In unconsolidated, heterogeneous aquifer systems, low rates of pore-pressure diffusion of applied effective stresses due to the drainage of thick, low-permeability, clay-rich layers with time constants of decades to centuries cause delayed, residual permanent compaction and land subsidence. Current application of satellite differential radar interferometry (DInSAR—differential interferometric synthetic aperture radar) to estimate aquifer hydraulic properties (compressibility and/or storage) in these systems is limited by the temporal availability of synthetic aperture radar data (1992–present). In this paper we study the degree of aquifer compaction due to water extraction using DInSAR through an example in southeast Spain. Ground deformation data indicate large-scale deformation and in particular the discovery of the highest rates of groundwater-related land subsidence recorded in Europe (>10 cm/yr), affecting the Guadalentín River basin (>200 km2), the largest tributary of the Segura River. Modeling of the ground surface time series of the Guadalentín Basin indicates that deformation is mainly driven by nonlinear time-delayed flow processes in the underlying aquifer. After a drought period (1990–1995), the aquifer responded with an exponential decay of the land subsidence (lasting ∼8 yr), suggesting transient groundwater pore-pressure flow. We show that multitemporal satellite radar interferometry analysis and its modeling can be a stimulating way to study nonlinear soil mechanics and groundwater flows at aquifers. A deeper understanding of such processes could help the management of water resources and land subsidence of unconsolidated coastal and Quaternary alluvial aquifers in a highly evolving climate region (the Mediterranean Sea and elsewhere).