Structural Knowledge Discovery Used to Analyze Earthquake Ac(3)

The Subdue structural discovery system is being used as the Data Mining tool to study the "Orizaba Fault " located in Mexico, as part of a research project of the geologist Dr. Burke Burkart. We analyze the information of the Earthquake Database

because the sampled earthquakes would have a largerrange over time and cause a loss of important information(there would be less near_in_time related records). So wejust randomly sampled from the information collected inone year creating a graph with 10135 events, 136,077vertices, 125,941 attribute edges and 757,417 undirected“near_in_distance” and “near_in_time” connections and asize of 26,963,605 bytes.

Minimum Encoding Heuristic Results

With the minimum encoding heuristic Subdue was ableto find structures that linked events with the“near_in_time” and “near_in_distance” edges. The firstsubstructure (substructure 1, not shown) linked one eventto four others with near_in_time edges and to a fifth eventwith a “near_in_distance” edge. The second substructure(substructure 2, not shown) linked one event to three otherevents with “near_in_distance” edges and to the categoryfield “PDE-W” that corresponds to the source of anearthquake’s catalog entry. The third substructure(substructure 3, not shown) linked one event to anotherevent and to one substructure_2 with “near_in_distance”edges. The fourth substructure is more complex and isshown in figure 3. This substructure is interesting becauseseveral earthquakes happened in a short period of time andcould be related to a fault placement.

The interesting issue here is the potential to findimportant relations between earthquakes that happened in alocalized region within a short period of time.

Near_in_time

Near_in_time

EventNear_in_time

Sub_1

Figure 3: Substructure 4, 90 Instances

Graph Size Heuristic Results

With the graph size heuristic we found moresubstructures in the Earthquake database. The reason isbecause it works faster and we could go deeper in thenumber of iterations. Subdue found relations betweenevents and substructures with the “near_in_time” and“near_in_distance” edges, but it also found relations thatincluded some other fields like “Catalog”, “Month”,“Mag1 Scale”, and “Depth”. Here, it was possible toconclude that the earthquakes related by the substructurewere provided by the “PDE-W” catalog which lists themost recent weeks in events and the “PDE-Q” catalog thatlists the most recent events that are still subject to change.It was also possible to conclude from the data that moreearthquakes occurred in the months of “June” and “May”and that a frequent depth for the related earthquakes was“33.0000” and “10.0000” kilometers. The fact that Subdue

found the depth characteristic of “33.0000” kilometers isvalidated in the Earthquakes database description where itis mentioned that this is the most common depth for anearthquake. As an example, figure 4 shows how in theeighth iteration Subdue found that 140 of the instances ofsubstructure 1 happened in a depth of 33 kilometers.Substructure 1 in figure 4 has 9465 instances and connectsan earthquake event to the category value “PDE_W”.Substructure 7 with 141 instances, connects an event tosubstructures found in previous iterations with “near-in-distance” and “near-in-time” edges and also contains the“PDE_Q” attribute.

Figure 4: Substructure 8, 140 Instances

Determining Earthquake Activity

We already mentioned how we used Subdue to findpatterns in the earthquakes database. Now we are going todescribe a project in which we used Subdue to determinethe earthquake activity of a specific area of Mexico. Dr.Burke Burkart, a Geologist at the University of Texas atArlington, who has studied Mexican geology andseismology for years, is interested in the study of theseismology caused by the Orizaba Fault (Burkart 1994,Burkart and Self 1985). This fault runs from the Vulcan“Pico de Orizaba” located in the state of Veracruz throughthe “Itsmo de Tehuantepec” in the state of Oaxaca.

A fault is defined as a fracture in a surface where adisplacement of rocks also happened. Faults are caused byforces acting over the rock bodies. When a rupture occurs,there is going to be two walls forming the fault. Faultsreceive a different name according to the rocks’ movement(Hamblin and Christianses 1998).

When the movement among the rocks happens in thevertical plane, the fault is called a Dip-Slip Fault, wherethe Hanging-wall is the one above the fault and the Foot-wall is the one below the fault. Dip-Slip Faults areclassified according to the direction of the rocks’movement. A Normal Dip-Slip Fault is created when apulling force generates the fracture, then by the gravityforce, the hanging wall is displaced downwards. ReverseDip-Slip Faults are created when a compression forceforms the fracture. In this case the hanging wall movesupward due to the compression force. A Thrust Fault is areverse fault with an inclination of less than 45o.

If the movement among the rocks happens in thehorizontal plane, the fault is called a Strike-Slip Fault. Thistype of fault is described as Left-Lateral Fault or Right-Lateral Fault.

Oblique Faults are those with the characteristics of both,Dip-Slip and Strike-Slip Faults, that is, the rocks move inboth planes, the vertical and horizontal. The “OrizabaFault” is a Strike-Slip Fault. We want to know the locationof the active zone of earthquakes, which will be located at

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