Abstract <p>The downward continuation of potential fields from the Earth’s surface into the subsurface is a critical task in gravity exploration, as it helps to identify the sources of gravity anomalies. This problem is often addressed by solving a first-kind integral equation using regularization techniques to stabilize an inherently unstable process. A similar approach is used in our work, where the continued field is represented as the potential of a simple layer or its vertical derivative. The constancy of the density sign of this equivalent simple layer preserves the sign of anomalies, provided that the layer’s surface encloses all anomalous sources. This constraint is a key feature of our algorithm for the downward continuation of potential fields. To enforce, for instance, non-negativity in the simple layer density, we employ the NNLS (Non-Negative Least Squares) method. The efficiency of the proposed method is demonstrated on model examples.</p>