#4191 map can be derived as follows.
You may infer from the strength of the last ping, how far away the plane was during the last ping. The "center" of the arc is eliminated, because this area is covered by some form of radar or other satellite, which did not see the aircraft. Based on the timing of the ping and the maximum speed of the aircraft, it would not be possible for the aircraft to make it to the left side of the circle.