  We describe the results of a new reverberation mapping program focused on the
nearby Seyfert galaxy NGC 3227. Photometric and spectroscopic monitoring were
carried out from 2022 December to 2023 June with the Las Cumbres Observatory
network of telescopes. We detected time delays in several optical broad
emission lines, with H$\beta$ having the longest delay at $\tau_{\rm
cent}=4.0^{+0.9}_{-0.9}$ days and He II having the shortest delay with
$\tau_{\rm cent}=0.9^{+1.1}_{-0.8}$ days. We also detect velocity-resolved
behavior of the H$\beta$ emission line, with different line-of-sight velocities
corresponding to different observed time delays. Combining the integrated
H$\beta$ time delay with the width of the variable component of the emission
line and a standard scale factor suggests a black hole mass of $M_{\rm
BH}=1.1^{+0.2}_{-0.3} \times 10^7 M_{\odot}$. Modeling of the full
velocity-resolved response of the H$\beta$ emission line with the
phenomenological code CARAMEL finds a similar mass of $M_{\rm
BH}=1.2^{+1.5}_{-0.7} \times 10^7 M_{\odot}$, and suggests that the
H$\beta$-emitting broad line region (BLR) may be represented by a biconical or
flared disk structure that we are viewing at an inclination angle of $\theta_i
\approx 33^{\circ}$ and with gas motions that are dominated by rotation. The
new photoionization-based BLR modeling tool BELMAC finds general agreement with
the observations when assuming the best-fit CARAMEL results, however BELMAC
prefers a thick disk geometry and kinematics that are equally comprised of
rotation and inflow. Both codes infer a radially extended and flattened BLR
that is not outflowing.
