  In the framework of general relativity (GR), gravitational waves (GWs) are
theorized to travel at the speed of light across all frequencies. However,
Lorentz invariance (LI) violation and weak equivalence principle (WEP)
violation may lead to frequency-dependent variations in the propagation speed
of GWs, which can be examined by comparing the theoretical and observed
discrepancies in the arrival times of GW signals at various frequencies. This
provides us with an opportunity to test these theories. In theories involving
LI violations, we focus on the massive gravity with the graviton mass $m_g$. In
the case of WEP violation, different massless particles exposed to the same
gravitational source should exhibit varying gravitational time delays. The
gravitational time delay induced by massive gravitational sources is
proportional to $\gamma+1$, where the parameter $\gamma=1$ in GR. Therefore, we
can quantify these two violations using the graviton mass $m_g$ and $|\Delta
\gamma|$, respectively. In this study, we use selected GW data from binary
black hole coalescences in the LIGO-Virgo catalogs GWTC-2.1 and GWTC-3 to place
constraints on the parameters $m_g$ and $|\Delta \gamma|$. Our most stringent
constraints suggest that $m_g \lesssim 1.40\times10^{-26}eV/c^2$ at the upper
limit of the 90% credible interval and $|\Delta \gamma| \lesssim 7.05 \times
10^{-16}$ at the 90% credible interval. We also compute Bayes factors for
models that assume LI and WEP violations compared to the standard GW model,
respectively. The absolute value of the natural logarithm of the Bayes factor
is generally less than 2. Our analysis reveals no statistically significant
preference for either model. Additionally, the Bayes factors between these two
models do not provide obvious evidence in favor of either one.
