We analyzed geologic-geophysical data, both from archives and collections in recent expeditions by the Shirshov Institute of Oceanology of Russian Academy of Sciences, and revealed many anomalies in the seismoacoustic wavefield. Anomalies are of two types: horizontal disturbed layers and vertical pipes. Anomalies form associations — pipes (chimneys) are rooted in disturbed layers and go through sediments up to the seafloor and form pockmarks. We consider all specified seismic anomalies and bottom microrelief as a possibility of vertical migration of gas and water via sediments (fluid from sediments to water and from seawater to sediments). It is expected that the fluids form a huge underground hydrosphere below the Caspian Sea. To test the fluid flow, we made a mathematical model of fluid discharge and absorption in bottom sediments. We hypothesize that the Caspian Sea level fluctuates, at least partially, due to cycles of the submarine ground water discharge and sea water absorption back into the sediments. This cyclicity of fluid discharge and absorption correlates with regional seismic events. The earthquakes cause tectonic relaxation, triggering the absorption process, and sea-level drop due to reverse flow into sediments. In other periods, the tectonic tension causes sediment compression and fluid discharge to sea water, which causes sea-level rise. The model was tested on the recent (past 100 years) sea-level change curve. As a result, we got a distribution of the general volume of fluid flows depending on the infiltration coefficient. The real change in the Caspian Sea volume is at the lower range of the calculated values, so we cannot neglect the effect of “gas pipes” (“chimneys”) on the Caspian Sea-level change.