Odds of Getting In
Get the right degrees, do the right internships, and your odds are pretty good. You'll face competition just like any other field, but the amount of jobs for seismologists is steadily growing, which is good news for you. Obviously, you won't start off at the top of the pay scale, but there are a good amount of jobs out there whether they be with private or public institutions, and you'll be able to work your way up.
Count yourself lucky that seismology is your thing rather than something artsy. School will be tough, but the job market will handle you far more gently.