The Real and Pseudo Dispersion Measures of FRB~20220912A

Fast radio bursts (FRBs) are millisecond-duration radio transients. As they propagate through the interstellar medium, they interact with free electrons, resulting in dispersion. The corresponding dispersion measure (DM) is referred to as the real DM (DM$_{\rm real}$). In practice, however, the dispersion measure derived from modeling (DM$_{\rm model}$) is often contaminated by intrinsic burst morphology, giving rise to a pseudo DM component (DM$_{\rm pseudo} = {\rm DM}_{\rm model} - {\rm DM}_{\rm real}$). In this work, we focus on the highly active repeating FRB~20220912A and utilize its microshots -- extremely short-duration (typically tens of microseconds), broadband emissions -- to investigate its DM$_{\rm real}$ and DM$_{\rm pseudo}$. We adopt two assumptions: first, that FRB~20220912A resides in a non-magneto-ionic environment and that its DM$_{\rm real}$ variation is smaller than $10^{-2}$\,pc\,cm$^{-3}$ over a few years; and second, that microshots have a negligible intrinsic morphological time delay. By identifying two new microshots and combining them with previously reported ones, we find that all four microshots exhibit remarkably consistent DM values over a one-month timescale, with an average of $219.380 \pm 0.004\,\mathrm{pc\,cm^{-3}}$. We define this value as the DM$_{\rm real}$ of FRB~20220912A. We further show that bright, narrow bursts with a width of less than 2\,ms also yield DM estimates consistent with the microshot-based DM$_{\rm real}$. A survey of five repeating FRBs reveals that DM$_{\rm pseudo}$ is a common phenomenon, with variations typically spanning a range of approximately $10\,\mathrm{pc\,cm^{-3}}$ at 1.2\,GHz. These findings highlight the importance of accounting for morphological contributions in DM interpretation and demonstrate that microshots and narrow bursts are powerful tools for probing DM$_{\rm real}$.