dMODELS: An Open-Source, Modular MATLAB Environment for Geodetic Deformation Analysis

Ground deformation can arise from tectonic and volcanic processes as well as from human activities, such as subsurface fluid withdrawal. Mathematical models describing crustal deformation in response to these processes are essential for characterizing driving mechanisms, constraining source location, size, orientation, and volume change. Models provide critical information for hazard forecasting and mitigation, assessing anthropogenic environmental impacts, land-use planning, and related applications.

In this context, analytical kinematic models remain essential tools for the rapid interpretation of deformation, particularly in operational and time-sensitive settings.

dMODELS is an open-source MATLAB environment designed primarily to model and interpret crustal deformation associated with volcanic activity and active fault systems by non-linear inversion of GNSS, InSAR, and tilt observations. The software consolidates a suite of analytical kinematic source models into a single, end-to-end framework that is modular (pre-processing → inversion → post-processing), consistent (standardized formulations across models), transparent (fully documented scripts with examples), and cross-platform (Windows and Linux). Although most analytical formulations originate from established literature, several equations have been verified, reformulated, standardized to ensure internal consistency, and validated against corresponding finite-element solutions.

The platform runs on Windows and Linux systems and is structured to support end-to-end modeling workflows, including: (a) preprocessing tools for data selection and formatting, (b) non-linear inversion routines for estimating source parameters and associated uncertainties, and (c) post-processing utilities for generating publication-ready figures. Each module is accompanied by examples and documentation, with a full user manual in release by the U.S. Geological Survey.

The deformation sources implemented in dMODELS are kinematic representations, including pressurized cavities (spherical, spheroidal, or penny-shaped) and planar dislocations embedded in a homogeneous, isotropic elastic half-space. These constructs do not represent physical reservoirs directly but approximate the stress and strain fields produced by real subsurface processes. As such, dMODELS allows users to constrain source geometry, location, volume change, and stress distribution, although total reservoir volume and fluid properties remain unresolved.

Despite the inherent simplifications of analytical models, their rigorous use, combined with high-quality geodetic datasets, provides powerful insights into active deformation sources and supports both research and monitoring applications. By making robust, reliable, and independently verified modeling tools readily accessible, dMODELS supports reproducible analyses and enables their use by a broader scientific and operational community.