code: def _compute_f1(self, C, mag, rrup):
          
          r = np.sqrt(rrup ** 2 + C['c4'] ** 2)
  
          f1 = (
              C['a1'] +
              C['a12'] * (8.5 - mag) ** C['n'] +
              (C['a3'] + C['a13'] * (mag - C['c1'])) * np.log(r)
          )
  
          if mag <= C['c1']:
              f1 += C['a2'] * (mag - C['c1'])
          else:
              f1 += C['a4'] * (mag - C['c1'])
  
          return f1
docs: Compute f1 term (eq.4, page 105)