How can I find strike and dip of a plane from equation of a plane?

I used xyz coordinates to find equation of a plane:

>> P1 = [X(1),Y(1),Z(1)];
>> P2 = [X(2),Y(2),Z(2)];
>> P3 = [X(3),Y(3),Z(3)];
>> normal = cross(P1-P2,P1-P3);
>> syms x y z
>> P = [x,y,z];
>> planefunction = dot(normal, P-P1)

[John D'Errico]

Define strike and dip.

[Star Strider]

You’re not from the West Coast!

Wikipedia: Strike and dip

Answer 1

[David Goodmanson]

Hello b,

I am assuming that x and y are dimensions along the earth's surface and that z is in the direction of up. You have a normal vector, and to make it a unit normal,

normal = normal/norm(normal);

The z component from the cross product may have come out either up or down, so you should check whether normal(3) is positive or negative. If it's negative, multiply the entire vector by -1, giving you a unit normal with positive z component.

The unit normal up vector to the earth's surface (e.s.) is n_e = [0 0 1]. The angle between the e.s. plane and the fault plane is the same as the angle between their normals, so

dip = acosd(dot(normal,n_e))

The strike angle depends a bit more on circumstances. [normal(1) normal(2)] is a vector on the e.s. that points toward directly downslope on the fault plane and so is perpendicular to the strike line. If x represents East and y represents North then

theta = atan2d(normal(1), normal(2)) + 90

is an angle going from North toward East. Here 90 degrees was added to get the strike line angle, but 90 could just as well be subtracted.

[David Goodmanson]

Yes there is. You have already constructed the unit normal to the fault plane with x,y,z coords [normal(1), normal(2), normal(3)]. From the end of the posted answer, [normal(1) normal(2)] is a vector on the earth's surface. That is the dip direction. (A vector right down the fall line, as if you were skiing, has these x and y coordinates and also a negative vertical coordinate).

If x represents East and y represents North then the dip direction angle

theta = atan2d(normal(1), normal(2))

is an angle going from North toward East. You just have to work out something similar if x and y represent different directions than that.

(Incidentally I kind of misspoke at the very end of the posted answer. The angle I was describing was the dip direction angle, same as here, not including the 90 degrees that were added to get the strike angle).

Answer 2

[Fabio Dias]

https://pangea.stanford.edu/ERE/db/GeoConf/papers/SGW/2016/Kiryukhin.pdf

[Walter Roberson]

In that paper, I do not see any method presented to calculate these quantities?