# How to differentiate between normal and reverse fault, given a stress tensor?

I want to generate synthetic fault slip data using a known stress tensor.

I am using a rotation matrix to get the orientation of the principal stress axes, and rotating the tensor [1 0 0, 0 phi 0, 0 0 0] to get a reduced stress tensor.

Then I have to create (strike, dip) of the plane and (trend, plunge) of the lineations.

Right now, my equations look like this-

T = [1 0 0, 0 phi 0, 0 0 0]

R = rotation matrix (each row of R will contain the direction cosines of the principal stress axes)

Reduced tensor (S) = R.T.(R_transpose)

Randomly generate a fault plane (strike and dip), get its normal vector N.

Stress Vector = S.N

Using Normal Vector and Stress Vector, get the component of stress vector along the fault plane, i.e., the shear stress component.

Get the trend and plunge of the shear stress component.

Right now, I am unable to differentiate between normal and reverse faults by only varying the stress tensor. Do I also have to change the trend, plunge for them?

I need the equations for implementing this on a computer program.