The Brute Force Hypocenter Estimation Algorithm

Earthquake is not an instantaneous phenomenon, rather point explosion in earth’s crust, whereby energy is released, carried forward by waves, called Seismic Waves.  These wave travel through earth’s crust to the surface and cause the shaking. Now since earth’s crust is composed of different layers, when a wave goes from medium of one density to another, diffraction occurs (see the figure below). Hence if details of earth’s crust were known for any given place, the time taken by waves to reach A point on earth’s surface from B point can be calculated. One such popular model which accomplishes this task is called TauP model.

The TauP plays a critical role in engendering of the model analyzed by the project. The working of Brute Force Model can be explained divided in to three steps:

1. Step 1: Divide Entire Area being monitored into Finite Space Points (Gridding)
2. Step 2: At each and every grid point, collect all picks in past T seconds for nearby sensors (sensors deployed less than D km away). One will obtain a pattern of picks for T seconds for each point, let’s call it observed pick pattern (OPP).
3. Step 2: Now assume an earthquake occurred T seconds ago. For each and every grid point, tabulate what an Actual pick pattern should look like using TauP Model and its arrival time calculation. Let’s call this Actual Pick pattern (APP)
4. Step 4: Now compute error between Observed pick pattern and Actual Pick Pattern. If the error falls below a certain threshold for few points, we may declare an earthquake did occur. We the point with lowest error is most likely to near the source of the earthquake.
5. Step 5: Repeat the steps 2-4 for each and every time step.

This is an oversimplified explanation of the algorithm. The actual algorithm takes care of a lot more parameters and conditions.

Note that the calculation for each grid point is independent of each any other point, and hence can be parallelized. Moreover, the for each grid point, error can be computed in linear time, given a particular distribution of sensors in space.

In the next post, we explain the algorithm in detail. Reader of may skip the next section since it is going to cover all the details of how the algorithm works