  Motivated by the recent scanning tunneling microscopy (STM) experiments [J.
E. Hoffman {\it et al.}, Science {\bf 297}, 1148 (2002); K. McElroy {\it et
al.}, Nature (to be published)], we investigate the real space local density of
states (LDOS) induced by weak disorder in a d-wave superconductor. We first
present the energy dependent LDOS images around a single weak defect at several
energies, and then point out that the experimentally observed checkerboard
pattern in the LDOS could be understood as a result of quasiparticle
interferences by randomly distributed defects. It is also shown that the
checkerboard pattern oriented along $45^0$ to the Cu-O bonds at low energies
would transform to that oriented parallel to the Cu-O bonds at higher energies.
This result is consistent with the experiments.
