I think that for those familiar with physics following International System of Units, it's more easy to consider (with "u" as per Dan notation)

Wp=g*mp where g is the vertical acceleration

Fp=u*Wp=u*g*mp=(u*g)*mp where u*g is the horizontal acceleration by seismic event

Because input of horizontal acceleration is expected to be in fractions of "g", input must be "u".