  High-order topological phases host robust boundary states at the boundary of
the boundary, which can be interpreted from their boundary topology. In this
work, considering the interplay between superconductors and magnetic fields to
gap the surface states of three-dimensional weak topological insulators, we
show that second-order topological superconductors (TSCs) featuring helical or
chiral Majorana hinge modes and third-order TSC featuring Majorana corner modes
can be realized. Remarkably, the higher-order TSCs in our models can be
attributed to their certain boundaries, surfaces, or hinges, which naturally
behave as first-order TSC in DIII or D symmetry class. Correspondingly, these
higher-order TSCs can be characterized by the boundary first-order topological
invariants, such as surface Chern numbers or surface $Z_2$ topological
invariants for surface TSCs. Our models can effectively capture the topology of
iron-based superconductors with desired inverted band structures and
superconducting pairings.
