Question

The displacement of the MOJA (Mojave) station is \(23.9 \mathrm{~mm} \mathrm{yr}^{-1}\) to the east and \(-26.6 \mathrm{~mm} \mathrm{yr}^{-1}\) to the north. Assuming the San Andreas fault to be pure strike-slip and that this displacement is associated only with motion on this fault, determine the mean slip velocity on the fault and its orientation. A MATLAB code for solving this problem is given in Appendix \(D\).

Short answer

Mean slip velocity is 35.75 mm/yr, oriented 48.81° south of east.

Step-by-step solution

Understanding the Problem

To solve this, we need to determine the mean slip velocity of the MOJA station based on its eastward and northward displacements, assuming these are caused by the San Andreas fault's slip.

Break Down Displacements

Record the given displacements along the east and north directions: East displacement = 23.9 mm/yr, North displacement = -26.6 mm/yr. These values indicate a movement vector in mm/yr.

Calculate Resultant Velocity

Use the Pythagorean theorem to find the resultant slip velocity: \( v = \sqrt{(23.9)^2 + (-26.6)^2} \). Calculate: \( v = \sqrt{571.21 + 707.56} = \sqrt{1278.77} \approx 35.75 \mathrm{~mm} \mathrm{yr}^{-1}\).

Determine the Orientation

To calculate the slip orientation, find the angle \(\theta\) with respect to the east direction using the tangent function: \( \theta = \tan^{-1}\left(\frac{\text{north displacement}}{\text{east displacement}}\right) = \tan^{-1}\left(\frac{-26.6}{23.9}\right)\). Calculate: \( \theta \approx -48.81^\circ \), meaning the orientation is towards the east slightly south.

Key concepts

San Andreas Fault

The San Andreas Fault is a continental transform fault that extends roughly 1,200 kilometers (750 miles) through California. It forms the boundary between the Pacific Plate and the North American Plate.
What makes this fault particularly interesting is its history of producing significant earthquakes. The shifting of tectonic plates along this fault has caused some of the most destructive earthquakes in North American history.
Several major segments of the San Andreas Fault have different seismic characteristics. For example, the southern segment, known as the "locked section," could lead to a major earthquake as stress continues to build.
Understanding the fault is crucial for earthquake prediction and preparedness. By examining slip rate, historical seismic activity, and field studies, scientists hope to predict potential seismic events more accurately.

Strike-slip Fault

A strike-slip fault is a type of fault where the predominant displacement is horizontal, parallel to the fault line. It is quite different from other types of faults, like normal and reverse faults, where the movement is primarily vertical.
The San Andreas Fault is an excellent example of a strike-slip fault. The tectonic plates move horizontally past each other in a shearing motion.
Features of strike-slip faults include:

• Horizontal Motion: Mainly sideways instead of up and down motion.
• Transform Boundaries: Typically occur at transform plate boundaries.
• Earthquake Potential: Can produce significant earthquakes due to the stress accumulation and eventual release along the fault.

Strike-slip faults can vary in their rate of movement, and studying these movements helps in understanding potential seismic risks associated with these faults.

Tectonic Displacements

Tectonic displacements refer to the movement of the Earth's lithospheric plates. These movements are driven by processes such as mantle convection, gravity pull at subduction zones, and ridge push at oceanic ridges.
In regions like California, these displacements are prominently observed along the San Andreas Fault. Plates move past each other causing the ground to shift, which is recorded in terms of displacement rates.
Displacements can be measured in:

• Millimeters per Year: Indicating how much the plates have moved over a year.
• Directional Components: Measured in terms of movement along specific directions, such as north, east, etc.

Understanding tectonic displacement is important not only for estimating the fault slip rates but also for assessing the earthquake hazards in a region.

Slip Velocity Calculation

Slip velocity calculation involves determining the rate at which a fault moves over time. This calculation is crucial for understanding the potential energy buildup along a fault that could lead to earthquakes.
For a strike-slip fault like the San Andreas Fault, the slip velocity is essential in quantifying how fast the tectonic plates are moving past one another. A common method to calculate this involves vector decomposition:

• First, identify the displacement components in two perpendicular directions, like north and east.
• Use these to calculate the resultant slip velocity using the Pythagorean theorem: \[v = \sqrt{( ext{east displacement})^2 + ( ext{north displacement})^2}\]
• The orientation of the slip can be calculated using trigonometric ratios to find the angle of slip direction relative to a fixed geographic direction. \[\theta = \tan^{-1}\left(\frac{ ext{north displacement}}{ ext{east displacement}}\right)\]

Calculating slip velocity helps predict future seismic activity by providing insights into the fault's movement rate and direction.