Auxiliary Material for Paper 2007GL030088
Pulse of the seafloor: Tidal triggering of microearthquakes at 9 degrees 50N East Pacific Rise
D. F. Stroup
Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York, USA
D. R. Bohnenstiehl
Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York, USA.
Also at Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina, USA
M. Tolstoy, F. Waldhauser, and R. T. Weekly
Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York, USA
Stroup, D. F., D. R. Bohnenstiehl, M. Tolstoy, F. Waldhauser, and R. T. Weekly (2007), Pulse of the seafloor: Tidal triggering of microearthquakes at 9°50N East Pacific Rise, Geophys. Res. Lett., 34, L15301, doi:10.1029/2007GL030088.
Introduction:
The statistical results for the Schuster test and circular statistics are given in the table "2007gl030088-ts01.xls" and "2007gl030088-ts01.txt. Analysis of the symmetry of the rose plots in Figure 3b is discussed in the text contained in "2007gl030088-txts01.txt" and "2007gl030088-txts01.pdf. The color figure, "2007gl030088-fs01.eps" shows the percentage of excess events at times of encouraging stress (-90 degrees < theta < 90 degrees) as a function of the peak-to-peak amplitude of the tidal cycle. See corresponding figure caption (contained in Part 3 of this readme file) for more information. Statistical analysis on the percentage of excess events as a function of peak-to-peak stress amplitudes is contained within the table "2007gl030088-ts02.xls" and "2007gl030088-ts02.txt".
1. 2007gl030088-ts01.xls, 2007gl030088-ts01.txt (Table S1)
Tidal Phase Statistics: Schuster Test and Circular Statistics Results.
The statistical values contained in the rows of the Table include: p probability value from Schuster test for original dataset and the declustered dataset (shown in parentheses); R-bar mean resultant vector length; theta-bar mean phase angle; K von Mises concentration parameter. Larger R-bar and K indicate a population that more closely clusters around theta-bar [see Jones, 2006]. Tidal phase assigned relative to sea surface height, and the volumetric stress (sigma-v) associated with OTL, Earth tide, and the combined OTL and Earth tide.
1.1 Column "Parameters, contains the statistics described above.
1.2 Column "Sea surface height", ranges from -0.4 to 0.2 meters, all statistical values are unitless except for the mean phase angle which is in degrees.
1.3 Column "OTL volumetric stress", ranges from -1.0 to 1.0 kPa, all statistical values are unitless except for the mean phase angle which is in degrees.
1.4 Column "Earth tide volumetric stress", ranges from -2.5 to 2.5 kPa, all statistical values are unitless except for the mean phase angle which is in degrees.
1.5 Column "Combined OTL and Earth tide volumetric stress", ranges from -2.3 to 2.3 kPa, all statistical values are unitless except for the mean phase angle which is in degrees.
2. 2007gl030088-txts01.txt, 2007gl030088-txts01.pdf (Text S1)
Discussion of Triggering During Times of Increasing versus Decreasing Tidal Stress.
Microearthquakes occur preferentially near times of peak extension resulting from the combined effect of Earth tide and ocean tidal loading. The distribution of phase angles (theta), however, is not perfectly symmetrical. The significance of the asymmetry can be tested against a binomial distribution, which is discussed within this text.
3. 2007gl030088-fs01.eps (Figure S1)
Percentage of excess events at times of encouraging stress (-90 degrees < theta < 90 degrees) as a function of the peak-to-peak amplitude of the tidal cycle. The full dataset is shown as black crosses and the declustered dataset is shown by red triangles. Constant size bins of 0.7 kPa are used with the data plotted at the mean within each bin (declustered results are offset by +0.05 kPa for clarity). Vertical error bars represent the standard error within each bin.
For tidal cycles with peak-to-peak stress amplitudes >0.7 kPa, the observed number of excess events occurring during times of encouraging stress is >99.99% significant relative to the binomial model. As only <10% of the tidal cycles between October 2003 to April 2004 have peak-to-peak amplitudes <0.7 kPa, these results indicate that a significant level of tidal triggering occurs throughout most of the observational period. Statistical results are summarized in Table A-3.
4. 2007gl030088-ts02.xls, 2007gl030088-ts02.txt (Table S2)
Excess Events Analysis Evaluated Against a Binomial Model
D declustered data; F original (full) dataset; Nex percentage of excess events during times of encouraging stress; Nenc number of events during times of encouraging stress; Nt total number of events. Significance levels are calculated from the binomial cumulative distribution function. For example, there are 656 earthquakes in the declustered data that occur within tidal cycles having peak-to-peak amplitudes between 2.1-2.8 kPa. If earthquakes were to occur randomly, there would be a <0.01% chance of obtaining Nenc > 376 (Nex > 7.3%). However, 428 out of 656 earthquakes (Nex = 15.3%) are observed to occur during times of encouraging tidal stress.
4.1 Column "Peak-to-Peak Tidal Stress", in kPa, tidal stress is binned in 0.7 kPa increments.
4.2 Column "Data", D declustered data; F original (full) dataset.
4.3 Column "Observations", Nex percentage of excess events during times of encouraging stress; Nenc number of events during times of encouraging stress; Nt total number of events.
4.4 Column "Significance Level", in percent, calculated from the binomial cumulative distribution function.