In the terminal phase, it's a straight shot with proximity detonation of the 2000 kilo warhead. But at a mile in less than six seconds, a large ship has very little time to react once the things lite off...less than a minute for 10 miles.
Several variants. Some are seeded like limpit mines and sit in hibernation mode at 1000ft waiting. Others cruise to the target acquisition area at 50kts and then go into acquisition mode. They target a vessel and then lite off when they are close enough to assure a hit. Some launched by aircraft, etc. Later, a variant is developed that does a pop-up manuever where it actually lifts out of the water and attacks accross the last couple of miles like a missile.
They use digital terrain maps of the ocean floor and have sophisticated sonar and acoustic target acquisition capabilities.
All fictional of course.