# Role of Plate Motion Obliquity in Rifting

## Summary

This is one component of the Rupturing Continental Lithosphere suite of mini-lessons.

This lab exercise uses Google Earth and/or Matlab (depending on the version) to investigate the relationship between relative plate motion, obliquity of rifting, and structural geology of the Gulf of California rift zone. The exercise introduces an Euler pole description of the motion between the Baja California microplate and the North American plate and relates plate motion to fault activity within the Gulf.

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## Learning Goals

The intended conceptual goals of this exercise are to demonstrate that:
• The current morphology of a rift zone may reflect the obliquity of opening, that is, the relative amounts of motion accommodated by transform faults and opening segments.
• Relative motion between tectonic plates must be described by rotation about an Euler pole.

The skills that this exercise will foster are:

• Evaluation of spatial variation in mapped variables, through description of relative plate motion along the plate boundary;
• Relation of fault slip rates to relative plate motion, fault strike, and plate boundary structure;
• Basic coordinate transformation skills, learning how to relate:
• Euler pole rotation to linear velocity magnitude (MATLAB and standard Google Earth versions);
• Euler pole rotation to velocity in the east and north direction (MATLAB version only);
• East and north velocity to strike-parallel and fault-normal relative motion (slip) rates;
• Collaborative critical thinking, when the exercise is completed in pairs or small groups;
• Open-ended reflection, applying students' quantitative calculations to the tectonics of the Gulf of California
In the exercise, students will:
• Contrast the speed and direction of plate motion along the Gulf of California, from north to south;
• Calculate the rate of strike-parallel and strike-perpendicular fault slip on rift and transform segments of the plate boundary;
• Draw connections between the density of faults and the obliquity of rifting calculated for the north, central, and south segments of the Gulf of California.
• Consider multiple hypotheses:
• The RCL sequence of mini-lesson exercises is designed to illustrate that rift morphology as indicated by the bathymetry of the Gulf of California is shaped by sedimentation, magmatism, magnitude of extension, and obliquity of rifting.
• The effects of rift obliquity may change through time, as illustrated by temporal variation in fault activity.

## Context for Use

This exercise is designed for an upper level global geophysics, geodynamics, tectonics, or structural geology course. The exercise employs calculation and visualization of relative plate motion across the Gulf of California, with trigonometric operations to relate plate motion to fault slip rates.

Three versions of the exercise, ranging in difficulty and amount of student calculation, are available depending on class background. All are designed to be used in a single 2–3 hour lab period.

Before carrying out the exercise, students should be familiar with basic plate tectonic concepts, including the ideas that relative plate motion gives rise to fault slip rates on plate boundaries, and that oblique slip can occur on plate boundaries. The exercise includes a brief introduction to describing relative plate motion using Euler poles, although the instructor may wish to devote more time to this topic in a full lecture preceding the exercise. Students should be comfortable with basic trigonometry. See the Description and Teaching Materials for more information on student background for specific version of the exercise.

## Description and Teaching Materials

Move all the above to Teacher's Stash along with "Supplementary Questions"

An introductory lecture briefly introduces the concept of plate motion on a sphere, described by Euler poles, although the instructor may wish to supplement this with a full lecture preceding the lab period (see Teaching Notes and Tips section).

The exercise, meant to be used in a 2–3 hour lab period, is provided in three versions, all involving the same conceptual material but differing in the amount and style of calculations done. All exercises relate relative plate motion to slip rates on the fault segments that comprise the Gulf of California plate boundary, using these slip rates to assess the variation in structural style along the margin's strike. The linked .zip files below contain an instructor folder, containing an "answer key" and supplementary files, and a student folder, which contains all materials students would need to complete the exercise.

uses the Euler pole calculations to extrapolate Euler pole rates over geologic intervals to examine the consistency in relative plate motion through time. (These questions most naturally fit as a supplement to the Google Earth versions of the exercise, as they require analysis of imagery and measurement of distances in Google Earth.)

1. Google Earth "lite" version (Zip Archive 1.1MB Oct1 15): Students are given Google Earth .kml files showing active faults in the Gulf of California region as well as a .kml file showing the rate and direction of relative plate motion between the Baja Microplate and the North American Plate. Calculations involved are basic trigonometric functions using measurements made with the Ruler tool in Google Earth (using the strike of faults and the trend of the local plate motion to determine strike-slip and opening rates on fault segments).
2. Google Earth "standard" version (Zip Archive 1.1MB Oct1 15): Same as above, but instead of being given the small circles that define rates of relative plate motion, students produce these small circles using algebraic manipulation of the equation relating Euler pole rotation to linear velocity, plugging their calculated values into an online Google Earth circle generator. A file is created for each small circle contour of relative motion (40–50 mm/yr, in 1 mm/yr increments).
3. Matlab version (Zip Archive 34.8MB Oct1 15): Students use included MATLAB functions to calculate the north and east components of relative plate motion directly on plate boundary fault segments, then convert these values to total magnitude, and resolve the velocity components into strike-slip and opening motion on the fault segments. This version could certainly be supplemented with the Google Earth files for better visualization, though some visualization is included in the MATLAB material. We recommend as part of the exercise that a brief Matlab tutorial is completed if students are not already familiar with the software. The supplied codes are heavily commented to help students understand the purpose of the lines of code.

## Teaching Notes and Tips

A brief introductory presentation gives a description of Euler poles and relative plate motion. A key point to make for the Google Earth versions is that the "rainbow" small circles that define contours of relative plate motion are best defined as describing the motion of the Baja Microplate relative to North America. Therefore, the circles may be better represented as arc segments solely on the Baja Microplate. That is, if the small circles are showing that plate's motion, they are defined only where they lie on that plate. A similar argument could be made if you use the circles to describe the motion of the North American Plate relative to the Baja Microplate. In that case, the arc segments would cover only the North American Plate, terminating at its boundary with the Baja Microplate.

As described in the introductory presentation, the mini-lesson can be introduced using a simple, hands-on demonstration of the relationship between Euler pole rotation and plate boundary activity using Seth Stein's Pacific-North America plate boundary exercise.

Instructor documents are included for each version of the exercise, with our comments provided in blue text.

## Assessment

Peer review:

- Students could work in pairs/small groups are assigned two rift zone fault segments: one opening, and one transform. Each group calculates the slip rates on these segments, and then as a class, the rates are placed on a map of the entire system. By comparing similarities and patterns in rates (rate as a function of distance between the segment and Euler pole), students will be able to evaluate how sensible each other's calculations are and together assemble the rift-wide set of fault slip rates. See Questions 2 and 3 of the exercises for a specific implementation of this "think-pair-share" activity.

Thought questions:

- Each version of the exercise has a suite of computation problems and associated thought/application question that students could complete in "worksheet" format or translate onto a concept sketch. The calculations and thought questions are:

1. Calculate (MATLAB and standard Google Earth versions) the total speed of relative plate motion between the Baja Microplate and North American Plate across the Gulf of California rift zone. Use these calculations to assess the relationship between location along the plate boundary, relative to the Euler pole, and the speed of relative plate motion.
2. Calculate the rate of fault-parallel (strike-slip) and fault-perpendicular (spreading/opening) relative motion on rift and transform segments of the plate boundary. Use these calculations to describe the relationship between the rate of opening on a rift segment and the rate of strike-slip on an adjacent transform segment.
3. Calculate the variation along the plate boundary in obliquity of rifting (angle between relative plate motion and the general strike of the plate boundary). Use these calculations to relate obliquity of plate motion to the structural style of the plate boundary though comparison with a MARGINS-derived map of active faults in the region.

Written report/concept sketch:

- Students could summarize whole-class results in a concept sketch or written report that highlights patterns of fault slip rates along the rift zone and specifically asks them to comment on the other RCL topics that have been covered so far. Our goal is to build a library of the ways in which the above mentioned factors can shape the rift evolution, so considering the ways that rift obliquity and, for example, sedimentation can act constructively or destructively to affect rift width will help to connect the current topics to those learned earlier in the mini-lesson sequence.

In addition to assessment specific to this mini-lesson, several synthesis test questions probe students' cumulative learning of the physical characteristics of the Gulf of California and the processes that have shaped it.

## References and Resources

The following papers are referenced as a resource to provide students with more information about the geology and faulting styles along the Gulf of California.

### Instructor Stories

There are no instructor stories currently available for this mini-lesson.

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