Current strategies and logistics for seismic data acquisition impose restrictions on the calendar-time temporal resolution obtainable for a given time-lapse monitoring program. One factor that restricts the implementation of a quasi-continuous monitoring program using conventional strategies is the time it takes to acquire a complete survey. Here quasi-continuous monitoring describes the process of reservoir monitoring at short time intervals. This dissertation describes an approach that circumvents the restriction by requiring only a subset of a complete survey data each time an image of the reservoir is needed. Ideally, the time interval between survey subset acquisitions should be short so that changes in the reservoir properties are small. The accumulated data acquired are used to estimate the unavailable data at the monitor survey time, and the combined known and estimated data are used to produce an image of the subsurface for monitoring. Quasi-continuous seismic monitoring can be used to monitor geologic reservoirs during the injection phase of a carbon dioxide sequestration project. It can also be used to monitor reservoir changes between injector and producer wells during the secondary recovery phase in an oil field. The primary advantage of a quasi-continuous monitoring strategy over the conventional strategy is the high temporal resolution of the reservoir changes obtainable. Naturally, the spatial resolution of the image obtained using a subset of the data from a full survey will be worse than the spatial resolution of the image obtained using the complete data from a full survey. However, if the unavailable data are estimated perfectly, the spatial resolution is not lost. The choice of estimation algorithm and the size of the known data play an important role in the success of the approach presented in this dissertation.