Kyle and Judith, thanks for another very thorough analysis. Your blogs and Quentin and Jean-Mathieu's follow-up work have provided a really interesting and high-level discussion on an important topic.
I agree that the lack of a short-term signal in the tiltmeter data of Hirose et al. (2024) (in addition to the seafloor pressure data described in Hino et al (2018 Mar Geophys Res) also suggests that there was no large hours-long precursor before the 2011 Tohoku-oki earthquake. However, another puzzle remains regarding the tilt data. Something else but postseismic slip seems to have produced the features seen in the tilt data after the March 9 foreshock.
You wrote
> Because the tilt meter data and the GPS displacement data are independent, the apparent
>agreement about the timing and shape of the crustal stretching suggests that they are measuring
> the same crustal deformation.
However, as the authors point out, the data do not appear to be capturing a coherent deformation signal associated with the March 9 foreshock that would be consistent with the GPS data (i.e., related to afterslip from that event). Fig. S5 of Hirose et al. (2024) shows a high-amplitude, but quite random distribution of post-March 9 tilt signals, - not at all like what the afterslip model (Fig. 4 of Hirose et al., 2024) predicts. Thus, some other foreshock-related process (Hirose et al. consider "instrument responses or mechanical coupling between the sensor and a borehole, in response to the strong ground shaking of the foreshock") appears to dominate the tilt observations and overwhelms the afterslip signal seen with GPS.
Thanks for your comment - it encouraged us to go back and read the paper more carefully.
As you note, there actually is an afterslip signal seen in the GPS for the largest foreshock of Tohoku-Oki (Ohta et al., 2012) - inferred to have a magnitude of ~50 cm - which really helps shed light on this issue.
Hirose et al.'s tilt meter curve is primarily influenced by a single station: SZGH, one of the stations closest to the epicenter. The shape of the overall curve looks a lot like the shape of the SZGH curve on its own (see their Fig. 2). But! When Hirose et al. model the tilting that the 50 cm of afterslip should have caused, they find that the actual tilting at SZGH was ~200x higher than their model.
So, like you point out, they suggest that something went wrong with the instrument, possibly triggered by the shaking in the foreshock. Or, maybe there is some other foreshock-related explanation, like ground settling triggered by the shaking.
This reinforces how vulnerable the method is to problems at specific stations - although all stations technically are averaged in, it is easy for one or two stations (or one or two earthquakes, in the global stack) to dominate the signal.
At Tohoku-Oki, it seems possible that the curve of GPS stack is telling us about the (known) afterslip. However, while the matched shapes between the GPS stack and the tilt meter stack are probably both indirectly related to the M7.3 foreshock (both start at the same time and decay afterwards), it seems like the actual physical mechanism must be different, as you say.
We have added a note to the text to clarify, and to point to your comment.
Nice analysis of an important topic! Have you considered whether seismicity showed an uptick during the possible slow slip intervals? Often, the presence of slow slip noticeably raises the seismicity in the volume around it. Probably it's been done and I don't remember.
Thanks, John! That would certainly be a good way to try to corroborate the existence (or lack of) slow slip.
I am not aware of any study that claims to identify a general increase in seismicity in the last two hours prior to large earthquakes. At Tohoku, there is evidence of foreshocks tied to apparent slow slip that started on two days before the mainshock. El Mayor-Cucupah also had extensive foreshock activity that started days before the mainshock, but as far as I know no one has linked that activity to slow slip. And of course there any many earthquakes with no seismicity changes prior to the mainshock.
I think that if you stacked seismicity you would necessarily see an apparent "acceleration" in seismicity simply because of how the individual components would add up, even though no individual earthquake would necessarily include an acceleration. (i.e. a few earthquakes would have foreshock activity beginning well in advance; more would have foreshocks closely linked in time; most would have no foreshocks at all.) So it's not immediately obvious to me how to compare seismicity to the calculated stacked GPS signal.
I would much rather look at individual earthquakes and try to understand them; then, there is a chance to actually investigate the physical process, and to confirm or exclude precursory slow slip (including, as you suggest, by looking at seismicity as well as GPS or tilt meters).
I vaguely recall that the M7 event 2 days prior to Tohoku had a lot of afterslip, which one could optimistically call foreslip to the mainshock, but in fact it was dying off with time rather than accelerating.
I agree causality can be misleading in stacking foreshock activity that can entirely be modeled by ETAS processes (i.e. no precursory activity).
Kyle and Judith, thanks for another very thorough analysis. Your blogs and Quentin and Jean-Mathieu's follow-up work have provided a really interesting and high-level discussion on an important topic.
I agree that the lack of a short-term signal in the tiltmeter data of Hirose et al. (2024) (in addition to the seafloor pressure data described in Hino et al (2018 Mar Geophys Res) also suggests that there was no large hours-long precursor before the 2011 Tohoku-oki earthquake. However, another puzzle remains regarding the tilt data. Something else but postseismic slip seems to have produced the features seen in the tilt data after the March 9 foreshock.
You wrote
> Because the tilt meter data and the GPS displacement data are independent, the apparent
>agreement about the timing and shape of the crustal stretching suggests that they are measuring
> the same crustal deformation.
However, as the authors point out, the data do not appear to be capturing a coherent deformation signal associated with the March 9 foreshock that would be consistent with the GPS data (i.e., related to afterslip from that event). Fig. S5 of Hirose et al. (2024) shows a high-amplitude, but quite random distribution of post-March 9 tilt signals, - not at all like what the afterslip model (Fig. 4 of Hirose et al., 2024) predicts. Thus, some other foreshock-related process (Hirose et al. consider "instrument responses or mechanical coupling between the sensor and a borehole, in response to the strong ground shaking of the foreshock") appears to dominate the tilt observations and overwhelms the afterslip signal seen with GPS.
Hi Roland,
Thanks for your comment - it encouraged us to go back and read the paper more carefully.
As you note, there actually is an afterslip signal seen in the GPS for the largest foreshock of Tohoku-Oki (Ohta et al., 2012) - inferred to have a magnitude of ~50 cm - which really helps shed light on this issue.
Hirose et al.'s tilt meter curve is primarily influenced by a single station: SZGH, one of the stations closest to the epicenter. The shape of the overall curve looks a lot like the shape of the SZGH curve on its own (see their Fig. 2). But! When Hirose et al. model the tilting that the 50 cm of afterslip should have caused, they find that the actual tilting at SZGH was ~200x higher than their model.
So, like you point out, they suggest that something went wrong with the instrument, possibly triggered by the shaking in the foreshock. Or, maybe there is some other foreshock-related explanation, like ground settling triggered by the shaking.
This reinforces how vulnerable the method is to problems at specific stations - although all stations technically are averaged in, it is easy for one or two stations (or one or two earthquakes, in the global stack) to dominate the signal.
At Tohoku-Oki, it seems possible that the curve of GPS stack is telling us about the (known) afterslip. However, while the matched shapes between the GPS stack and the tilt meter stack are probably both indirectly related to the M7.3 foreshock (both start at the same time and decay afterwards), it seems like the actual physical mechanism must be different, as you say.
We have added a note to the text to clarify, and to point to your comment.
Best,
Judith
I think Roland's comments on how to interpret the tiltmeter signals are compelling.
Very impressive analysis. Thank you for performing it.
Thanks, Ross!
Nice analysis of an important topic! Have you considered whether seismicity showed an uptick during the possible slow slip intervals? Often, the presence of slow slip noticeably raises the seismicity in the volume around it. Probably it's been done and I don't remember.
Thanks, John! That would certainly be a good way to try to corroborate the existence (or lack of) slow slip.
I am not aware of any study that claims to identify a general increase in seismicity in the last two hours prior to large earthquakes. At Tohoku, there is evidence of foreshocks tied to apparent slow slip that started on two days before the mainshock. El Mayor-Cucupah also had extensive foreshock activity that started days before the mainshock, but as far as I know no one has linked that activity to slow slip. And of course there any many earthquakes with no seismicity changes prior to the mainshock.
I think that if you stacked seismicity you would necessarily see an apparent "acceleration" in seismicity simply because of how the individual components would add up, even though no individual earthquake would necessarily include an acceleration. (i.e. a few earthquakes would have foreshock activity beginning well in advance; more would have foreshocks closely linked in time; most would have no foreshocks at all.) So it's not immediately obvious to me how to compare seismicity to the calculated stacked GPS signal.
I would much rather look at individual earthquakes and try to understand them; then, there is a chance to actually investigate the physical process, and to confirm or exclude precursory slow slip (including, as you suggest, by looking at seismicity as well as GPS or tilt meters).
I vaguely recall that the M7 event 2 days prior to Tohoku had a lot of afterslip, which one could optimistically call foreslip to the mainshock, but in fact it was dying off with time rather than accelerating.
I agree causality can be misleading in stacking foreshock activity that can entirely be modeled by ETAS processes (i.e. no precursory activity).
Thank you for so detailed analysis and writing.
Learned a lot.