**6.1 Cost function methods**

These methods share the definition of a proper cost function followed by the search of its minimum within the 3D volume of a grid with the indexes (k, l, m) in X (east), Y (north), and Z (upward) directions. The computational complexity comprises four nested loops, three over the grid dimensions (k, l, m) and one fourth over the number of stations that recorded particular data. We present three cost function methods based on each of the three data sets (PGV, Tp, Tps) described before. We take the liberty to name the various methods after scientists who defined the principles of the relevant cost functions.
