
The Bathyspere - 1930 (image is from Wikipedia Commons)
Sperm Whale Diving
The sperm whale, seen in the picture above, is the diving world champion of marine mammals. The whale can stay under water for over 90 minutes and dive to depths of nearly 10,000 ft. It has an extraordinary array of adaptations that allow it to dive so deep. Read below to see how marine mammals, in general, deal with the problems associated with going deep.

Austrailian Sea Lion
When you and I go underwater, the first thing we may notice is that our ears hurt. This is because of the difference in pressure between the air in our ears and the water outside. Air (as a gas) can be compressed while water cannot. At sea level a body experiences 14.7 pounds per square inch of pressure (1 atmosphere.) For a diving marine mammal, another atmosphere of pressure is added every ten meters that they go down. Thus a male elephant seal diving to 1000 meters is experiencing 100 times the pressure that he would at the surface.
Over time, most marine mammals have lost their external ears and sinuses. Without these air chambers, a diving marine mammals does not suffer the effects of changing pressure. Sea lions and fur seals do have ears, but during a dive theirs will fill with a bloody fluid, forcing any air out.
Mammals store more air in their lungs than any other place. If you were to swimming, it would only make sense that you would take a deep breath before you went under. This is a problem for two reasons. First, air is buoyant, making diving difficult. Second, as was mentioned above, air is easily compressed, leading to a potential collapse of the lungs. Most marine mammals have lungs that are designed to collapse. They tend to be long and tubular with built-in protective rings to keep valves open. Also, unlike you and I, marine mammals exhale right before a dive. They have very muscular and effcient lungs which can exhale up to 90% of the air in their lungs in any give breath (an athletic human can do around 10%.) Thus, by removing the air from their body, a diving marine mammal has very little problems with changing pressure.
An elephant seal's heart rate during a dive (Image is from Alaska Sea Grant, used with permission)
So if marine mammals exhale before they dive, how do their muscles get the oxygen they need to work? The answer is that they store oxygen in their blood and in their muscles rather than in their lungs. Marine mammals have a very high blood to body volume ratio. Mare mammas also have a higher percentage of red blood cells than most mammals (human = 36%, seals = 50%.) By comparison, this makes their blood very thick and viscous. Marine mammals also have a high concentration of hemoglobin in their blood and myoglobin in their muscles. Both of these molecules are used to store oxygen.
The mammalian diving reflex allows mammals to lower their heart rate and ultimately survive submersion in water for extended periods of time. Bradiacardia, as it is also know is triggered by cold water contact to the nerves of the face. It occurs in all mammals, but to a much greater extent in marine mammals. Wedel seals have been measured to lower their heart rate to as low as four beats per minute.
When exercising humans run out of oxygen we say that they have gone into anaerobic respiration. This is very taxing on our muscles and leads to soreness and fatigue. Most body organs marine mammals appear to switch to anaerobic respiration while diving without suffering the same effects. We still don't know exactly how they do this.
This figure shows the diving behavior of a male elephant seal. Dives lasting 20-40 minutes of nearly verticle profiles are followed by very short breaks. (Image from the National Marine Mammal Labratory)
When human scuba divers come up too quickly from a dive, gases that were dissolved into their blood can come out of solution too quickly and form bubbles inside the blood vessels. These bubbles can get lodged in capillaries and migrate to critical organs, causing pain and possibly organ damage. DCS increases with intensity the deeper you go and the faster you surface. Marine mammals go very deep and surface very quickly. So why don't they have problems with "the bends?" Its simple - they exhale before they dive. No air, no problem. In addition, many marine mammals have an extensive "net" of blood vessels feeding into their brain. Its known as the "retia mirabilia," and it likely serves several functions, but one of them is capturing bubbles that may form in the blood stream.

Bowhead whales can have as much as two feet of blubber insulating acting to insulate their body
Many human scuba divers have known the pain and discomfort associate with having a small hole in their wetsuit during a cold water dive. Water dissipates heat from the body much faster than air. A person who falls in water near the freezing point will be hypothermic within a few minutes, yet marine mammals dive to depths where the temperatures approach freezing. The most obvious way that marine mammals stay warm is that they tend to be large and rather "sausage shaped." This shape gives them a low surface area to volume ratio. Per unit volume, there is less of them exposed to cold moving water. Marine mammals also have a lot of blood relative to their body size. Water has a high heat capacity and does a nice job of maintaining body temperature.
Most marine mammals have a thick layer of fat know as "blubber." This fat layer also serves as calorie storage for marine mammals that undergo long periods of fasting. Smaller marine mammals tend to have highly insulated layers of fur. The extreme example of this is the sea otter. Sea otter fur is two layers thick, and very effective at trapping air to aide in insulation. Sea otters may have as many as one million hairs per square inch. That's ten times as many hairs as the average human has on their whole head.
No part of a mammal is more buyant than the air in their lungs. For marine mammals the key to reducing this buoyancy is to exhale before diving.

Thick billed murres weigh only a pound or two yet can dive up to 100 meters, image from Wikipedia Commons)