  We consider a tsunami wave equation with singular coefficients and prove that
it has a very weak solution. Moreover, we show the uniqueness results and
consistency theorem of the very weak solution with the classical one in some
appropriate sense. Numerical experiments are done for the families of
regularised problems in one- and two-dimensional cases. In particular, the
appearance of a substantial second wave is observed, travelling in the opposite
direction from the point/line of singularity. Its structure and strength are
analysed numerically. In addition, for the two-dimensional tsunami wave
equation, we develop GPU computing algorithms to reduce the computational cost.
