Towards universal PGD scaling law derived from GNSS and seismic data

Peak Ground Displacement (PGD) plays a fundamental role in the description of strong ground motion and is increasingly important in earthquake early warning systems for real-time estimation of earthquake source parameters, including moment magnitude estimation. In this study, we aim to derive a universal PGD scaling law based on the integration and joint analysis of seismic and GNSS observations, under the explicit assumption that a physically consistent PGD scaling relationship should be valid across different sensor types. In other words, the same PGD scaling law is expected to describe observations from both GNSS receivers and seismometers, providing a unified framework for rapid moment magnitude estimation.
The dataset consists of more than 20,000 observations from strong motion sensors - ESM FlatFiles (Lanzano et al. 2019) and over 3,000 observations from GNSS receivers (Ruhl et al., 2018; DeGrande & Crowell, 2025; INGV, GEONET (GSI)), all thoroughly checked and rigorously filtered to remove erroneous and unreliable records. The data cover 1,802 earthquakes that occurred between 1969 and 2025, with moment magnitudes ranging from Mw 3.0 to 9.1. To our knowledge, this is the largest dataset ever used for the estimation of PGD scaling relationships.
The analysis is based on the PGD functional form originally proposed by Crowell et al. (2013), which serves as a reference model. In addition, two alternative PGD scaling models are introduced and evaluated. Special attention is given to the treatment of observational uncertainties: several observation-weighting strategies are tested, and systematic issues inherent in commonly used PGD weighting approaches are identified and discussed. The results demonstrate that the choice of weighting scheme has a significant impact on the estimated scaling parameters.
By combining high-quality seismic and GNSS data over an unprecedented range of magnitudes and distances, and by enforcing a unified description across sensor types, this study provides new constraints on PGD scaling behaviour and highlights methodological aspects that are critical for the development of robust, physically consistent, and transferable PGD scaling laws. The proposed approach delivers the moment magnitudes (Mw) from GNSS and/or strong motion sensors PGD observations with the average bias less than 0.02 and 0.23 RMSE. 

Crowell, B. W., D. Melgar, Y. Bock, J. S. Haase, and J. Geng (2013). Earthquake magnitude scaling using seismogeodetic data, Geophys. Res. Lett. 40, 6089–6094, doi: https://doi.org/10.1002/2013GL058391

DeGrande, J. V., and B. W. Crowell (2025). A Combined PGD–PGV Scaling Law with Rproxy Distance for the G-FAST Earthquake Early Warning Module, Bull. Seismol. Soc. Am. XX, 1–16, doi: https://doi.org/10.1785/0120250168

Lanzano, G., Sgobba, S., Luzi, L. et al. (2019). The pan-European Engineering Strong Motion (ESM) flatfile: compilation criteria and data statistics. Bull Earthquake Eng 17, 561–582. https://doi.org/10.1007/s10518-018-0480-z

Ruhl, C. J., Melgar, D., Geng,et al. (2018). A Global Database of Strong‐Motion Displacement GNSS Recordings and an Example Application to PGD Scaling. Seismological Research Letters 90 (1): 271–279. doi: https://doi.org/10.1785/0220180177