  Orphan afterglows from short $\gamma$-ray bursts (GRB) are potential
candidates for electromagnetic (EM) counterpart searches to gravitational wave
(GW) detected neutron star or neutron star black hole mergers. Various jet
dynamical and structure models have been proposed that can be tested by the
detection of a large sample of GW-EM counterparts. We make predictions for the
expected rate of optical transients from these jet models for future survey
telescopes, without a GW or GRB trigger. A sample of merger jets is generated
in the redshift limits $0\leq z\leq 3.0$, and the expected peak $r$-band flux
and timescale above the LSST or ZTF detection threshold, $m_r=24.5$ and $20.4$
respectively, is calculated. General all-sky rates are shown for $m_r\leq26.0$
and $m_r\leq21.0$. The detected orphan and GRB afterglow rate depends on jet
model, typically $16\lesssim R\lesssim 76$ yr$^{-1}$ for the LSST, and
$2\lesssim R \lesssim 8$ yr$^{-1}$ for ZTF. An excess in the rate of orphan
afterglows for a survey to a depth of $m_r\leq26$ would indicate that merger
jets have a dominant low-Lorentz factor population, or the jets exhibit
intrinsic jet structure. Careful filtering of transients is required to
successfully identify orphan afterglows from either short or long GRB
progenitors.
