We have investigated how well the depth extent of rupture can be determined for a shallow dip-slip earthquake from long-period WWSSN body waves. The 16 October 1981 Chilean outer-rise earthquake (MW = 7.2) is analyzed as an example. Calculation of the resolution matrix for the vertical distribution of displacement rate on the fault plane shows that the depth extent of rupture cannot be resolved better than 20 km, even when the data set consists of both P and S waves. Although the depth extent of rupture of the 1981 earthquake is too small to be resolved, it is possible to infer some constraints from the point-source depth in combination with the source duration. While inversion for the depth extent of rupture can be formulated as a linear problem, determination of the point-source depth is nonlinear, and a formal resolution study cannot be conducted. The point-source depth estimate for the 1981 earthquake is 28 to 32 km (80% confidence interval); the source duration is 8 sec. Assuming a rupture velocity of 3 km/sec, we have explored several rupture models in a synthetic experiment to shed light on the relation between point-source depth and centroid depth. The experiments show that point-source depths agree with the centroid depth. Given that there is poor resolution of the depth extent of rupture of the 1981 earthquake, we conclude from the synthetic experiments that the earthquake may have ruptured updip to a depth as shallow as 17 km or downdip to a depth as deep as 43 km.