Gas mining leads to saucer-like surface depressions. In the North Sea, gas is currently mined at several offshore locations. The associated bed depression has a similar spatial extent as offshore tidal sandbanks, which are large-scale bed patterns covering a significant part of the North Sea bottom. The morphological time scales of bed depressions and tidal sandbanks are similar, so that significant interaction between these features is expected. In this paper we allow the bed depression to become morphologically active. A simple depression model based on a homogeneous soil is tuned with data of a bed depression near the Dutch barrier island of Ameland. Next, this subsidence model is included in a morphodynamic model. We show that this model is able to explain tidal sandbanks, which represent natural bed behavior. Here we approximate the solution by an expansion up to first order. The zeroth-order solution of the model is a flat bed with a spatially uniform, time-independent current. The first-order solution is investigated using a Fourier transformation. In general, we observe significant interaction between the bed depression and the natural sandbank formation process. The process of induced bed depression triggers and intensifies the natural morphological behavior of the offshore seabed. The model also shows essential differences between modeling a morphodynamically active marine bottom depression and a bottom depression below the threshold for sediment motion. The maximum bed level depression in the active case is significantly larger, and the circular shape of depression contours is affected by stretching toward the preferred orientation of the tidal sandbank formation process.