Method for restoring the orientation of ocean bottom seismometers using distant earthquakes records

TL;DR

This work introduces a cross-spectral method to recover the vertical orientation of seafloor seismometers by leveraging the linear pressure–vertical acceleration coupling $p = \rho H \cdot a_v$ within the forced-oscillation band. By projecting the three acceleration components onto candidate directions with angles $(\eta,\kappa)$, computing the MSC with bottom pressure, and integrating over $f_g$ to $f_{up}$ to form $I_{norm}$, the vertical axis is identified as the direction maximizing coherence. Validation on six S-net stations for three Mw earthquakes shows angular differences mostly within $1^{\circ}$ relative to a gravity-based reference, with larger discrepancies for deep stations or near-vertical alignments, and smeared peaks during the Noto event due to orientation changes. The approach is versatile (also for velocimeters), robust for moderate depths and magnitudes, and provides a practical tool for in-situ sensor calibration and orientation monitoring in ocean-bottom observatories.

Abstract

A method is presented for determining the vertical direction relative to the axes of seismometers installed in seafloor observatories. The method is based on the linear relationship between the vertical component of seafloor acceleration and pressure variations at the ocean bottom, which follows directly from Newton's second law and holds within the frequency range of forced oscillations. The method's performance was validated using data from ocean bottom seismometers (accelerometers) and pressure gauges of six S-net stations during three seismic events: Gulf of Alaska Mw 7.9 (23.01.2018), Chignik Mw 8.2 (29.07.2021) and Noto Mw 7.5 (01.01.2024). The results were compared with an independent alternative method, showing discrepancies within 1 degree for most stations. A key advantage of the proposed method is its applicability not only to accelerometers but as well to velocimeters.

Figures (5)

• Figure 1: Location of the selected events and the S-net on a map of the North Pacific Ocean. (a). Detailed map of the S-net stations. (b) Stations selected for analysis are marked with red stars.
• Figure 2: Cross-spectra (magnitude-squared coherence — MSC) of pressure variations at ocean bottom $p$ with acceleration $a_{I_{norm}}(\eta, \kappa, t)$, corresponding to the vertical direction, for two S-net stations. Red dashed lines mark the frequencies $f_{ac}$, $f_g$, $0.1Hz$.
• Figure 3: Coherence diagrams $I_{norm}(\eta, \kappa)$. Left column corresponds to station S2N17; right column --- S2N18. Rows from top to bottom: Noto (2024), Chignik (2021), Gulf of Alaska (2018).
• Figure 4: Coherence diagrams $I_{norm}(\eta, \kappa)$. Left column corresponds to station S4N06; right column --- S4N11. Rows from top to bottom: Noto (2024), Chignik (2021), Gulf of Alaska (2018).
• Figure 5: Coherence diagrams $I_{norm}(\eta, \kappa)$. Left column corresponds to station S4N25; right column --- S6N08. Rows from top to bottom: Noto (2024), Chignik (2021), Gulf of Alaska (2018).