Math and Method

While the code will be included in an appendix and is a tad complex and unreadable, the underlying mathematics remain fairly simple. To contour over the globe the density of intersections of extended stress azimuths the following calculations were made at every map location to be considered

$$\sum_{n=1}^{{\it dataset-trash}} \vert Az_{\it{back}} - Az_{\it{stress}}\vert$$

where $Az_{\it{back}}$ is the back-azimuth over the surface of the globe from the WSM data point to the current map point, and $Az_{\it{stress}}$ is the azimuth from the WSM data set.

Each iteration in the sum results in a zero value when the data azimuths are the same and at most 90^o as the code maintains all comparisons to one quadrant. Therefor, as more and more data points don't intersect at the location being calculated, the value grows larger and larger. Thus one needs be mindful to focus on values at the bottom of the color bar of the pictures to come.

There are many options included in the code to delimit the quantity and region of data to use as input as well as the section of the map to perform the calculations over. The WSM data is divided into the following stress regimes, regions, and plates:

Plate Code:
1    North American Plate           Regime Code:
2    South American Plate           1.0 NF - normal faulting
3    Nazca Plate                    1.5 NS - w/ SS component
4    Cocos Plate                    2.0 TF - thrust faulting
5    Eurasian Plate                 2.5 TS - w/ SS component
6    Indian-Australian Plate        3.0 SS - strike-slip faulting
7    Pacific Plate                  4.0  U - undetermined stress regime
8    African Plate                  1.3 for NF and NS
9    Antarctic Plate                2.3 for TF and TS
10  Arabian Plate
11  Juan de Fuca Plate
12  Philipine Plate
13  Sandwich Plate

Subregion Code:
0.........oceanic part of plate
1,4,7,....major continental region in plate
2,5,8,....adjacent continental shelf to above
3,6,9,....adjacent sea or inland sea, generally not oceanic crust

where the number corresponds to a parameter passed into the code to focus only on that data type or region. As it is possible to combine plate, subregion, and regime delimiters (as well as subtracting 90^o from the NF and NS regimes as can be understood from figure 4), many many maps are possible to construct.

For the sake of clarity, it is also possible to seed the data azimuths with normally distributed random values (at the proper locations) to convince yourself that any patterns observed are not simply a product of the spherical earth. Notice that all maps are antipodally symmetric which gives assurance that the codes are performing properly on a spherical coordinate system and then plotted to two dimensions later. It would be interesting to input variable radius of the earth data at a later date.

All code utilizes the Stanford Exploration Project i/o, storage and plotting structure for reproducible research.(9)