Why 27.306(x)^2 - 238.96(x) + 510.08?

To get ArcGIS to properly calculate the radius of the buffers for each earthquake I looked at Keefer, 1984 - Landslides caused by earthquakes. In his paper he noted that with an increase in earthquake magnitude landslides occurred in a larger area around the epicenter. I had to work backwards from one of his figures (Figure 2B) as he gave no formula for the curves in his figures. 

Keefer, 1984 Figure 2B

I snipped the figure out of the PDF and brought it into Illustrator. I could now find out what the distance from the epicenter each magnitude was plotted as. I made a grid and measured the distances, and with a little algebra could find out each one. I then plotted those into Excel and had it make me a curve. Finding that curve by hand would have been rather difficult. 

Keefer's curve as plotted in Excel. 

The curve was polynomial with the formula being y = 27.3606(x)^2 - 238.96(x) + 510.08. This is pretty close. It is actually gives a value a bit larger than what it should truly be. As you can see the trend line matches more closely beginning around a magnitude of 7 and above. I tested it using a magnitude of 7 which had an original value of 163. The formula gave 175. Close enough. A little large is probably better than smaller. One important thing to note is that earthquakes with a magnitude below 5.06 cannot be used. This is because the calculation gives a negative number below 5.06. 

These columns were added to ease computation of the radius.

To make this whole this work I had to make new fields in the attribute table. I found it worked best when I used one for 27.306(magnitude)^2, 238.96(magnitude), and 510.08 as its own column. For whatever reason ArcGIS didn't like to calculate correctly when I plugged in the formula straight forward. So I broke it into pieces and fed each one back in. It also calculated the radius of the buffer circle in meters, so I had to convert to km by multiplying by 1000. These buffers were way bigger than I would have expected. For a magnitude 7 it drew a circle 350 km in diameter!

Just about anywhere along the Alaskan coast would have been suitable, however a larger city seemed more suitable for this study.

Earthquake induced landslide hazards in Anchorage, Alaska and Los Angeles, California - A comparison

For this project I decided to compare the risk of earthquake induced landslides around Anchorage, Alaska and western Los Angeles, California as both areas are affected by active seismicity. 
To do my comparison I first acquired data on cataloged earthquakes in Alaska and California. The following were done on data for both study areas:

- Drew buffers around earthquakes where the radius = 27.306(x)2 – 238.96(x) + 510.08, based on Keefer, 1984 and derived using Excel. I explain it here.
- Slopes were derived from 10 DEMs.
- Ran Con on the rasters of the slopes for all slopes above 30° and all slopes above 45°, then converted them to polygons.
- Land cover rasters were converted to polygons and all but the urban sections were removed. 
- All slopes of 30°+ were selected within 50m of urban areas, buffered and dissolved. Same for 45° for 50m and 150m.
I chose 30° and 45° as they are a bit below and above, respectively, the angle of repose for most geological materials. 

Figure 1 - Earthquakes in Alaska with buffers drawn around them. All earthquakes were magnitude 6 and above.

Figure 2 - Earthquakes in California above magnitude 5.06.

Significantly more areas with steep slopes near or intersecting urban areas were found in California. The Anchorage DEM covered approx. 5824 km2 with roughly 37 km2 at risk (Figure 3). The California DEM covered approx. 10192 km2 with about 1262 km2 at risk (Figure 4). 

Figure 3 - Alaska, Anchorage Area

Figure 4 - California, Los Angeles Area

To ‘ground truth’ how well my model worked I used Google Earth’s Street View in a few selected places. Street View seems to have corroborated my GIS findings as seen in figures 6 and 8.

Figure 5 - One of the few areas with steep slopes in the Anchorage Area. 

Figure 6 - Google Earth Street View Image of the the area in the above map. Going south along Hatcher Pass Road, north of Fishhook, Matanuska-Susitna County, Alaska, . It is evident that the DOT is aware of this area as a hazard as the outcrop has been cut back from the road and a fence has been put in to keep loose boulders from making it to the road. The rocks here are sedimentary.

Figure 7 - A section of the Pacific Coast Highway near Big Rock, Los Angeles County, California. Significant areas at risk can be seen here, the red being areas with slopes of 45° or more within 50m of urban areas (roads included).  

Figure 8 - The same stretch of the Pacific Coast Highway shows in Figure 6. Note how close the slope comes to the road, and how steep it is. 

This model is far from perfect as it doesn’t consider lithology, soil conditions, engineered slopes, the role of vegetation, or precipitation, which all factor into landslide occurrence.

The full report can be viewed here.