Earthquake focal depth vs. magnitude: Are they correlated?

Lately I began to wonder: does the depth of focus of an earthquake correlate to its magnitude? I asked some colleagues. They said no. But I wanted to find out for myself. So I did. 

I decided to go back to the NCEDC to get some data. I did a search and set the lower limit for magnitude to 3, no limits for depth or long/lat. I limited it to nothing before 1970 because some of the data such as depth or magnitude were missing before then. I asked to to return it to me in "csv format" (which still comes as a webpage). Then I set the line limit to 1,000,000. I wanted all the data points I could get. And I got them. All 583,000 or so points. I initially asked for 50,000, and got those too, but they weren't enough. Each point comes with long/lat, magnitude, depth, data, and more that I am not concerned with. Turns out the 583,000 entry .csv is ~46 mb as a .csv or .txt. If I convert it to points in ArcGIS the .dbf (database file) is 500+ mb alone. Damn. 

To find the answer to my question I did two things. First, I played with some Python to let it to the stats on the magnitude and depth to find the correlation. Python suggests that no, they aren't correlated. You can see the iPython Jupyter Notebook I created for it here. Gotta love Python.

Earthquakes 1970-1978:
Depth standard dev: 1.708
Depth variance: 2.917
Magnitude standard dev: 2.882
Magnitude variance: 8.306
depth vs. magnitude correlation:
[[ 1.          0.00593409]
 [ 0.00593409  1.        ]]
The two middle values are the correlation for depth amd magnitude to one another.

Earthquakes 1970-2018:
Depth standard dev: 1.708
Depth variance: 2.918
Magnitude standard dev: 2.872
Magnitude variance: 8.248
depth vs. magnitude correlation:
[[ 1.          0.00236923]
 [ 0.00236923  1.        ]]
The two middle values are the correlation for depth amd magnitude to one another.

For the bit in brackets, the important number are the middle two. They are the calculated correlation values between depth and magnitude. Python's Numpy library displays it that way. I would write a function to do the same thing and output in a nice format, but why re-invent the wheel?


Secondly, while number are all fine and good, it might be nice to see this a little more visually. This is where the interpolation comes in. As I had over 500,000 points, covering the whole globe, we can get a good picture of both the depth and magnitude of earthquake across the whole planet. I went with IDW interpolation as Kriging 500,000+ points makes Arc lose its mind. Running the Kriging interpolation never finished. 

Figure 1 - Map of global earthquakes from 01/01/1970 to 12/31/2017. Red values are deeper depth and darker green depth are shallower depths. Dark points are locations of earthquakes; they unsurprisingly correspond to plate boundaries. Bright red spots also correspond to active subduction zones such as in the Aleutian Islands, the west coast of South America, Indonesia, and Japan. Not that the earthquake points line up with plate boundaries and active subduction zones.

Figure 2 - Map of global earthquakes from 01/01/1970 - 12/31/2017. Red values show higher magnitudes and green values show lower values; larger dots show higher magnitude. The map appears chaotic as there is less of a trend related to earthquake magnitude as there is with earthquake depth.

I am forced to conclude that there appears to be little mathematical evidence for a correlation between earthquake magnitude and depth as well as the more qualitative representation on a map. The map, however, shows  an interesting pattern that the smaller earthquakes are concentrated in Europe, North America, and Australia. I don't fully know why as of yet. 

HAZUS, Earthquakes, and Tsunamis

Predicting when an earthquake will occur can be very difficult, likewise with tsunamis. While we may not be able to predict them, we can at least create models to aid in preparedness in the event that one does occur. FEMA's HAZUS software allows us to do just that with the power of ArcGIS® 10.5.1. In this project I decided to revisit my two study areas in Anchorage and Los Angeles from my second project (Figure 1). I went with HAZUS since modeling tsunamis requires extensive maths and the modeling software TSUNAMI-N2 by Goto et al., 1997 is written in FORTRAN. HAZUS is quite large, power, and complex.

Figure 1 - Location of both study areas. The Anchorage study area includes parts of both Anchorage and Matanuska-Susitna  counties. The Los Angeles study area encompasses the entirety of Los Angeles County to include both Catalina and San Clemente Islands.

To model the tsunamis, I gave HAZUS default parameters laid out in the HAZUS Tsunami User Manual. I set the maximum runup to 20m for both study areas. I was expecting Anchorage to get completely inundated and coastal California to be protected by the coastal cliffs. My predictions were incorrect (Figures 2 and 3). Tables 1 & 2 compared damages and casualties.

Table 1 – Tsunami Damage to Buildings by Count by General Occupancy

	Agriculture	Commercial	Education	Government
Anchorage	32	978	72	12
Los Angeles	57	110	3	1
	Industrial	Religion/Non-Profit	Residential	Total
Anchorage	164	26	3488	1094
Los Angeles	657	9	44780	171

Table 2 - Tsunami Casualties by Community Preparedness

					Community Preparedness
Day		Good			Fair
	Fatalities	Injuries	Total Casualties	Fatalities	Injuries	Total Casualties
Anchorage	8602	1055	9657	10533	665	11198
Los Angeles	1005899	71948	1077847	2412297	70164	2482461
Day	Poor
	Fatalities	Injuries	Total Casualties
Anchorage	11137	397	11534
Los Angeles	5465410	62210	5527620
Night		Good			Fair
	Fatalities	Injuries	Total Casualties	Fatalities	Injuries	Total Casualties
Anchorage	7355	1362	8717	9981	973	10954
Los Angeles	1001019	71720	1072739	2357493	68267	2425760
Night	Poor
	Fatalities	Injuries	Total Casualties
Anchorage	10937	577	11514
Los Angeles	5304326	60138	5364464

Figure 2 - Tsunami runup in the Anchorage area. Surprisingly, most of Anchorage is untouched. I hadn't realized that most of Anchorage actually sits at about 100' of elevation.

Figure 3 - Tsunami Runup in Los Angeles County, California. I expected the coastal cliffs to provide more protection, however certain low lying areas such as Venice (1), Long Beach (2), Huntington Beach (3), and Newport Beach (4) would experience the effects of a tsunami. Movement along the San Andreas fault would NOT cause a tsunami, however movement along the Catalina fault certainly could. 

Similar to the tsunami model, I followed a basic earthquake model, though with some modifications. For Anchorage I set the earthquake model to Alaska or Puerto Rico / VI – Reverse as I assumed a reverse fault would rupture given Alaska is in an active subduction zone. For Los Angeles I ran two models, one strike-slip for the San Andreas fault and one reverse for the Catalina fault. Table 3 compares casualties Table 4 shows damages to buildings.

Table 3 - Combined Earthquake Economic Loss and Casualties in Magnitude 7 Event

	Economic Loss - Buildings ($)	Economic Loss - Transportation  ($)
Anchorage	2,909,951,000	182,302,000
Los Angeles (strike-slip)	7,933,660,000	69,821,000
Los Angeles (reverse)	4,340,831,000	73,512,000
	Economic Loss - Utilities ($)	Shelter Req's (# people)
Anchorage	0	1647
Los Angeles (strike-slip)	16,480,000	2234
Los Angeles (reverse)	6,150,000	791
Anchorage	Casualties - 2am	Casualties - 2pm
Los Angeles (strike-slip)	454	1250
Los Angeles (reverse)	1231	362
	472	902
Anchorage	Casualties - 5pm
Los Angeles (strike-slip)	867
Los Angeles (reverse)	1959
	627

Table 4 - Earthquake Damage to Buildings by Count by General Occupancy

Location	Agriculture	Commercial	Education	Government	Industrial
Anchorage	5033	2916	110	178	762
Los Angeles (strike-slip)	425	16916	511	275	4770
Los Angeles (reverse)	269	13491	360	232	3855
Location	Other Residential	Religion	Single Family	Total
Anchorage	8127	258	91922	8999
Los Angeles (strike-slip)	29377	1242	177547	22897
Los Angeles (reverse)	21409	1002	96055	18207

Figure 4 - Ground motion in Anchorage at 1 second (top) and 0.3 seconds (bottom).

Figure 5 - Ground motion due to movement along the San Andreas fault at 1 second (top) and 0.3 seconds (bottom).

Figure 6 - Ground motion due to movement of a reverse fault offshore at 1 second (top) and 0.3 seconds (bottom).

In conclusion, HAZUS can provide some useful data for predicting what could happen and where. The model predicts that casualties due to an earthquake would be much lower than those from a tsunami, however building damages from an earthquake would be much more devastating. A link to the report can be found here.