I had posted the question below on a New York Times article, but did not get any useful replies.
The series of six successful Inmarsat pings known to exist, MAY carry enough information to say if the plane most likely went along the S or the N arc we see in reports. Unfortunately, only the last ping (at 8:11AM) is available publicly.
Here is the basic idea on extracting the information: A Malaysian military satellite gave the last geographic fix of ML370 at 2:15AM. A circle can be drawn with this point as the center and distance traveled at maximum speed as diameter, confining the plane's position at 3:11AM. From the ping at 3:11AM, another circle can be drawn, like the one drawn at 8:11AM. The intersection of the two circles give an arc of most likely 3:11 AM positions. At 4:11AM, we will have a series of circles from max distance and one circle from the ping. These intersections will give a series of possible arcs.
This process can be repeated (with increasing complexity, of course) giving us a series of most likely positions at 3:11AM, 4:11AM, 5:11AM, etc. If the trajectory of these sequence of spaces has a N/S directionality, we can say with some confidence that the aircraft went that way.
In reality, this would be more complicated. For example, the plane most probably did not go along a straight path at max speed. However, useful inferences can be made by adding other information available. For example, from the ping circles separated by one hour, we can get plausible directions the plane may have taken. Why isn't anyone pursuing this line of analysis?
There is a bit more detail here. Anyone estimating possible paths of MH370 quantitatively?