Microseismic event locations obtained from seismic monitoring data sets are often a primary means of determining the success of fluid-injection programs, such as hydraulic fracturing for oil and gas extraction, geothermal projects, and wastewater injection. Event locations help the decision makers to evaluate whether operations conform to expectations or parameters need to be changed and may be used to help assess and reduce the risk of induced seismicity. However, obtaining accurate event location estimates requires an accurate velocity model, which is not available at most injection sites. Common velocity updating techniques require picking arrivals on individual seismograms. This can be problematic in microseismic monitoring, particularly for surface acquisition, due to the low signal-to-noise ratio of the arrivals. We have developed a full-wavefield adjoint-state method for locating seismic events while inverting for P- and S-wave velocity models that optimally focus multiple complementary images of recorded seismic events. This method requires neither picking nor initial estimates of event location or origin time. Because the inversion relies on (image domain) residuals that satisfy the differential semblance criterion, there is no requirement that the starting model be close to the true velocity. We determine synthetic results derived from a model with conditions similar to a field-acquisition scenario in terms of the number and spatial sampling of receivers and recorded coherent and random noise levels. The results indicate the effectiveness of the methodology by demonstrating a significantly enhanced focusing of event images and a reduction of 95% in event location error from a reasonable initial model.