= Solution
The reflected P-wave is propagating only while its normal wavenumber is real, equivalently while $|\sin\phi|\leq1$. Since
$$
\sin\phi=\frac{c_P}{c_S}\sin\theta,
$$
it is <evanescent wave>[evanescent] when
$$
\boxed{\sin\theta>\frac{c_S}{c_P}}.
$$
Put
$$
s=\frac{c_P}{c_S}\sin\theta>1,
\qquad
q=\sqrt{s^2-1},
\qquad
\cos\phi=iq.
$$
Then its spatial factor is
$$
e^{ik_Psx+k_Pqz},
$$
which decays as $z\to-\infty$. The reflected SV amplitude becomes
$$
R=-\frac{iq\cos\theta-s\sin\theta}
{iq\cos\theta+s\sin\theta}.
$$
The numerator and denominator have equal <modulus>[complex modulus], so
$$
\boxed{|R|=1}.
$$
\b[Thus evanescent mode conversion changes the reflected SV phase but not its amplitude, as described by <Unit-modulus SV reflection with evanescent P conversion>.]
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