with great detail many different kind of data for earthquakes, giving a much clearer idea of the situation than the usual maps or cross sections.
The next step will be to import focal mechanisms into gOcad and use them as constraints for fault surface. Also, I will try to apply the thread criterion  to further constrain the geometry of fault surfaces generated from earthquake hypocenters.
 Van Dusen, A.B., Determining the Three-dimensional Fault Shape from Earthquake Hypocenters, Senior Thesis, Princeton University, 1997.
 Zimmer, V., Three-dimensional Surface Model of the 1989 Loma Prieta Earthquake Fault, Junior Independent Work, Princeton University, 1997.
 Dietz, L.D., and Ellsworth, W.L., Aftershocks of the 1989 Loma Prieta Earthquake and their Tectonic Implications, Preprint, 1993.
 Jones, R.R., and Stewart, R.C., A Method for Determining Significant Structures in a Cloud of Earthquakes, JGR 102, 1997, 8245-8254.
 Beroza, G. C., Near-source Modeling of the Loma Prieta Earthquake, Bull. Seis. Soc. of America, 81(5), 1991, 1603-1621.
 Thibaut, M., Gratier, J.P., Léger, M., and Morvan, J.M., An Inverse Method for Detrmining Three-dimensional Fault Geometry with Thread Criterion: Application to strike-slip and Thrust faults (Western Alps and California), Journ. Struct. Geol., 18(9), 1996, 1127-1138.
Section : Modeling surfaces
Area of applications : Structural Geology
Speaker : Carena
Names of participants :Carena