  While long period variables (LPVs) have been extensively investigated,
especially with MACHO and OGLE data for the Magellanic Clouds, there still
exist open questions in their pulsations regarding the excitation mechanisms,
radial order and angular degree assignment. Here, we perform asteroseismic
analyses on LPVs observed by the 4-year Kepler mission. Using a
cross-correlation method, we detect unambiguous pulsation ridges associated
with radial fundamental modes ($n=1$) and overtones ($n\geqslant2$), where the
radial order assignment is made by using theoretical frequencies and observed
frequencies. Our results confirm that the amplitude variability seen in
semiregulars is consistent with oscillations being solar-like. We identify that
the dipole modes, $l=1$, are dominant in the radial orders of $3\leq n \leq6$,
and that quadrupole modes, $l=2$, are dominant in the first overtone $n=2$. A
test of seismic scaling relations using Gaia DR2 parallaxes reveals the
possibility that the relations break down when $\nu_{\rm max}$ $\lesssim$ 3
$\mu$Hz (R $\gtrsim$ 40 R$_{\odot}$, or log $\rm L/L_{\odot}$ $\gtrsim$ 2.6).
Our homogeneous measurements of pulsation amplitude and period for 3213 LPVs
will be very valuable for probing effects of pulsation on mass loss, in
particular in those stars with periods around 60 days, which has been argued as
a threshold of substantial pulsation-triggered mass loss.
