Magnetic Anomaly Profile Analysis

This question analyzes a total field anomaly magnetic profile across a body resembling a single pole at the magnetic equator. We need to determine the depth and symmetry of the anomaly.

Observed Anomaly Extremes

• Maximum anomaly: $x_{max} = 35\text{ m}$
• Minimum anomaly: $x_{min} = 135\text{ m}$

Determining Pole Location and Symmetry

For a magnetic anomaly caused by a single pole (or approximating a vertical magnetic dipole) at the magnetic equator, the total field anomaly profile typically exhibits odd symmetry. This means the profile is antisymmetric about the horizontal position of the source. The horizontal location of the pole ($x_0$) is found at the midpoint between the maximum and minimum anomaly positions.

Calculation of the pole's horizontal coordinate:

$x_0 = \frac{x_{max} + x_{min}}{2}$

Substituting the given values:

$x_0 = \frac{35\text{ m} + 135\text{ m}}{2} = \frac{170\text{ m}}{2} = 85\text{ m}$

Thus, the pole is located horizontally at $85\text{ m}$, and the profile shows odd symmetry.

Calculating Pole Depth

The distance between the observed maximum and minimum anomaly points is:

$ \Delta x = x_{min} - x_{max} = 135\text{ m} - 35\text{ m} = 100\text{ m} $

For a vertical magnetic dipole anomaly model at the magnetic equator, the total field anomaly is antisymmetric. The extrema are observed at a horizontal distance related to the depth ($h$) of the pole. A common relationship is that the distance from the pole's horizontal location ($x_0$) to the extrema is approximately $h/\sqrt{2}$.

The horizontal distance from the pole ($x_0 = 85\text{ m}$) to the maximum anomaly ($x_{max} = 35\text{ m}$) is:

$ |x_{max} - x_0| = |35\text{ m} - 85\text{ m}| = 50\text{ m} $

Similarly, the distance to the minimum anomaly ($x_{min} = 135\text{ m}$) is:

$ |x_{min} - x_0| = |135\text{ m} - 85\text{ m}| = 50\text{ m} $

Using the relationship $|x_{extrema} - x_0| \approx \frac{h}{\sqrt{2}}$, we have:

$ 50\text{ m} \approx \frac{h}{\sqrt{2}} $

Solving for the depth ($h$):

$ h \approx 50\text{ m} \times \sqrt{2} $

$ h \approx 50\text{ m} \times 1.414 \approx 70.7\text{ m} $

This calculated depth is approximately $70\text{ m}$.

Final Statement

Combining the findings: The pole is located at a depth of approximately $70\text{ m}$ below the horizontal coordinate $85\text{ m}$, and the anomaly profile exhibits odd symmetry.