Trolling vs jigging

I only started fishing very recently, So this is probably a dumb question, but I figure I'd rather be a fool for 5min than a fool for life, so here it goes:

What is the advantages of trolling over jigging for salmon?

Seems to me like jigging is more manage on a kayak, easier to control the depth and bypass the depth uncertainty of trolling without a down rigger.
I can see that trolling can cover more water, but with fishfinder ubiquitous on kayaks, why not ride around in some search pattern until fish is located and then jig?
Thanks in advance for your thoughts!

This is a very good question. One that has come up before, but is worth revisiting every so often because it makes us think about why we're doing something instead of just saying, "Well that's what everyone else is doing" or "That's just the way we've always done it."   In the Willamette and Columbia River systems, most of the time you will see people trolling for salmon. The main reasons behind this have to do with the fact that there's usually a decent current to deal with and salmon typically don't stay in the same place for very long. There are spots in the Willamette where you may see people jigging for springers. These spots are essentially all above the 205 bridge and below the falls. However, when the river gets really slow late in the season, there are plenty of spots where jigging may actually work.  In the ocean or in the Puget Sound, you'll see much more jigging since one can simply find a school of fish that aren't moving in one specific direction too quickly and hang with them while jigging.

Additionally, even though the slow current conditions may make jigging easier later in the season, the fish tend to move through the system more quickly as the water slows. So that makes them tough to target by jigging.

In general (and I'm not talking specifically about salmon), if you are over a big school of fish, and there isn't too much wind and/or current, jigging can be a real effective way of catching fish.  However, if the school is small or the fish are widely scattered, even if the fish and your jig appear at the same depth on your fish finder, your jig may in fact be some distance away from the fish.  In these situations, trolling in figure 8 or cloverleaf patterns through the area of the fish with the help of the GPS screen on your fish finder may be more successful than jigging, because you can buzz your lure past more fish when trolling.  Trolling also allows you to cover a lot of territory, and increases the chance that you will blunder into a bunch of fish.

Another issue involves paddle kayaks versus pedal kayaks in situations in which there is much wind and/or current.  In a pedal kayak you can put your nose into the wind or the current, or some combination of them, and pedal and steer as necessary to hold yourself stationary over the bottom, with the help of the GPS screen on your fish finder, while jigging the whole time.  This is harder to do in a one-person paddle kayak, because most of us only have two arms, and you have to keep switching between paddling and jigging.  In a paddle kayak, in many wind and current conditions I find it easier to troll than to jig.

AK offshore view, in a nutshell, it can be hard to stay on top of the fish.   I have successfully located big offshore bait balls or schools of salmon multiple times just to get blown or carried off them, only to try and go back - with only mixed success. 

Winds in one direction, ocean currents in another, fish actively feeding - and often not on a school of baitfish over fixed structure.  it's a really great day when the forces of nature can keep you on top of them with little work, though. 

I LOVE jigging and mooching for salmon and other species, but the conditions have to be right to make it work from my Kayak, so I generally go out prepared to troll and to drift fish either bait/jigs/baited jigs if I think I'll be in an area of high current or tidal motion. 

Wow, thanks guys for your thoughtful answers and quick responses!
The challenge to stay on top of the fish was underestimated when I first thought about the issue. With that challenge in mind, it makes total sense that a lot of popular fisheris here are trolling fisheries.
pmmpete's cloverleaf troll pattern is an very interesting way to shotgun an area of water suspecting of holding fish.