Question

imagine that there are two faults that slip the same amount over a long time. all the slip happens in earthquakes. on fault a, all the earthquakes have a slip of 1 m. on fault b, all the earthquakes have a slip of 2m. select the option which is most likely.
fault a will have twice as many earthquakes as fault b.
fault a and fault b will have the same number of earthquakes.
fault b will have twice as many earthquakes as fault a.
we cant draw any conclusions about the relative number of earthquakes on the faults.

Explanation:

Step1: Set up variables

Let the total slip amount be \(S\), the number of earthquakes on fault \(A\) be \(n_A\), and on fault \(B\) be \(n_B\). For fault \(A\), \(S = 1\times n_A\) (since slip per earthquake is \(1m\)). For fault \(B\), \(S=2\times n_B\) (since slip per earthquake is \(2m\)).

Step2: Equate the total slips

Since the total slip \(S\) is the same for both faults (given "two faults that slip the same amount over a long time"), we have \(n_A\times1=n_B\times2\).

Step3: Solve for the ratio of number of earthquakes

From \(n_A = 2n_B\), we can see that the number of earthquakes on fault \(A\) is twice the number of earthquakes on fault \(B\).

Answer:

Fault A will have twice as many earthquakes as fault B.