# The Prompt ElastoGravity Signals (PEGS) : Detection capabilities and limitations of very broadband seismometers

Martin Vallée, Kévin Juhel, Pascal Bernard, Jean Paul Ampuero, Jean-Paul Montagner, Matteo Barsuglia

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## ► To cite this version:

Martin Vallée, Kévin Juhel, Pascal Bernard, Jean Paul Ampuero, Jean-Paul Montagner, et al. The Prompt ElastoGravity Signals (PEGS) : Detection capabilities and limitations of very broadband seismometers. Rencontres scientifiques et techniques RESIF 2019, Nov 2019, Biarritz, France. hal-02446614

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Submitted on 21 Jan 2020

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Distributed under a Creative Commons Attribution 4.0 International License
Introduction on PEGS

Gravitational perturbations due to mass redistribution associated with tectonic processes :

➤ Static (final) gravitational perturbations:
* Known solution for shear or tensile faults in half-space [Okubo et al., 1992]
* Observed by Earth gravimeters [2003 Tokachi earthquake, Imanishi et al., 2004] and space gravimetry [static gravitational changes of the 2011 Tohoku earthquake detected by GRACE, e.g. Matsuo & Heki, 2011]

➤ Dynamic gravitational perturbations :
* Such perturbations also occur immediately after an earthquake [Harms et al., 2015; Montagner et al., 2016] :
  * The Earth masses are perturbed, both at the source location and at the places affected by the transient dilatant/compressive elastic waves
  * These perturbations propagate at the speed of light... even if their signature is small, the quiet period before the P-wave arrival may allow to observe them

Context

Such a tiny signal requires large earthquakes and excellent stations to be recorded
The 2011 (Mw=9.1) Tohoku earthquake

<figure><img src="image_3.png" /></figure>

Acceleration signals in the [0.002-0.03Hz]
frequency range, cut at their P wave arrival time

<figure><img src="image_4.png" /></figure>

After downloading all the available stations
from IRIS Wilber III (hundreds of stations), map
of all the stations able to detect the signal,
based on a Signal-to-Noise ratio criterion

Most of the stations are FDSN stations (IRIS or
GEOSCOPE) known for their high quality

Some stations from F-NET are also included

But what are exactly these signals that we observe ?

What do we expect to record with a ground-attached seismometer (or gravimeter) ?

<figure><img src="image_5.png" /></figure>

Without gravitational changes, gravity only controls
the equilibrium position of the mass, and we have :

$$
\frac{d^2 \xi}{dt^2} + \frac{D}{M} \frac{d \xi}{dt} + \frac{k}{M} \xi = - \frac{d^2 u}{dt^2} \quad (1)
$$

With Δg, (1) is simply modified as :

$$
\frac{d^2 \xi}{dt^2} + \frac{D}{M} \frac{d \xi}{dt} + \frac{k}{M} \xi = \Delta g - \frac{d^2 u}{dt^2} \quad (2)
$$

A seismometer is therefore a seismo-gravimeter, which records, after
correction from the instrumental response, the difference between
the ground acceleration and the gravitational perturbations

One approach to
understand
and model PEGS

How to compute Δg ?

Let us consider an earthquake in r_s, starting at
t=0, and generating elastic waves, with the
fastest (P) one arriving at T_p at the station in r_0

<figure><img src="image_6.png" /></figure>

* At a given time t (0<t<TP), transient elastic displacements affect the volume V_s^P around the source

* These displacements can be calculated in every point r of V_s^P (use of AXITRA method, moment tensor version) with :

$$
u_i(\mathbf{r}, t) = M_{jk}m(t) * \mathcal{G}_{ij,k}(\mathbf{r}_s, \mathbf{r}, t)
$$

* The pre-P gravitational perturbation is controlled by an integral over V_s^P of the form (Dahlen & Tromp 1998):

$$
\Delta g^P(\mathbf{r}, t) = G \int_{V_s^P} \frac{\rho(\mathbf{r}') [u(\mathbf{r}', t) - 3(e_{\mathbf{r}'} \cdot u(\mathbf{r}', t))e_{\mathbf{r}'}]}{|\mathbf{r}' - \mathbf{r}|^3} d\mathbf{r}'
$$

But note that there is a gravitational perturbation not only at r₀, but everywhere in the medium

Ag is also a body force acting in the whole medium, which will cause the station to move EVEN BEFORE the arrival to the direct P wave. This can be seen as a try of the Earth to elastically re-equilibrate after the gravitational perturbations.

Concretely, all the gravitational perturbations occurring in the volume V₀^P defined
by V₀^P = {r' ∈ V / T^P(r₀, r') < T_P}

can generate elastic waves arriving before the hypocentral P arrival at the station

<figure><img src="image_7.png" /></figure>

This gravitational-induced
acceleration can be computed
with the integral

$$
\ddot{u}_z^P(\mathbf{r}, t) = \frac{d^2}{dt^2} \int_{V_0^P} \underbrace{\rho(\mathbf{r}') \Delta g_i^P(\mathbf{r}', t) * \mathcal{G}_{iz}(\mathbf{r}', \mathbf{r}, t)}_{\text{AXITRA method (single force)}} d\mathbf{r}'
$$

AXITRA method (single force)

We now have all the ingredients to compute the prompt
vertical acceleration recorded by the broadband seismometers
$$ = \Delta g_z^P(r_0, t) - \ddot{u}_z^P(r_0, t) $$

Data & simulations at INU (GEOSCOPE, G) and MDJ (IRIS-China, IC)

<figure><img src="image_8.png" /></figure>

Vallée et al.,
Science, 2017

Remark : at INU station, the recorded signal is negative while the gravitational perturbation is positive : the signal is dominated by the induced acceleration

PEGS observations to date

PEGS observations and modeling for 5 additional
earthquakes of the last 25 years (Mw =7.9-8.8).
PEGS detection is made using individual (yellow) of
stacked (green) seismometers signals

PEGS observations and modeling for the
2011 (Mw=9.1) Tohoku earthquake

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

Good agreement
between observed and
modeled signals

Strong sensitivity to
earthquake magnitude
[A smaller Tohoku-type
earthquake (Mw <8.5)
would not have been
detected]

<figure><img src="image_11.png" /></figure>

Vallée et al., Science, 2017

<figure><img src="image_12.png" /></figure>

What are the limitations of PEGS observation with today seismometers ?

<figure><img src="image_13.png" /></figure>

Spectrum amplitude of PEGS signals, compared to rms noise amplitudes
(model and observed at some stations), for an Mw=8.4 scenario

➤ PEGS simulation for a typical subduction mechanism at 120 fictitious stations around the earthquake, in the 100~2000km distance range

➤ For a typical Mw=8.4 scenario, good quality very broadband seismometers are expected to detect the signal in the [0.002-0.03Hz] frequency range, except if sensors are located in unfavorable directions (here along the N-S direction)

➤ For a typical Mw=7.5 scenario, signals never reach values above the « noise » (physical or instrumental) :

* Detection requires to model/mitigate the background seismic noise, or to develop fully new instruments which are much less sensitive to it.

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

Spectrum amplitude of PEGS signals, compared to rms noise amplitudes
(model and observed at some stations), for an Mw=7.5 scenario

References :

Harms, J., J.-P. Ampuero, M. Barsuglia, E. Chassande-Mottin, J.-P. Montagner, S. Somala, and B. Whiting, Transient gravity perturbations induced by earthquake rupture. *Geophys. J. Int.*, **201**, 1416–1425, 2015.

Imanishi, Y., T. Sato, T. Higashi, W. Sun and S. Okubo, A network of superconducting gravimeters detects submicrogal coseismic gravity changes, *Science* **306**, 476–478, 2004.

Matsuo, K. and K. Heki, Coseismic gravity changes of the 2011 Tohoku–Oki earthquake from satellite gravimetry, *Geophys. Res. Lett.*, **38**, L00G12, 2011.

Montagner, J.-P., K. Juhel, M. Barsuglia, J. P. Ampuero, E. Chassande-Mottin, J. Harms and P. Lognonné, Prompt gravity signal induced by the 2011 Tohoku-Oki earthquake. *Nat. Comm.*, **7**, 13349, 2016.

Okubo, S., Gravity and potential changes due to shear and tensile faults in a half-space. *J. Geophys. Res.*, **97**, 7137–7144, 1992.

Vallée, M., J. P. Ampuero, K. Juhel, P. Bernard, J.-P. Montagner and M. Barsuglia, Observations and modeling of the elastogravity signals preceding direct seismic waves, *Science*, **358**, 1164–1168, 2017.

Vallée, M. and K. Juhel, Multiple observations of the prompt elastogravity signals heralding direct seismic waves, *J. Geophys. Res.*, **124**, 2970–2989, 2019.