POTENTIAL METHODS 2018 2019 Part 3 Geometric bodies

POTENTIAL METHODS 2018 -2019 Part 3 Geometric bodies modeling Carla Braitenberg Trieste University, DMG Home page: http: //www 2. units. it/~braitenberg/ e-mail: berg@units. it Tutor Tommaso Pivetta Email: tommasopivetta@yahoo. it 1

Theory of geometrical bodeis modeling Up to now we have expressed the potential field of the earth in terms of spehrical harmonic expansion. We have defined the gravity anomaly. One method to model the local gravity anomaly is through modeling with geometric bodies, as sphere, cylinder, prism. We refer to theory explained in chapter 3 of the textbook Hinze et al. 2013.

We report the expression of potential field, gravity acceleration and gravity gradient for a point mass. Observation point in (x, y, z), mass point in (x’, y, ’, z’). Vector pointing from mass point to observation point, and it’s length: Force field: is the gradient of the potential field Φ:

• The derivative of the force field gives the gradient tensor: • The force field for the point mass, as gradient of the potential:

The gradient components for the point mass:

Gravity Potential effect of extended mass body, with spatial limits xa’, xb’, ya’, yb’, za’, zb’. Gravity force of extended mass body, with spatial limits xa’, xb’, ya’, yb’, za’, zb’.

Force field components

Gradient field components

Integrated field for specific geometrical bodies

Integrated field for specific geometrical bodies