BACKGROUND The programs apply a simple "elastic half space" strike-slip model to high precision GPS velocity data from a transect across the Carrizo segment of the San Andreas Fault (SAF), probably the most famous strike slip fault in the world. Strike-slip faults form when two tectonic plates slide past eachother. These plates do not move underneath eachother nor are they moving apart. In between major strike-slip earthquakes, the ground accrues stress from tectonic plates that are trying to slide past each other. The walls of the fault are stuck together (known as "locked"), which causes the ground to deform. Both the fault rate (R) and the locking depth (d) are important parameters in seismic hazard since it is thought that areas that are stuck will slip in the next big earthquake. Larger rates and larger slip areas would produce larger earthquakes.
The surface velocity for a profile across a vertical strike-slip fault can be described by the function::
vel = (R/pi) * arctan ( x / d)
where vel = calculated profile velocity field at the surface, pi = 3.14159..., x is distance from the fault and d is the distance from the surface to a depth at which the fault is 'stuck'. Beneath this depth is a shear zone that moving at the fault rate, R
The equation is from Savage and Burford, 1973, JGR.
To better understand what is observed at the surface (and estimated by this equation), imagine a fence built perpendicularly across a strike-slip fault. When the fault is first built it is nice and staight, but over time it starts to deform and look kind of like an "S". When the earthquake occurs the ground (and the fence) will snap, and the two sides of the fence will become straight again at some time after the earthquake, although displaced. ehalf.f describes the "S" phase.
FORTRAN PROGRAM DESCRIPTION ehalf.f will read in parameters from the input file param. Those parameters are used in calculating the velocity profile, which is output to vel.txt. The program also takes the GPS velocity, position and uncertainty estimates contained in the file data.txt, and estimates how well the model fits the GPS data by calculating the chi2 statistic which is given by::
chi2 = SUM ((dataR -vel)/(sig))**2
where chi2 = chi2 statistic, dataR = GPS estimated rate for a position aling the profile, vel = model
calculated velocity, and sig = GPS velocity uncertainty. SUM is the sum of all chi2 for each GPS datum.
The reduced chi2 is also calculated and is given by::
reduced chi2 = chi2 / (N-v-1)
where N = number of data, v = number of variable parameters (in this case 2, R and d). An ideal reduced chi2 should equal 1.
Data and model profiles are plotted in the shell script display_me. You will need General Mapping Tools (GMT) 5 to display results. To easily make changes in the fortran code, compile and plot results you can use the shell script ./runme.
You can estimate the low misfit model -- ie., find the model with the smallest reduced chi2 by using the shell script wrapper.
PYTHON PROGRAM DESCRIPTION
The Python progam (savburf.py) provides the same functionality as the fortran program, except I include an alternative method to solve for the low misfit model given a defined locking depth. Here I invert the data using singular value decomposition. In addition, the python program offers the user to display either the line graph, which essentially provides the same figure as the FORTRAN code, or a contour plot which shows the chi2 values contoured according to the rate and locking depth estimates.