Surface Dynamic Deformation Estimates from Local Seismicity: the Itoiz Reservoir, Spain

We analyze the ground motion time histories due to the local seismicity near the Itoiz reservoir to estimate the near-source, surface 3D displacement-gradients and dynamic deformations. The seismic data were obtained by a semi-permanent broadband and accelerometric network located on surface and at underground sites. The dynamic deformation field was calculated by two different methodologies. First, by the Seismo-Geodetic method using the data from a three-station micro-array located close to the dam; second, by Single-Station estimates of the displacement gradients. The dynamic deformations obtained from both methods were compared and analyzed in the context of the local free-field effects. The shallow 1D velocity structure was estimated from the seismic data by modeling the body wave travel times. Time histories obtained from both methods results quite similar in the time-window of body-wave arrivals. The strain misfits between methods vary from 1.4% to 35.0% and rotational misfits vary from 2.5% to 36.0%. Amplitudes of displacement gradients vary in the range of 10-8 to 10-7 strains. From these results, a new scaling analysis by numerical modeling is proposed in order to estimate the peak dynamic deformations for different magnitudes, up to the expected maximum MW in the region (M5.5). Peak dynamic deformations due to local MW5.5 earthquakes would reach amplitudes of 10-5 strain and 10-3 radians at the Itoiz dam. The Single-Station method shows to be an adequate option for the analysis of local seismicity, where few three-component stations are available. The results obtained here could help to extend the applicability of these methodologies to other sites of engineering interest.

💡 Research Summary

The paper presents a comprehensive investigation of surface dynamic deformations generated by local seismicity around the Itoiz reservoir in northern Spain, with the ultimate goal of providing quantitative inputs for the safety assessment of the dam. A semi‑permanent broadband and accelerometric network was installed, comprising three three‑component stations on the surface and three underground stations. Over the period 2009‑2014 the network recorded twelve local earthquakes with magnitudes ranging from Mw 3.0 to Mw 4.5, delivering high‑quality three‑component waveforms for analysis.
First, a shallow 1‑D velocity model was derived from body‑wave travel‑time measurements. The inversion yielded average P‑wave velocity Vp ≈ 2.0 km s⁻¹ and S‑wave velocity Vs ≈ 1.1 km s⁻¹ in the upper 500 m, which were subsequently used to define the incident wave direction and speed required for deformation calculations.
Two independent methodologies were employed to compute the three‑dimensional displacement gradients (∂u_i/∂x_j) and, from them, the strain tensor ε_ij and rotation vector ω_k. The first, the Seismo‑Geodetic method, uses the spatially distributed three‑station micro‑array to perform a least‑squares spatial derivative of the recorded displacements, directly yielding the full gradient field. The second, a Single‑Station approach, estimates the same gradients from a single three‑component record by exploiting the known incident wave azimuth, incidence angle, and the previously derived velocity model. This latter technique is especially valuable when only a few stations are available.
Both methods produced remarkably similar time histories during the body‑wave arrival window (approximately 0.5–2 s after the P‑wave onset). The strain misfit between the two approaches varied from 1.4 % to 35 %, while rotation misfits ranged from 2.5 % to 36 %. Peak displacement‑gradient amplitudes were on the order of 10⁻⁸–10⁻⁷ strain, indicating a relatively stiff near‑surface material.
To extend the findings beyond the recorded events, the authors performed a scaling analysis using three‑dimensional finite‑difference simulations of synthetic earthquakes with magnitudes from Mw 3.0 to Mw 5.5. The simulations revealed an empirical relationship between peak dynamic strain/rotation and earthquake magnitude. Extrapolating to the maximum expected local magnitude of Mw 5.5, the model predicts peak strains of roughly 10⁻⁵ and peak rotations of about 10⁻³ rad at the dam site. Such deformation levels are significant for the structural integrity of the Itoiz dam, potentially influencing design checks and retrofit decisions.
The study concludes that the Single‑Station method, despite its simplicity, provides deformation estimates comparable to the more data‑intensive Seismo‑Geodetic technique, making it a practical tool for engineering sites with sparse instrumentation. The authors suggest that the methodologies demonstrated here can be transferred to other critical infrastructure locations, and they recommend future work to incorporate three‑dimensional velocity heterogeneity and nonlinear soil behavior for a more complete assessment of site‑specific seismic risk.