Processing large mongo collection offsite

I have a system writing logs into mongodb (about 1kk logs per day). On a weekly basis I need to calculate some statistics on those logs. Since the calculations are very processor and memory consuming I want to copy collection I'm working to powerful offsite machine. How do I keep offsite collections up to date without copying everything? I modify offsite collection, by storing statistic within its elements i.e. adding fields {"alogirthm_1": "passed"} or {"stat1": 3.1415}. Is replication right for my use case or I should investigate other alternatives?