Question

The measured declination and inclination of the paleomagnetic field in Upper Triassic rocks at \(41.5^{\circ} \mathrm{N}\) and \(72.7^{\circ} \mathrm{W}\) are \(D=18^{\circ}\) and \(I=12^{\circ} .\) Deter- mine the paleomagnetic pole position. A MATLAB code for solving this problem is given in Appendix \(D\).

Short answer

The paleomagnetic pole position involves converting geographic to magnetic coordinates using given declination and inclination, then applying adjustments for continental drift.

Step-by-step solution

Understanding Declination and Inclination

Declination (D) represents the angle between magnetic north and the true north on the horizontal plane. Inclination (I) is the angle made with the horizontal plane by the Earth's magnetic field lines. The given values are \(D = 18^\circ\) and \(I = 12^\circ\).

Geographic Location

The geographic coordinates of the rock sample are given as latitude \(41.5^\circ N\) and longitude \(72.7^\circ W\). These coordinates will represent the location from which paleomagnetic readings are taken.

Convert to Magnetic Coordinates

The goal is to find the paleomagnetic pole position, which involves converting the measured declination and inclination to a magnetic latitude and possible pole location. Begin by converting inclination \(I\) to colatitude (\(\Theta\)), where \(\Theta = 90^\circ - I = 90^\circ - 12^\circ = 78^\circ\).

Calculate Paleolatitude

Using the equation for paleolatitude, \( \theta = \arctan{\left(\frac{\tan(I)}{2}\right)} \), calculate the paleolatitude. Compute \( \tan(12^\circ)/2 \) and then take the arcsine of the resulting value to determine the paleolatitude.

Adjust for Continental Drift

Considering continental drift, adjust the paleolatitude to determine the paleomagnetic pole. This involves taking into account any known shifts of the tectonic plates.

Find the Paleopole

Combine the adjusted paleolatitude with the original sample location data to locate the paleomagnetic pole. This step usually involves iterative calculations or using software/Matlab scripts to finalize the paleomagnetic pole's position.

Key concepts

Declination

Declination is measured when studying paleomagnetism. It represents the angle between magnetic north and true north on a horizontal plane. This angle helps in understanding historical magnetic fields captured in rocks. When we measure declination, we're essentially looking at how far off magnetic north is from the geographic north. This discrepancy arises due to the movement and changes of the Earth's magnetic field over millions of years.
For example, in the context of Upper Triassic rocks, a declination of 18° means that magnetic north was 18° to the east of true north when the rocks were magnetized. This information can help geologists and researchers determine the ancient positions of earth's magnetic poles and the movement of tectonic plates over geological time periods.

Inclination

Inclination is the angle at which magnetic field lines intersect the Earth's surface. It varies from place to place across the globe and reflects how deeply the magnetic lines penetrate the Earth at a particular point. Inclination helps us understand the tilt of the Earth's past magnetic fields.
For instance, an inclination of 12° implies that the past Earth's magnetic field lines intersected the earth's surface at a shallow angle of 12°. This measurement is most useful when determining the direction of ancient magnetic forces. It provides insight into the past latitudinal position of the tectonic plates, as steeper inclinations often suggest closer proximity to the poles, while lower inclinations suggest a location nearer to the equator.

Paleomagnetic pole

The concept of a paleomagnetic pole is central to understanding Earth's historical magnetic field. It refers to the past positions of the magnetic poles, which are determined through the magnetic records held within rocks. By calculating both declination and inclination, we can estimate where the magnetic poles were at various points in the Earth's history.
To find the paleomagnetic pole position, paleontologists use the measured inclination and declination to derive a magnetic coordinate system. The paleomagnetic pole provides pivotal information on the movement and drift of continents over geologic timescales. As tectonic plates shift, the paleomagnetic pole data help reconstruct past continental configurations and allow us to trace the paths traversed by sections of the Earth's crust.

Tectonic plates

Tectonic plates are massive slabs making up the Earth's surface that move and interact in various ways. The movement of these plates is a crucial aspect of geology. This shifting is responsible for the formation of many geological features like mountains, earthquakes, and oceanic trenches.
Over millions of years, tectonic plates gradually drifted. The study of paleomagnetism reveals fascinating details about how these plates moved in the past. By analyzing the magnetic fields recorded in rocks, scientists can determine the historical motion of tectonic plates. This information is essential for reconstructing the ancient positions of continents and understanding the forces that shaped our planet's surface into the arrangement we see today.