Question

What is the relative plate velocity between the Nazca and South American plates at Lima, Peru \(\left(12^{\circ} \mathrm{S},\right.\) \(\left.77^{\circ} \mathrm{W}\right) ?\) A MATLAB code for solving this problem is given in Appendix \(D\).

Short answer

Use MATLAB code to calculate; Lima's relative plate velocity is about 7-8 cm/year (Nazca moving under South America).

Step-by-step solution

Define Relevant Variables

First, identify the geographic coordinates where to calculate the relative plate velocity. For this problem, the location is Lima, Peru, at latitude \(12^{\circ} S\) and longitude \(77^{\circ} W\). These coordinates will be used in the MATLAB code to estimate the relative velocity between the plates.

Understand the Provided MATLAB Code

Review the MATLAB code given in Appendix D. This code is likely structured to use existing plate motion models or data to calculate the relative velocity between tectonic plates. The exact workings of the code are crucial and may include calculations such as vector operations, transformations from geodetic to Cartesian coordinates, or applying tectonic motion models.

Execute the MATLAB Code

Run the MATLAB code with the geographic coordinates of Lima, Peru. This step involves inputting these coordinates into the code and executing it in MATLAB. The code will perform the necessary computations to output the relative velocity vector of the Nazca plate relative to the South American plate.

Interpret the Results

Once the code is executed, interpret the results. The MATLAB output should include the magnitude and direction of the relative plate velocity, typically given in mm/year or cm/year. Ensure you understand if the result is given in a specific coordinate reference or if additional conversions are needed.

Key concepts

Tectonic Plates

Tectonic plates are massive slabs of the Earth's lithosphere, which is the outermost layer of Earth. These plates fit together like a giant puzzle and cover the surface of the Earth.
They are constantly moving, albeit very slowly, at rates typically measured in centimeters per year. This movement is driven by forces such as mantle convection, slab pull, and ridge push.

• Convergent boundaries: Plates move towards each other, which can cause mountains or trigger volcanic activity.
• Divergent boundaries: Plates move apart, allowing magma to rise and form new crust.
• Transform boundaries: Plates slide past each other, often causing earthquakes.

The interaction between the Nazca and South American plates near Lima, Peru, occurs at a convergent boundary. The Nazca plate is subducting beneath the South American plate, contributing to the Andes mountain range formation and regional seismic activity.

MATLAB

MATLAB is a high-performance language and interactive environment for technical computing and data visualization. It is particularly powerful in handling mathematical calculations and data analysis tasks.
In the context of tectonic plate calculations, MATLAB provides functionalities for processing geospatial data and applying complex models to simulate or analyze plate movements.
Below are some key features of MATLAB that are relevant to this topic:

• Vector and Matrix Operations: Essential for manipulating the data involved in plate motion calculations.
• Programming Environment: Allows users to write scripts and functions that automate repetitive calculations, such as analyzing relative plate velocity.
• Data Visualization: Enables users to create plots and graphs to visualize tectonic data effectively.

Using MATLAB for this exercise involves inputting geographic coordinates and utilizing provided algorithms to compute the relative velocity between tectonic plates.

Relative Velocity

Relative velocity in plate tectonics refers to the speed and direction at which one tectonic plate moves relative to another. This is a crucial measure for understanding plate interactions and their potential consequences, such as earthquakes or volcanic activity.
Calculating relative velocity usually involves:

• Identifying the plates in question and their movement characteristics.
• Using vector calculations to determine the velocity vector that quantifies both magnitude and direction.

With tools like MATLAB, these calculations are simplified, making it easier to model and analyze the complex motions involved. For the Nazca and South American plates, this means determining how quickly and in what direction the Nazca plate is moving relative to the South American plate at a specific point, like Lima, Peru.

Geographic Coordinates

Geographic coordinates are a system used to specify locations on Earth's surface. Coordinates are expressed as latitude and longitude, and they are crucial for many geospatial analysis tasks, including plate tectonics studies.

• Latitude: Measures how far north or south a point is from the equator, with values ranging from 0° at the Equator to 90° at the poles.
• Longitude: Measures how far east or west a point is from the Prime Meridian, with values ranging from 0° at the Prime Meridian to 180° east or west.

In the exercise related to Lima, Peru, the geographic coordinates are 12° South and 77° West. These specific coordinates are inputted into computational tools like MATLAB to determine local plate behaviors by precisely defining the location of interest for any analysis of tectonic activity.