YourName-HW02

your name
the date you completed the first version;  date of most recent revision
This template was revised February 28, 2021.

Introduction and Statement of Problem

The purpose of this notebook is to gain some experience finding the angular and circumferential distance between two points on a spherical Earth.

Statement of Problem.  In the early Miocene ~23 million years ago, a volcano erupted in California.  Sometime later in the Miocene, the San Andreas fault propagated through the volcanic field, and separated it into what is now the Pinnacles National Monument (36°29’13”N, 121°10’01”W) on the west side of the fault and the Neenach volcanic field (34°44’24”N, 118°37’24”W) on the east side (Matthews, 1973).  
This Mathematica notebook is used to analyze the input data to complete the following tasks.
     (a) Convert the given geographic coordinates to decimal geographic coordinates (see section 2.2.3).
     (b) Convert the decimal geographic coordinates to unit location vectors, recalling that south latitudes and west longitudes are negative numbers.
     (c) Determine the angular distance between the Pinnacles and Neenach (see section 2.2.9).
     (d) Find the circumferential distance between the Pinnacles and Neenach, assuming that Earth is a sphere of radius 6,371.01 km (see section 2.3.4).
     (e) What broad geological statement(s) can you make about the rate and magnitude of displacement along the San Andreas fault, based only on the information provided and your calculations?

Input Data

The geographic coordinates of a given point within Pinnacles National Monument are 36°29’13”N, 121°10’01”W.

The geographic coordinates of a given point within the Neenach volcanic field are 34°44’24”N, 118°37’24”W.

User-defined Function

The user-defined function makeLocationVector[] acts on input geographic coordinates (decimal latitude and decimal longitude, both expressed in degrees) and returns the cartesian-geographic coordinates of the unit location vector to that point.  This user-defined function is copied from the document “Kinematics-Chapter-2.nb.pdf” by Vince Cronin.

makeLocationVector[lat_, long_]:={Cos[lat Degree] Cos[long Degree],Cos[lat Degree] Sin[long Degree],Sin[lat Degree]};

Computation

Convert the given geographic coordinates to decimal geographic coordinates (Kinematics chapter 2, sec. 2.2.3)

The variables decimalLatPinnacles and decimalLongPinnacles are the decimal geographic coordinates associated with a point within Pinnacles National Monument in California (36°29’13”N, 121°10’01”W).  Remember that west longitudes are negative.

The variables decimalLatNeenach and decimalLongNeenach are the decimal geographic coordinates associated with a point within the Neenach volcanic field in California (34°44’24”N, 118°37’24”W).  Remember that west longitudes are negative.

Convert the decimal geographic coordinates to cartesian geographic coordinates (Kinematics chapter 2, sec. 2.2.3)

The user-defined function makeLocationVector[] acts on the arguments decimalLatPinnacles and decimalLongPinnacles to yield the unit location vector locVectPinnacles.

The user-defined function makeLocationVector[] acts on the arguments decimalLatNeenach and decimalLongNeenach to yield the unit location vector locVectNeenach.

Determine the angular distance (in radians) between Pinnacles and Neenach (Kinematics chapter 2, sec. 2.3.4)

The built-in Mathematica function VectorAngle[] acts on the arguments locVectPinnacles and locVectNeenach to yield the angular distance between Pinnacles and Neenach (thetaRadians).

Determine the circumferential or great-circle distance (in kilometers) between Pinnacles and Neenach (Kinematics chapter 2, sec. 2.3.4)

The variable circumfDistKm is defined as the circumferential distance between two points on a sphere of radius 6327.01 km given an angular distance between the points of thetaRadians.

Output Data

Decimal geographic coordinates of the input points

decimalLatPinnacles

decimalLongPinnacles

decimalLatNeenach

decimalLongNeenach

Cartesian geographic coordinates of the input points

locVectPinnacles

locVectNeenach

Angular distance between Pinnacles and Neenach (radians)

thetaRadians

Circumferential or great-circle distance between Pinnacles and Neenach (kilometers)

circumfDistKm

Analysis

The following broad geological statement(s) about the rate and magnitude of displacement between Pinnacles and Neenach along the San Andreas fault seem to follow from the output data:

(Replace this text with your analytical statement)

References

Cronin, V.S., 2021, Kinematics-Chapter-2.nb:  unpublished draft, http://croninprojects.org/Vince/PlateKinematics/KinematicsCourse/Kinematics-Chapter-2.nb.pdf

Cronin, V.S., 2017, A brief primer on plate kinematics, with Mathematica:  unpublished draft, http://croninprojects.org/Vince/PlateKinematics/KinematicsPrimer/KinematicsCh2.nb