Journal of Geophysical Research – Solid Earth
Supporting Information for
Effects of long-term fluid injection on induced seismicity parameters and
maximum magnitude at northwestern The Geysers geothermal field
Grzegorz Kwiatek(1), Patricia Martínez-Garzón(1), Georg Dresen(1,2), Marco Bohnhoff(1,3),
Hiroki Sone(1,4) and Craig Hartline(5)
(1) GFZ Potsdam German Research Centre for Geosciences, Section 3.2: Geomechanics and Rheology,
Potsdam, Germany
(2) University of Potsdam, Institute of Earth and Environmental Sciences, Potsdam, Germany
(3) Free University Berlin, Institute of Geological Sciences, Berlin, Germany
(4) University of Wisconsin-Madison, Madison, Wisconsin, USA
(5) Calpine Corporation, Middletown, California, USA
Contents of this file
1. Guidelines to calculate the similarity of earthquakes for the purpose of mesh
spectral ratio technique
1. Calculation of the similarity level between seismic events
Three parameters are considered while calculating the “distance" (D𝑖𝑗 ) (level of similarity)
between two events i and j forming a cluster for the purpose source parameters refinement
using mesh spectral ratio technique:
a) Cartesian distance between hypocenters of two events R 𝑖𝑗 ,
b) Absolute magnitude difference between two events Δm𝑖𝑗 , and
c) 3D rotation angle between P/T axes directions between two events αij [Kagan, 2007]:
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The general formula for the “distance” used in this study is:
Dij = c1 rij + c2 Δmij + c3 αij ,
where c1 , c2 , and c3 are arbitrarily defined constants. Before calculating the “distance”, all
three matrices of parameters: 𝐫 = [rij ], 𝚫𝐦 = [Δmij ], and 𝛂 = [αij ] containing data from all
possible pairs of earthquakes forming a cluster are all rescaled linearly to 0-1 range. In
the case of our study, the rij is 0 when hypocenters overlaps and rij = 1 for inter-eventdistances exceeding 150m. The Δmij is 0 when absolute magnitude difference exceeds
1.0 and Δmij=1 when absolute magnitude difference is smaller than 0.5. Finally, αij = 0 for
overlapping (i.e. identical) fault planes and αij = 1 for events for which rotation angle of
P/T axes is more than 60 degrees. The choices made are subjective but they can be
physically rationalized and optimized by the observation of fault sizes and hypocenter
errors, available magnitude span and variations in focal mechanism. The choices should
be overall made following the criteria for application of the empirical Green’s function (eGf)
technique [Hartzell, 1978; Mueller, 1985; Kwiatek, 2008] for the pair of event:

Absolute difference in magnitude between event pair should exceed 1.0,

Events should occur close by,

Focal mechanisms should be similar.
The event pairs with very large 𝐷𝑖𝑗 (for example those with 𝐷𝑖𝑗 > 3 assuming 𝑐1 = 𝑐2 =
𝑐3 = 1) did not contributed at all to the spectral ratio mesh generation and they were not
used in inversion. The 𝐷𝑖𝑗 was used to weight the cost function written in equation (3) of
the manuscript for the remaining pairs (e.g. 𝑤𝑖𝑗 = 3 − 𝐷𝑖𝑗 ). In consequence, the event
pairs with large “distances” contributed less to the cost function whereas events with small
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“distances” had larger influence on the inversion results. The constants 𝑐𝑘 as well as the
weighting were refined by trial-and-error procedure to balance between the number of
accepted links in a mesh (increased computational effort) and the stability of derived
source parameters (investigated by inspection of resulting 2D marginal distributions). It
turned out that typically the stable results for a particular events are produced where event
is linked to at least 4 surrounding and similar events.
References
Hartzell, S. H. (1978), Earthquake aftershocks as Green’s functions, Geophys Res Lett,
5, 1–5.
Kagan, Y. Y. (2007), Simplified algorithms for calculating double-couple rotation, Geophys.
J. Int., 171(1), 411–418.
Kwiatek, G. (2008), Relative source time function deconvolution at the Rudna copper
mine: Uncertainty Estimation, J. Seismol., 12(4), 499–517, doi:10.1007/s10950-008-91008.
Mueller, C. S. (1985), Source pulse enhancement by deconvolution of an empirical
Green’s function, Geophys Res Lett, 12(1), 33–36.
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