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E
The Effects of Varying Injection Rates in Osage
County, Oklahoma, on the 2016 Mw5.8 Pawnee
Earthquake
by Andrew J. Barbour, Jack H. Norbeck, and Justin L. Rubinstein
ABSTRACT
The 2016 Mw5.8 Pawnee earthquake occurred in a region
with active wastewater injection into a basal formation group.
Prior to the earthquake, fluid injection rates at most wells were
relatively steady, but newly collected data show significant in-
creases in injection rate in the years leading up to earthquake.
For the same time period, the total volumes of injected waste-
water were roughly equivalent between variable-rate and con-
stant-rate wells. To understand the possible influence of these
changes in injection, we simulate the variable-rate injection his-
tory and its constant-rate equivalent in a layered poroelastic
half-space to explore the interplay between pore-pressure
effects and poroelastic effects on the fault leading up to the
mainshock. In both cases, poroelastic stresses contribute a sig-
nificant proportion of Coulomb failure stresses on the fault
compared to pore-pressure increases alone, but the resulting
changes in seismicity rate, calculated using a rate-and-state fric-
tional model, are many times larger when poroelastic effects are
included, owing to enhanced stressing rates. In particular, the
variable-rate simulation predicts more than an order of mag-
nitude increase in seismicity rate above background rates com-
pared to the constant-rate simulation with equivalent volume.
The observed cumulative density of earthquakes prior to the
mainshock within 10 km of the injection source exhibits re-
markable agreement with seismicity predicted by the variable-
rate injection case.
Electronic Supplement: Animations of the evolution of pore pres-
sure, vertical displacement, and cylindrical tensor strains in the
injection simulation domain, and a set of input commands for
running simulation A using poel in ASCII format.
INTRODUCTION
Injection-induced earthquakes are well documented in Okla-
homa (Ellsworth, 2013;Keranen et al., 2013;Walsh and
Zoback, 2015), where the rate of earthquakes has increased
sharply since 2009. Studies of the recent sequences in Okla-
homa explain the increased seismicity as a result of increased
pore pressures reactivating pre-existing faults (e.g., Keranen
et al., 2014). Hubbert and Rubey (1959) demonstrate this
behavior analytically, whereby increases in fluid pressure can
cause slip on pre-existing structures. The influence of fluid
pressure on the frictional stability of faults in the subsurface has
been argued to explain the earliest known cases of injection-
induced seismicity at Rocky Mountain Arsenal and Rangely
(Evans, 1966;Healy et al., 1968;Raleigh et al., 1976;Hsieh
and Bredehoeft, 1981).
Although direct pore-pressure effects are typically believed
to be the cause of injection-induced earthquakes, poroelastic
effects may be important to consider. For instance, recent stud-
ies consider the possibility that aseismic processes resulting
from injection can be responsible for changes in seismicity on
faults with frictional instability (Bourouis and Bernard, 2007;
McClure and Horne, 2011;Segall and Lu, 2015;Deng et al.,
2016;Fan et al., 2016;Norbeck and Horne, 2016a). In general,
this has been difficult to establish because of a lack of obser-
vations of pore-fluid pressure in proximity to earthquake
sequences, but measured slip histories from controlled fluid-
injection experiments (Guglielmi et al., 2015) demonstrate this
effect clearly. Furthermore, numerical simulations (Zhang et al.,
2013;Chang and Segall, 2016;Norbeck and Horne, 2016b)
demonstrate that fault-related variations in permeability can
influence the location and timing of induced seismicity; careful
analyses of seismicity and injection patterns (McNamara et al.,
2015;Yeck, Weingarten, et al., 2016) support this conclusion.
In this article, we explore the possibility that poroelastic
effects arising from fluid injection influenced the Mw5.8
Pawnee earthquake (Fig. 1). Notably, new injection data in
nearby Osage County show significant variability in the years
preceding the earthquake, whereas other wells show relatively
constant rates of injection (Fig. 2). This provides an opportu-
nity to compare the influence of the direct pore-fluid pressure
effect and the poroelastic effect on the generation of seismicity,
focusing on the difference between constant-rate and variable-
rate wastewater disposal. We compare simulations of the time-
varying poroelastic stresses and pore pressure resulting from
1040 Seismological Research Letters Volume 88, Number 4 July/August 2017 doi: 10.1785/0220170003
transient fluid injection with the equivalent constant-rate in-
jection history based on an equivalent volume of fluid. Our
results show clear differences in spatial and temporal patterns
in Coulomb failure stress, depending on whether or not po-
roelastic effects are considered. Our model predicts more than
an order of magnitude increase in the maximum seismicity rate
prior to the mainshock, about a factor of 3 larger than the con-
stant-rate result because of differences in the stressing rate
history.
DATA AND METHODS
Injection Data
There are numerous wells within 15 km of the mainshock epi-
center, but we restrict our study to the nine wells (Table 1) with
injection rates into the Arbuckle Group greater than
0:3 kbbl=mo (Fig. 1), wells that could have had the largest in-
fluence on the seismicity. Much of this injection activity has
been either fairly small compared with similar wells in Okla-
homa or continued at a relatively constant rate (Fig. 2). This
includes the two closest wells to the mainshock epicenter,
OLDHAM and SCROGGINS, ∼2:4and ∼5:4km from
the mainshock, respectively; these wells were injecting at
relatively constant rates between 146 and 211 kbbl=mo since
2012. Because we are interested in looking at the interplay
between the poroelastic effects and hydrologic effects of var-
iable fluid-injection rates, we examine the two closest wells
with the largest changes in injection behavior: SOUTH BEND
2A-11 (OS6301) and RICE 2A-9 (OS6379), located ∼6:5and
∼8:7kmfrom the epicenter of the mainshock, respectively
(SOUTH BEND is ∼3:2kmfrom RICE). More specifically,
injection rates at SOUTH BEND and RICE increased from 0
to 288 and 404 kbbl=mo, respectively, over a period of ∼6
months beginning in early 2013. This rapid change is followed
by a steady reduction in rates to level the characteristic of the
average in this period for all wells within 15 km of the main-
shock, ∼92 kbbl=mo, and following the Mw5.8 mainshock
these wells were shut-in. (All wells within a zone of regulatory
action were shut-in after the mainshock.) These data are used
in our poroelastic simulations.
Poroelastic Reservoir Modeling
Our model domain comprised four major lithologic units
representing the relatively uniform lithology in north-central
Regulatory Body
OCC
EPA
0 20 40 60 km
N
K
O
P
0 100 200 km
0
(a)
(b)
(c)
100 200 km
Injection Well
OCC
EPA
Fault Stability
High
Moderate
Low
0 5 10 km
B
SHmax
▴Figure 1. The 2016 Mw5.8 Pawnee sequence. (a) Mapped faults from the Oklahoma Geological Survey and counties surrounding the
sequence (K, Kay; N, Noble; P, Pawnee; O, Osage). (b) Locations of Mw≥5earthquakes, disposal wells by regulatory body, and regional
earthquakes. The relative size of a given disposal-well symbol shows the relative size of the total volume of fluid injected since 2015.
(c) Map of the Pawnee sequence (Yeck, Hayes, et al., 2016) with mapped faults colored by their stability with respect to the maximum
horizontal stress direction (Holland, 2013;Alt and Zoback, 2016;Walsh and Zoback, 2016). The Sooner Lake fault (dashed line) is inferred
from aftershock epicenters. Contours of radial distance are shown at 10 and 20 km (as in b). OCC, Oklahoma Corporation Commission; EPA,
Environmental Protection Agency. The color version of this figure is available only in the electronic edition.
Seismological Research Letters Volume 88, Number 4 July/August 2017 1041
Oklahoma (Luza and Lawson, 1980;Christenson et al., 2011).
Injection is assumed to be entirely within the Arbuckle Group,
a laterally extensive basal carbonate formation group which we
treat as a single layer between 1300 and 1900 m depth (below
ground surface [bgs]) based on information from well-comple-
tion diagrams. The injection interval overlies semi-infinite
crystalline basement rock and is overlain by a confining layer
of finite thickness. An unconfined layer representing sedimen-
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OLDHAM
(2.4 km)
SCROGGINS
(5.4 km)
SOUTH BEND
(5.9 km)
STRICKER
(6.5 km)
RICE
(8 km)
RAINEY
(8.3 km)
CARTMELL
(9 km)
ROGERS
(10.7 km)
CARTER
(12.1 km)
OLDHAM
(2.4 km)
SCROGGINS
(5.4 km)
204
211
288
235
404 46
49
214
340
2012 2013 2014 2015 2016
325 kbbl/mo
per div
2012 2013 2014 2015 2016
0.0
0.5
1.0
1.5
Total
OCC
EPA
Mbbl/mo
204
211
288
235
404 46
49214
340
OCC
EPA
(a)
(c)
(b)
▴Figure 2. Injection histories of active Arbuckle disposal wells within 15 km of the epicenter (Table 1)from2012throughthemainshock
origin time. (a) Time series for each well on the same scale (shifted for visualization purposes) with epicentral distances given in parentheses
below the name. Peak injection rates are labeled for each curve. Each division of the vertical scale represents 325 kbbl=mo. The injection
histories used in the poroelastic simulations are marked with asterisks. (b) Aggregate injection time series for each regulatory body com-
pared to total disposal volumes per month, in Mbbl/mo. (c) Map of the earthquake sequence (Yeck, Hayes, et al.,2016) with the locations of
injection wells, regulatory classifications, and peak rates shown in (a). The gray lines are county boundaries, and the dotted circle shows a
radial distance of 10 km; zero-volume, low-rate (see the Injection Data section), or non-Arbuckle wells are marked by the symbol ×. The color
version of this figure is available only in the electronic edition.
Table 1
Active Arbuckle Disposal Wells within 15 km of the Pawnee Mainshock Epicenter
ID
Name Number Longitude (°) Latitude (°) Distance (km)
Injection Interval (m bgs)
OCC (API) EPA (OS) Upper Lower
3511701087 OLDHAM 6 −96.940230 36.449992 2.4 1283 1630
3511723382 SCROGGINS 1 SWD −96.994580 36.421030 5.4 1301 1459
6301 SOUTH BEND 2A-11 −96.949900 36.480900 6.5 1337 1610
3511722902 STRICKER 9D −96.865170 36.443755 6.5 1237 1463
6430 RAINEY 1D −96.877800 36.488100 8.4 1222 1477
6379 RICE 2A-9 −96.985900 36.488200 8.7 1336 1722
3511722558 CARTMELL 15-1D −96.855070 36.381214 8.9 1274 1640
3511723470 ROGERS 1-13D −96.833876 36.377607 10.7 1273 1615
3510324349 CARTER 1-5SWD −96.997119 36.332713 12.1 1467 1842
OCC, Oklahoma Corporation Commission; EPA, Environmental Protection Agency.
1042 Seismological Research Letters Volume 88, Number 4 July/August 2017
tary units overlies the confining layer. Figure 3shows the gen-
eral model setup. We assume that all layers behave as homo-
geneous linear poroelastic media with varying responses, which
we describe in detail next.
We solve the general boundary value problem of fluid-
mass flux into a system governed by the equations of linear
poroelasticity (compare with, Wang, 2000); these are based
on isothermal equilibrium, Hooke’s law of elasticity, and
Darcy’s flow law (conservation of mass). We use the spectral
element method of Wang and Kümpel (2003), which calcu-
lates time-varying cylindrically symmetric solutions in a layered
half-space. We assume an unconfined free-surface boundary
condition (p0) and a volumetric source time function
for injection based on real data (described above). The injec-
tion simulation captures the injection-rate variability in Osage
County from 2013 through late 2016, predominately from the
wells RICE and SOUTH BEND (see Fig. 2).
The particular poroelastic parameters specified for each
layer in the half-space include Skempton’s coefficient B,the
drained and undrained Poisson’s ratios νand νu, the hydraulic
diffusivity D, and the elastic shear modulus μ. Poroelastic sol-
utions are affected by four coupled parameters
EQ-TARGET;temp:intralink-;df1a;52;136α3νu−ν
B1−2ν1νu1a
EQ-TARGET;temp:intralink-;df1b;52;103β91−2νuνu−ν
2μB21−2ν1νu21b
EQ-TARGET;temp:intralink-;df1c;323;733χ9D1−νuνu−ν
2μB21−ν1νu21c
EQ-TARGET;temp:intralink-;df1d;323;703λ2νμ
1−2ν1d
(Kümpel, 1991;Wang and Kümpel, 2003;Segall, 2010), in
which αis Biot’s coefficient of effective stress, βis the bulk
compressibility, χis the Darcy conductivity, and λis Lamé’s
first constant of elasticity. We treat these coupled parameters
as homogeneous within each layer except in the basement, for
which we use a variable hydraulic diffusivity that decreases log-
arithmically from the top of the layer to 8 km depth (then is
constant at all depths below). We combine this depth-depen-
dent diffusivity with a homogeneous shear modulus to re-
present a typical depth-dependent permeability profile in
fractured crystalline rock (Ingebritsen and Manning, 2010).
This type of permeability structure is known to control hy-
draulic conductivity in critically stressed crystalline rock (Bar-
ton et al., 1995;Townend and Zoback, 2000).
We perform two simulations of the same variable injection
rates with the goal of isolating the sensitivity to elastic param-
eters in the four layers (see Table A1). The first, referenced as
simulation A, uses elasticity constants representative of the
general rock lithology, adapted from Roeloffs (1996),Wang
(2000), and Jaeger et al. (2007). The second, referenced as sim-
ulation B, fixes the parameters in each layer to those for the
basement layer in simulation A. In both simulations, the
Skempton’s coefficient is set to a single value across all layers,
B0:75; this may be unrealistically high for some units in the
sedimentary section (Lockner and Stanchits, 2002), but is gen-
erally valid for granitic basement (Wang, 2000;Jaeger et al.,
2007), and direct pore-pressure observations (Kroll et al.,
2017) suggest a comparable value for the Arbuckle Group.
We set the drained Poisson’s ratio to ν0:25, and the
undrained Poisson’s ratio to νu0:38. With the Skempton’s
coefficient stated earlier, this gives an effective stress coefficient
of α0:75. This value of αis higher than the value generally
assumed for bulk granite, α0:47, because the undrained
Poisson’s ratio is higher than expected for the same rock type
(see Wang, 2000, their table C.1); however, published values of
αare generally calculated from laboratory measurements (e.g.,
Rice and Cleary, 1976) and are thus subject to the influence of
measurement variability. We use statistical inference to quan-
tify the conditional probability distributions of each parameter
because uncertainties are not generally reported, to our knowl-
edge. Based on 104realizations in a Monte Carlo simulation of
α(equation 1a), with the values used in simulation A for the
basement layer (Table A1) and two assumed levels of relative
uncertainty (5% and 10%), we find broad distributions of α:
standard deviations are 0.11 and 0.23 for 5% and 10% relative
uncertainty, respectively, and lower bounds are 0.53 and 0.27 at
95% confidence. The details of these distributions demonstrate
that, although the inferred value of αis perhaps unlikely for
bulk material, it is not implausible statistically. Furthermore,
the effects of pervasive hydraulically conductive (critically
Simulation time, years
10−2 m3s
0 (2013) 1 2 3 3.84
0
1
2
3
4
(a)
(b)
(c)
▴Figure 3. Details of the injection simulation domain. (a) Time-
varying injection is modeled in a cylindrically symmetric layered
poroelastic half-space with four major layers (dimensions not to
scale). (b) The injection source in map view (to scale), based
on the location of RICE (see Table 1), with the vertical receiver
fault used to calculate Coulomb failure stresses; the seismic se-
quence is shown for reference. (c) Injection rates used in the tran-
sient-injection simulation; zero time represents 1 January 2013. The
color version of this figure is available only in the electronic edition.
Seismological Research Letters Volume 88, Number 4 July/August 2017 1043
stressed) fractures in crystalline rock include elevated compli-
ance and specific storage (Barbour, 2015;Xue et al., 2016);
thus, although our simulations may represent a limiting case
of bulk material properties, they likely capture the enhanced
sensitivity to external stresses (e.g., injection of wastewater) ex-
pected for the Precambrian basement.
Seismicity Rate Modeling
The coupled geomechanical and hydrologic simulations pro-
vide spatial and temporal distributions of stress and fluid pres-
sure throughout the model domain. We assume that the
orientation and location of the fault plane that hosted the
mainshock follows the distribution of relocated aftershocks
(Yeck, Hayes, et al., 2016) and is vertical. The top of the fault
plane begins at the intersection of the injection layer and base-
ment. Then, we calculate the Coulomb stress changes along the
fault (Pollard and Fletcher, 2005) caused by fluid injection
EQ-TARGET;temp:intralink-;df2;40;541ΔτfΔτfΔσΔp;2
in which Δτis the change in shear stress, Δσis the change in
normal stress on the fault, Δpis the change in fluid pressure
within the fault zone, and fis the static friction coefficient.
Tensile normal stresses are taken as positive in this sign con-
vention; hence, positive ΔσΔpindicates unclamping of the
fault. Furthermore, positive Δτrepresents left-lateral shear;
hence, positive Δτfrepresents failure-promoting shear stress
changes, assuming the maximum principal stress is compres-
sional and oriented at N85°E (Walsh and Zoback, 2016).
At each point along the fault, the changes in shear and normal
stresses are obtained by rotating the principal stress tensor from
the poroelastic simulation into the direction of the fault pole.
The fault surface is assumed to have a uniform static coefficient
of friction f0:65, as laboratory studies of basement rock in
Oklahoma indicate (Carpenter et al., 2016).
Following the empirical approach introduced originally by
Dieterich (1994) and expanded upon by Segall and Lu (2015)
and Chang and Segall (2016), we use a rate-and-state friction
framework to model the evolution of seismicity rate along the
fault in response to changes in the pre-existing state of stress. In
this model, seismicity rate evolves according to
EQ-TARGET;temp:intralink-;df3;40;254
dR
dt R
tc_τf
_τ0
−R;3
in which _τfis the Coulomb stressing rate, _τ0is the background
stressing rate, tcA¯σ=_τ0is a characteristic timescale over
which the seismicity rate returns to background levels, Ais
the rate-and-state direct-effect parameter, ¯σσpis the
effective normal stress, and Ris defined as the ratio between
the current seismicity rate and a reference seismicity rate.
When R1, the predicted seismicity rate is equal to the back-
ground rate. We solve equation (3) numerically using an
explicit Runge–Kutta method (Griffiths and Smith, 2006).
The rate-and-state frictional properties used in our model
are representative of granite at hydrothermal conditions (Blan-
pied et al., 1995) and are listed in Table A2.
An advantage of this frictional model is that it is possible
to consider arbitrary loading conditions. In this study, we ex-
amine the effects of a relatively rapid change of injection rates
over a period of roughly 3.7 yrs in two wells near the fault, in
Osage County; seismicity rate calculations are based on the
simulated Coulomb stress changes (from the poroelasticity
model) associated with the idealized disposal well operations.
We repeat these calculations with the direct pore-pressure
effect isolated, wherein only pore-pressure changes are taken
from the solution; we verified this approach with a traditional
hydrologic model using an equivalent layered structure
(P. Hsieh, personal comm., 2016). It is important to recognize
that these idealizations are not a representation of the full his-
tory of injection leading up to the mainshock; but they can
help explain the effects of variations in injection rate. It is also
important to recognize that the seismicity rate model used in
this study does not simulate the nucleation, rupture, or arrest
processes of individual earthquake events in a deterministic
manner: changes in seismicity rate can only be interpreted
in terms of their effect on earthquake statistics.
RESULTS
Stress Changes from Injection
The poroelastic injection simulations show features consistent
with general hydrologic models. That is, the strongest changes
are seen in pore-fluid pressure changes, which are strongly de-
pendent on the hydraulic diffusivities of each rock layers. The
presence of a confining layer promotes fluid diffusion radially
in the Arbuckle-Simpson layer and, to a lesser extent, in the
vertical direction into the basement, resulting in a pore-
pressure distribution that decays both in depth and radial dis-
tance from the injection source. Based on supplementary
simulations, the realistic depth-decreasing diffusivity in the
semi-infinite basement layer enhances the depth-decay in pore-
pressure diffusion rates.
Despite the general consistency between our poroelastic
simulations and hydrologic models, the poroelastic model in-
cludes significant variations in the stress field at all locations
that cannot be replicated in a decoupled or partially coupled
hydrologic model. Figure 4shows snapshots of the evolution of
stresses and pore pressure for simulation A (Table A1). There is
a nonlinear relationship between the change in excess pore
pressure Δpand the change in mean stress Δσm, defined by
changes in principal stress (Δσ1≥Δσ2≥Δσ3)
EQ-TARGET;temp:intralink-;df4;311;181ΔσmΔσ1Δσ2Δσ3=3;4
indicating the influence of laminar fluid-volume flux (χ∇p)
through the model domain. Figure 4also shows elevated differ-
ential stresses
EQ-TARGET;temp:intralink-;df5;311;116ΔσdΔσ1−Δσ3;5
that are initially concentrated near the injection source during
the injection transient and eventually focus around the main-
1044 Seismological Research Letters Volume 88, Number 4 July/August 2017
shock centroid depth. Although elastic stresses initially domi-
nate pore-pressure changes, increases in Δσdare on the order
of the size of Δσmand Δp, indicating that poroelastic shear
stresses exhibit considerable influence on the stress state of the
rock, even at distances much greater than the injection source
depth. The strongest changes in pore pressure and stresses are
close to the injection source, and the sharpest contrasts in pore-
pressure and stress changes are related to contrasts in material
properties. In the sedimentary layer for example, significant
stress changes are generated but very little pore-pressure diffu-
sion occurs because of the relatively low diffusivity of the con-
fining layer.
At depths of the mainshock centroid, the effect of material
contrasts controls regions of high Δσdthat are localized. In
particular, the depth-dependent hydraulic diffusivity structure
has the strongest influence on localization, as the following
▴Figure 4. Simulated changes in poroelastic stresses and pore pressure using a realistic source time function and variable elastic param-
eters—Simulation A (see Table A1). Snapshots are at (a) 0.5 yrs, (b) 1.51 yrs, (c) 2.52 yrs, (d) 3.68 yrs, just after the mainshock (arrows point to
the centroid); and (e) 3.84 yrs, when seismicity had declined to a few earthquakes per week. (Left) The source time function with vertical lines
showing the time of the snapshot and the earthquake sequence. (Middle two columns) The mean stress (equation 4) and differential stress
(equation 5). The circles show the locations of seismicity relative to the injection source, and are colored gray if they have not yet occurred at
the given snapshot. (Right) The pore pressure. Color scales are linear from 0 to 100 kPa, and contours are logarithmic for decadal factors of 1
(solid lines), 2 (dashed lines), and 5 (short dashed lines). The color version of this figure is available only in the electronic edition.
Seismological Research Letters Volume 88, Number 4 July/August 2017 1045
comparison between the two simulations demonstrates. In sim-
ulation B, the elastic parameters are set equivalently in all
layers, based on the values for the basement fault (Table A1).
Even though this fixed-elasticity equivalent of simulation A is
unrealistic, especially in shallow sedimentary layers, it is an in-
structive exercise for understanding the sensitivity of the simu-
lated stress changes to variations in elastic parameters of the
rock. Figure 5compares the evolution of stresses and pore pres-
sure at the centroid of the mainshock for both simulations; the
simulations are nearly identical at each point in time, with the
exception of the minimum principal stress at early times and
the pore pressure at later times. We find that elastic stresses
dominate pore-pressure effects at the mainshock centroid
when the principal stress aspect ratio
EQ-TARGET;temp:intralink-;df6;40;577rΔσ2−Δσ3=Δσ1−Δσ36
(e.g., Bott, 1959) is less than 1/2. The transition from r≤1=2
to r>1=2occurs ∼1:7 yrs after the variable-rate injection be-
gins, around when peak differential stresses occur, with peak
pore-pressure changes occurring roughly 0.5 yrs later. Elevated
levels of differential stress at centroid depths are apparent in
both the homogeneous elasticity and layered elasticity cases,
but the maximum difference between the two solutions is less
than 1 kPa; hence, even with homogeneous elastic structure,
stress localization is controlled by the hydraulic diffusivities in
each layer. The pronounced dependence of both pore-pressure
and stress changes on hydraulic diffusivity is a direct conse-
quence of interrelated hydromechanical parameters (Kümpel,
1991;Barbour and Wyatt, 2014).
In addition to the effects of elasticity, there is another dif-
ference between the poroelastic and hydrologic models; the
timing of peak pore-pressure changes at centroid depths is dif-
ferent. Although a hydrologic model predicts a pressure in-
crease everywhere in the model domain assuming boundary
continuity, the poroelastic simulation predicts a decrease in
pore pressure in the basement caused by instantaneous elastic
strain in the rock at the initiation of injection that is roughly
0.5 yrs long. This is a phenomenon sometimes observed in
shallow water wells in crystalline aquifers (e.g., Wolff, 1970).
Despite the small size of the pressure reduction relative to pres-
sure increases at later times, the observed lag represents a tem-
porary fault-stabilizing pressure reduction Δp<0prior to
imminent pressure rise Δp>0from pressure diffusion. The
duration of this delay depends on distance to the source and
exhibits sensitivities to the difference between the drained and
undrained Poisson’s ratios (Rice and Cleary, 1976)νand νu
and the initial conditions of the simulation. The magnitude
of the initial change in injection rate is particularly important,
but the opposite effect occurs in the transition to zero injec-
tion; thus, in certain faulting regimes it is theoretically possible
to mitigate damaging effects of rapid shut-in by carefully taper-
ing injection rates (Segall and Lu, 2015).
Seismicity Rate Evolution
In the seismicity rate change model, the extent of the Sooner
Lake fault is represented as a 4 km (along depth) by 8 km
▴Figure 5. Simulated temporal variation in stress changes at
centroid depths. (a) Simulated injection rates. The vertical line
shows the timing of the mainshock relative to the beginning of
the simulation; wells were shut-in shortly after the mainshock.
(b) Changes in pore pressure and principal stresses. Solid lines
show the quantities at the mainshock centroid; shaded regions
show the variation from the centroid to where the fault intersects
the injection interval at ∼2km(at the same radial distance). Peak
values occur more than a year after peak injection. (c) Principal
stress aspect ratio (equation 6); elastic stress changes dominate
pore-pressure changes when this is less than 1/2. (d) Changes in
the Coulomb failure stress Δτf, the differential stress Δσd,the
mean stress Δσm, and the maximum shear stress Δτmax with pore
pressure Δpshown for reference. Peak Δτfoccurs at the time of
peak Δσm, after peak Δτmax and slightly before peak Δp. The color
version of this figure is available only in the electronic edition.
1046 Seismological Research Letters Volume 88, Number 4 July/August 2017
(along strike) vertical plane with a strike of N65°E and an ori-
entation of ∼45° to the injection source. The fault tip is located
at ∼4:2kmrelative to the injection source (RICE) and 1.9 km
below the surface. The Coulomb stress change acting on the
fault is used to inform the seismicity rate model, and the
stressing rate is assumed to be constant between the weeklong
timesteps from the injection model, and is not sensitive to
small variations in dip angle. In Figure 6, we show the distri-
bution of Coulomb stresses resolved on the fault, and the as-
sociated seismicity rate changes, at several snapshots in time
during simulation A. There is a general correspondence be-
tween the spatial pattern of stress and seismicity rate, with
▴Figure 6. Simulated changes in (left) Coulomb failure stresses (CFS; equation 2; in kPa), and (right) seismicity rate (equation 3) on the
Sooner Lake fault associated with the variable injection-rate simulation. Snapshots are shown at (a) 0.5 yrs, (b) 1.51 yrs, (c) 2.52 yrs, and
just after the mainshock at (d) 3.68 yrs, as in Figure 4. The vertical axes are true depth, and the horizontal axes are distance along strike,
both in kilometers. The color version of this figure is available only in the electronic edition.
Seismological Research Letters Volume 88, Number 4 July/August 2017 1047
some aftershocks following isostress contours. The maximum
Coulomb stress change is on the order of Δτf≈40 kPa at the
mainshock centroid, and the maximum seismicity rate change
is R≈16, suggesting more than an order of magnitude increase
above the background rate.
In our simulations, the maximum predicted seismicity rate
occurs roughly one year following the period of peak injection
rate. During 2015, the predicted seismicity rate declines
steadily until early 2016, at which point the rate stabilizes
at an average rate of R≈5. The predicted seismicity rate tracks
the stress changes closely and resembles a time-shifted and
smoothed version of the injection rate, which appears to be
a consequence of the sensitivity of equation (3) to the stressing
rate for these loading conditions. We do not observe an im-
mediate correlation between the predicted peak seismicity rates
and the timing of the seismic sequence. Comparing the seis-
micity rate calculation using the full poroelastic solution with
the pore-pressure effect isolated—only fluid pressure changes
affect the state of stress along the fault—reduces the maximum
rate to R≈3. Furthermore, the value of Rappears to be rel-
atively insensitive to elastic structure, which again implies that
hydraulic diffusivities exhibit the strongest influence on the
fully coupled solution.
DISCUSSION
The frictional stability of the Sooner Lake fault prior to the
2016 Mw5.8 sequence may have been reduced by active waste-
water injection in close proximity to the fault. Although pres-
sure diffusion is indeed the dominant mechanism for reducing
the effective stress on the fault, the magnitudes of shear and
normal stresses induced by coupling between elastic deforma-
tion of the solid matrix and pressure diffusion are comparable
to pore-pressure changes, to within a factor of 2. The distri-
bution of Coulomb failure stresses predicted by our simula-
tions between the centroid depth and the top of the fault
at the same radial distance (shaded region in Fig. 7) implies
that even though high-permeability pathways may be impor-
tant to consider, they are not necessary to explain the relative
timing between this injection transient and the seismic se-
quence; a stronger control on this timing is due to gross per-
meability structure, which depends on both the hydraulic and
elastic properties.
We have not yet considered the effects of steady injection
rates at wells closer to the rupture (e.g., wells in Pawnee
County). Appealing to the same physical mechanism used
to inform the seismicity rate changes, we assume that injection
at these wells must have influenced stressing rates on the fault;
however, without strong changes in injection rate their influ-
ence may have been subtle, albeit important. For example, the
seismicity rate model (equation 3) is highly sensitive to
stressing rates as we found in the variable-rate case; but, after
nearly a decade of steady injection, as annual records of injec-
tion volume extending back to 2006 indicate (e.g., OLD-
HAM), stress and pore-pressure accumulation would be
relatively slow. To test this, we simulated the effect of long-
term constant injection beginning in 2011, two years prior to
the previous simulations. To make the results comparable, we
use a constant-rate injection with the same total volume of
fluid as in the variable-rate case. We find that constant-rate
injection loads the fault slower than in the transient cases
(Fig. 7). Additionally, this constant-rate simulation produces
a much different temporal change in R, which roughly ap-
proaches steady-state conditions with the square root of time,
and decreases rapidly after shut-in (Fig. 8). This comparison
strongly suggests that long-term injection may have been
responsible for a gradual loading of the fault to the point where
it primed the fault for failure triggered by the short-term high-
rate injection transient. In the absence of transient injection
activities, however, frictional failure may still have occurred
at a much later time.
In addition to computing the rate increase R, we examine
the integral of the rate increase to test our results against ob-
served seismicity (Fig. 8). This quantity, referred to as ΣR,
▴Figure 7. Variation in Coulomb failure stress and stressing rate
at the mainshock centroid for the variable injection-rate simula-
tion (Fig. 5) compared to the constant injection-rate simulation;
the shaded region shows the range from the mainshock to the
fault tip at 2 km depth at the same radial distance (Fig. 6). Note
that the total volumes injected in each simulation are equivalent,
and that the horizontal axes are time normalized by the relative
time between the start of the simulation and the mainshock origin
time. The color version of this figure is available only in the elec-
tronic edition.
1048 Seismological Research Letters Volume 88, Number 4 July/August 2017
represents the forecast increase in earthquake rate at an indi-
vidual point in time. In some sense, it is analogous to an earth-
quake probability density function, whereby the probability of
an earthquake is the highest at times for which Ris highest.
Accordingly, we could consider ΣRto be an empirical cumu-
lative density function. Examining this function for simulation
A(Fig.8) shows that although the instantaneous probability of
an earthquake may be lower at later times in the simulation, the
overall probability for a given earthquake or a collection of
earthquakes to have occurred is still increasing.
Foreshock activity and temporal variations in magnitude
distributions (Walter et al., 2017) lend support to this predic-
tion. We also note that seismicity was not observed within a
10 km radius of the modeled injection source until late-2013,
when a clear increase in rate occurred. Even though the ma-
jority of these events are not considered foreshocks, their
10−2 m3s
Simulated
injection rates
constant rate
variable
0
1
2
3
(a)
(b)
(c)
R
Solid: includes
poroelastic stresses
Dashed: neglects
poroelastic stresses
constant−rate
Modeled seismicity
rate changes
5
10
15
background
rate = 1
0.0
0.2
0.4
0.6
0.8
1.0
ΣR density
M>2.7 within 10 km of inj. source
Noble County (n=23)
Osage County (n=1)
Pawnee County (n=13)
M 5.8
2011 2012 2013 2014 2015 2016 2017
Cumulative seismicity
above background
2011 2012 2013 2014 2015 2016 2017
▴Figure 8. Seismicity rate calculations for variable and constant-rate injection models (simulation A). (a) The simulated injection rates.
(b) The time-varying ratios of R—the induced seismicity rate (equation 3)—when considering the full poroelastic solution for stresses on
the fault (solid lines) versus the direct pore-pressure effect (dashed lines). (c) Simulated cumulative seismicity densities above back-
ground levels prior to the Mw5.8 mainshock. For comparison, the points show the cumulative density of observed earthquakes above the
magnitude of completeness (∼2:7statewide) inside a 10 km radius away from the injection source (see Fig. 3); no earthquakes were
detected prior to late 2013. The legend shows the number of earthquakes by county; the closest events to the injection source are 2.4, 6.3,
and 8.8 km for Osage, Pawnee, and Noble, respectively. The color version of this figure is available only in the electronic edition.
Seismological Research Letters Volume 88, Number 4 July/August 2017 1049
cumulative density function resembles the predicted Rdensities
for the variable injection-rate case. In general, detectable seis-
micity occurs approximately one year after variable-rate injec-
tion begins, and is nearly coincident with peak injection rates.
If the poroelastic stresses modeled for the Sooner Lake fault are
equivalent for similarly oriented fault planes around the injec-
tion source, assuming cylindrical symmetry is justified (Segall
and Lu, 2015), then these events may be related to changes in
injection rate. And if earthquake magnitudes are random in
time (e.g., Kagan and Knopoff, 1987), the overall probability
of a large earthquake owing to increases in injection is expected
to increase even though it may be instantaneously lower at
later times.
The apparent connection between injection rate, pre-
dicted seismicity rate, and observed cumulative density is
consistent with the results of Weingarten et al. (2015) that
demonstrate that, although large total disposal volumes are
not a necessary condition for elevated seismicity, high injection
rates do imply a higher probability of inducing seismicity. One
possible explanation for the lack of seismicity in other parts of
Osage County, where moderately high rates of fluid injection
occur (Murray, 2014), may be from regional variations pore-
pressure changes that occur because of compartmentalization
of the sedimentary section, which includes the Arbuckle
Group. This is supported by myriad faults with appreciable
throw that show up in comparable hydrostratigraphy in south-
central Oklahoma (Christenson et al., 2011;Mashburn et al.,
2013) and a general deepening of basal formation depths to the
southwest (Luza and Lawson, 1980).
Fluid pressures in a compartmentalized reservoir will
remain high in response to injection mass if flow is inhibited.
In a region with highly variable injection histories (Weingarten
et al., 2015) and a set of mapped faults with both diverse ori-
entations and preferential regional directions (Holland, 2013;
Alt and Zoback, 2016;Walsh and Zoback, 2016), the effect of
compartmentalization and its influence on heterogeneous pres-
sure distributions would be especially pronounced. Further-
more, injection in Osage County is predominantly on the
west side of a frictionally stable north–south-trending fault
that intersects the Sooner Lake fault (Fig. 1c), which suggests
that pore-pressure changes may have localized until transient
postseismic flow (Sibson, 1994) caused pressure equalization
(Manga et al., 2016). In any case, the effects of reservoir com-
partmentalization in the Arbuckle can be investigated directly
with data from a network of downhole pore-pressure monitor-
ing systems.
One complicating factor in these interpretations is the
possibility of anisotropic or temporal variations in permeabil-
ity. Active crustal shear strain maintains shear dilatancy over
hydrothermal sealing processes, diminishing the response to
quasi-static deformation in favor of enhanced flow in high
strain-rate plate-boundary regions (Barbour, 2015). Even
though strain rates in Oklahoma inferred from intraplate seis-
micity (Anderson, 1986) and geodetic measurements (Calais
et al., 2006) are low compared to those at plate boundaries,
for example, they may still outpace hydrothermal sealing
processes in the region (Nathenson and Guffanti, 1988). Spa-
tial variations in permeability exist, especially near faults, but
these may be compensated by variations in specific storage,
which implies that hydraulic diffusivity may be relatively uni-
form over large regions (Xue et al., 2016).
A shortcoming of the seismicity rate model used in this
study is that it calculates changes relative to the background
seismicity rate. The question then becomes: What is the back-
ground rate? In the Pawnee study area, it is difficult to infer a
reliable estimate of the background seismicity rate because of
the extremely small sample size of documented earthquakes
prior to 2009 and because all major seismic sequences in
Oklahoma have been on unmapped faults (Yeck, Hayes, et al.,
2016). The model results we show must be interpreted within
the context of a probabilistic analysis; however, it is not
possible to quantify the effect on the seismic hazard without
establishing a background seismicity rate, which is subject to
current debate. The background seismicity rate in Oklahoma
has been estimated (Ellsworth, 2013;Langenbruch and Zo-
back, 2016) to be roughly one Mw≥3earthquake per year
inside the areas of interest defined by the Oklahoma Corpo-
ration Commission (∼26 ×103km2). If the seismicity rate
for our model domain can be inferred from this regional es-
timate by accounting for the relative area covered by the
model (∼314 km2), the local background seismicity rate is
roughly one Mw≥3earthquake per century. Our modeling
results suggest an increase in seismicity from a background
rate of roughly 0.01 earthquakes per year to roughly 0.15
earthquakes per year in mid-2014. As we mentioned above,
seismicity rates did increase in the years prior to the Pawnee
earthquake, around the time of peak-predicted seismicity rate
(Fig. 8), but these observations are limited and possibly tied to
changes in detection thresholds (i.e., network changes).
The present set of poroelastic injection- and seismicity-
rate models do not incorporate any detailed information about
the initial state of stress acting on the fault, the fault’s initial
proximity to shear failure, stress transfer effects during earth-
quake rupture, or variations in stress owing to either geometric
variation, frictional asperities, or aseismic slip. In future studies,
it would be worthwhile to use deterministic earthquake
mechanical and hydrological models to identify the conditions
that would have influenced earthquake nucleation and rupture
during the Pawnee sequence (e.g., McClure and Horne, 2011;
Norbeck and Horne; 2016b).
CONCLUSIONS
Simulations of time-varying Coulomb failure stresses on the
fault induced by injection activities indicate that the combined
effect of stress changes associated with a high-rate fluid-
injection transient and long-term injection may have influ-
enced the timing and location of the Pawnee earthquake. Even
though diffusion is the principal mechanism for transmitting
pore-fluid pressure changes in basement rock, the effects of
strain coupling between the rock and fluid are significant
and should not be ignored. Seismicity rate calculations using
1050 Seismological Research Letters Volume 88, Number 4 July/August 2017
a rate-and-state friction model are sensitive to the rate of
change of Coulomb failure stresses and predict increases of
more than an order of magnitude above background rates. Pre-
dicted seismicity rate increases generally resemble a lagged
smoothed version of the injection-rate history, and the ob-
served seismicity leading up to the mainshock follows the cu-
mulative density function of rates predicted by the variable-rate
injection simulation. If seismicity rates are affected by poroe-
lastic stress changes, our models suggest that they may remain
elevated for at least a year following shut-in of injection wells
after the earthquake, which emphasizes the importance of
incorporating accurate geomechanical properties of the subsur-
face in understanding the hazards associated with injection-in-
duced seismicity, especially in low strain-rate environments.
DATA AND RESOURCES
Injection data for Osage County are from the Environmental
Protection Agency (EPA) and are available in Ⓔthe electronic
supplement to this article; data for other counties are from
the Oklahoma Corporation Commission (OCC) Oil and
Gas Database (http://www.occeweb.com/og/ogdatafiles2.htm).
Mapped faults are from the Oklahoma Geological Survey
(http://www.ou.edu/content/ogs/data/fault.html). We used
poel (i.e., Wang and Kümpel, 2003), version 2012, for numeri-
cal simulations of injection. Regional earthquakes are from the
Advanced National Seismic System (ANSS) earthquake catalog
(http://www.ncedc.org/anss/catalog-search.html). All websites
were last accessed March 2017.
ACKNOWLEDGMENTS
We thank Nancy Dorsey at the Environmental Protection
Agency (EPA) for help accessing injection records from Osage
County and thank Xiaowei Chen and Paul Hsieh for helpful
discussions. Elizabeth Cochran and Paul Hsieh graciously pro-
vided thorough preliminary reviews on short notice. We thank
two anonymous reviewers for comments that led to improve-
ments in the clarity and presentation of this work. Jack
Norbeck was supported by the Stanford Center for Induced
and Triggered Seismicity and a Mendenhall Postdoctoral
Fellowship.
Any use of trade, firm, or product names is for descriptive
purposes only and does not imply endorsement by the U.S.
Government.
REFERENCES
Alt, R. C., and M. D. Zoback (2016). In situ stress and active faulting in
Oklahoma, Bull. Seismol. Soc. Am. 107, no. 1, doi: 10.1785/
0120160156.
Anderson, J. G. (1986). Seismic strain rates in the central and eastern
United States, Bull. Seismol. Soc. Am. 76, no. 1, 273–290.
Barbour, A. J. (2015). Pore pressure sensitivities to dynamic strains:
Observations in active tectonic regions, J. Geophys. Res. 120,
no. 8, 5863–5883, doi: 10.1002/2015JB012201.
Barbour, A. J., and F. K. Wyatt (2014). Modeling strain and pore pressure
associated with fluid extraction: The Pathfinder Ranch experi-
ment, J. Geophys. Res. 119, no. 6, 5254–5273, doi: 10.1002/
2014JB011169.
Barton, C. A., M. D. Zoback, and D. Moos (1995). Fluid flow along po-
tentially active faults in crystalline rock, Geology 23, no.8,683–686,
doi: 10.1130/0091-7613(1995)023<0683:FFAPAF>2.3.CO;2.
Blanpied, M. L., D. A. Lockner, and J. D. Byerlee (1995). Frictional slip of
granite at hydrothermal conditions, J. Geophys. Res. 100, no. B7,
13,045–13,064, doi: 10.1029/95JB00862.
Bott, M. H. P. (1959). The mechanics of oblique slip faulting, Geol. Mag.
96, 109–117, doi: 10.1017/S0016756800059987.
Bourouis, S.,and P. Bernard (2007). Evidence for coupled seismic and aseis-
mic fault slip during water injection in the geothermal site of Soultz
(France), and implications for seismogenic transients, Geophys. J. Int.
169, no. 2, 723–732, doi: 10.1111/j.1365-246x.2006.03325.x.
Calais, E., J. Y. Han, C. DeMets, and J. M. Nocquet (2006). Deformation
of the North American plate interior from a decade of continuous
GPS measurements, J. Geophys. Res. 111, no. B6402, doi: 10.1029/
2005JB004253.
Carpenter, B., C. Morgan, D. Lockner, and Z. Reches (2016). Strength
and stability of Oklahoma basement rock: Preliminary observations
from experiments at in-situ conditions, presented at 2016 Fall Meet-
ing, AGU, San Francisco, California, 12–16 December, Abstract
S44C–06.
Chang, K. W., and P. Segall (2016). Injection-induced seismicity on base-
ment faults including poroelastic stressing, J. Geophys. Res. 121,
no. 4, 2708–2726, doi: 10.1002/2015JB012561.
Christenson, S., N. I. Osborn, C. R. Neel, J. R. Faith, C. D. Blome, J.
Puckette, and M. P. Pantea (2011). Hydrogeology and simulation
of groundwater flow in the Arbuckle-Simpson aquifer, south-cen-
tral Oklahoma, U.S. Geol. Surv. Sci. Invest. Rept. 2011-5029, avail-
able at https://pubs.usgs.gov/sir/2011/5029/ (last accessed April
2017).
Deng, K., Y. Liu, and R. M. Harrington (2016). Poroelastic stress trigger-
ing of the December 2013 Crooked Lake, Alberta, induced seismic-
ity sequence, Geophys. Res. Lett. 43, 8482–8491, doi: 10.1002/
2016GL070421.
Dieterich, J. (1994). A constitutive law for rate of earthquake production
and its application to earthquake clustering, J. Geophys. Res. 99,
no. B2, 2601–2618, doi: 10.1029/93JB02581.
Ellsworth, W. L. (2013). Injection-induced earthquakes, Science 341,
no. 6142, doi: 10.1126/science.1225942.
Evans, D. M. (1966). The Denver area earthquakes and the Rocky Moun-
tain Arsenal disposal well, Mt. Geol. 3, no. 1, 23–36.
Fan, Z., P. Eichhubl, and J. F. W. Gale (2016). Geomechanical analysis of
fluid injection and seismic fault slip for the Mw4.8 Timpson, Texas,
earthquake sequence, J. Geophys. Res. 121, 2798–2812, doi:
10.1002/2016JB012821.
Griffiths, D. V., and I. Smith (2006). Numerical Methods for Engineers,
Second Ed., CRC Press, Boca Raton, Florida.
Guglielmi, Y., F. Cappa, J.-P. Avouac, P. Henry, and D. Elsworth (2015).
Seismicity triggered by fluid injection-induced aseismic slip, Science
348, no. 6240, 1224–1226, doi: 10.1126/science.aab0476.
Healy, J. H., W. W. Rubey, D. T. Griggs, and C. B. Raleigh (1968). The
Denver earthquakes, Science 161, no. 3848, 1301–1310, doi:
10.1126/science.161.3848.1301.
Holland, A. A. (2013). Optimal fault orientations within
Oklahoma, Seismol. Res. Lett. 84, no. 5, 876–890, doi: 10.1785/
0220120153.
Hsieh, P. A., and J. D. Bredehoeft (1981). A reservoir analysis of the
Denver earthquakes: A case of induced seismicity, J. Geophys.
Res. 86, no. B2, 903–920, doi: 10.1029/JB086iB02p00903.
Hubbert, M. K., and W. W. Rubey (1959). Role of fluid pressure in the
mechanics of overthrust faulting, Geol. Soc. Am. Bull. 70, no. 2, 115–
166, doi: 10.1130/0016-7606(1959)70[115:ROFPIM]2.0.CO;2.
Ingebritsen, S. E., and C. E. Manning (2010). Permeability of the
continental crust: Dynamic variations inferred from seismicity
Seismological Research Letters Volume 88, Number 4 July/August 2017 1051
and metamorphism, Geofluids 10, nos. 1/2, 193–205, doi: 10.1111/
j.1468-8123.2010.00278.x.
Jaeger, J. C., N. G. W. Cook, and R. Zimmerman (2007). Fundamentals
of Rock Mechanics, Wiley-Blackwell, Malden, Massachusetts.
Kagan, Y. Y., and L. Knopoff (1987). Random stress and earthquake sta-
tistics: Time dependence, Geophys. J. Int. 88, no. 3, 723–731, doi:
10.1111/j.1365-246X.1987.tb01653.x.
Keranen, K. M., H. M. Savage, G. A. Abers, and E. S. Cochran (2013).
Potentially induced earthquakes in Oklahoma , USA: Links between
wastewater injection and the 2011 Mw5.7 earthquake sequence,
Geology 41, no. 6, 699–702, doi: 10.1130/G34045.1.
Keranen, K. M., M. Weingarten, G. A. Abers, B. A. Bekins, and S. Ge
(2014). Sharp increase in central Oklahoma seismicity since 2008
induced by massive wastewater injection, Science 345, no. 6195,
448–451, doi: 10.1126/science.1255802.
Kroll, K. A., E. S. Cochran, and K. E. Murray (2017). Poroelastic proper-
ties of the Arbuckle Group in Oklahoma derived from well fluid
level response to the 3 September 2016 Mw5.8 Pawnee and 7 No-
vember 2016 Mw5.0 Cushing earthquakes, Seismol. Res. Lett. 88,
no. 4, doi: 10.1785/0220160228.
Kümpel, H. J. (1991). Poroelasticity: Parameters reviewed, Geophys.
J. Int. 105, no. 3, 783–799, doi: 10.1111/j.1365-246X.1991
.tb00813.x.
Langenbruch, C., and M. D. Zoback (2016). How will induced seismicity
in Oklahoma respond to decreased saltwater injection rates? Sci.
Adv. 2, no. 11, e1601542, doi: 10.1126/sciadv.1601542.
Lockner, D. A., and S. A. Stanchits (2002). Undrained poroelastic re-
sponse of sandstones to deviatoric stress change, J. Geophys. Res.
107, no. B12, doi: 10.1029/2001jb001460.
Luza, K. V., and J. E. Lawson Jr. (1980). Seismicity and Tectonic Relation-
ships of the Nemaha Uplift in Oklahoma, Part III, U.S. Nuclear
Regulatory Commission, NUREG/CR-1500, available at http://
ogs.ou.edu/docs/specialpublications/SP81‑3.pdf (last accessed April
2017).
Manga, M., C.-Y. Wang, and M. Shirzaei (2016). Increased stream
discharge after the 3 September 2016 Mw5.8 Pawnee, Oklahoma
earthquake: Stream response to an induced earthquake, Geo-
phys. Res. Lett. 43, no. 22, 11,588–11,594, doi: 10.1002/
2016GL071268.
Mashburn, S. L., D. W. Ryter, C. R. Neel, S. J. Smith, and J. S. Magers
(2013). Hydrogeology and simulation of groundwater flow in
the central Oklahoma (Garber-Wellington) aquifer, Oklahoma,
1987 to 2009, and simulation of available water in storage,
2010–2059, U.S. Geol. Surv. Sci. Invest. Rept. 2013-5219, avail-
able at https://pubs.usgs.gov/sir/2013/5219/ (last accessed April
2017).
McClure, M. W., and R. N. Horne (2011). Investigation of injection-
induced seismicity using a coupled fluid flow and rate/state friction
model, Geophysics 76, no. 6, WC181–WC198, doi: 10.1190/
geo2011-0064.1.
McNamara, D. E., H. M. Benz, R. B. Herrmann, E. A. Bergman, P. Earle,
A. Holland, R. Baldwin, and A. Gassner (2015). Earthquake hypo-
centers and focal mechanisms in central Oklahoma reveal a complex
system of reactivated subsurface strike-slip faulting, Geophys. Res.
Lett. 42, no. 8, 2742–2749, doi: 10.1002/2014gl062730.
Murray, K. E. (2014). Class II underground injection control well data
for 2010–2013 by geologic zones of completion, Oklahoma, Okla.
Geol. Surv. Open-File Rept. OF1 (2014), 32 pp.
Nathenson, M., and M. Guffanti (1988). Geothermal gradients in the
conterminous United States, J. Geophys. Res. 93, no. B6, 6437–
6450, doi: 10.1029/JB093iB06p06437.
Norbeck, J. H., and R . N. Horne (2016a). Physical mechanisms related to
microseismic-depletion-delineation field tests with application to
reservoir surveillance, Soc. Petrol. Eng. J. 21, no. 4, 1279–1288,
doi: 10.2118/178926-PA.
Norbeck, J. H., and R. N. Horne (2016b). Evidence for a transient hydro-
mechanical and frictional faulting response during the 2011 Mw5.6
Prague, Oklahoma earthquake sequence, J. Geophys. Res. 121, doi:
10.1002/2016JB013148.
Pollard, D., and R. Fletcher (2005). Fundamentals of Structural Geology,
Cambridge University Press, Cambridge, United Kingdom.
Raleigh, C. B., J. H. Healy, and J. D. Bredehoeft (1976). An experiment in
earthquake control at Rangely, Colorado, Science 191, no. 4233,
1230–1237, doi: 10.1126/science.191.4233.1230.
Rice, J. R., and M. P. Cleary (1976). Some basic stress diffusion solutions
for fluid-saturated elastic porous media with compressible
constituents, Rev. Geophys. 14, no.2,227–241, doi: 10.1029/
rg014i002p00227.
Roeloffs, E. (1996). Poroelastic techniques in the study of earthquake-
related hydrologic phenomena, in Advances in Geophysics,R.
Dmowska and B. Saltzman (Editors), Vol. 37, Elsevier, Amsterdam,
The Netherlands, 135–195.
Segall, P. (2010). Earthquake and Volcano Deformation, Princeton Uni-
versity Press, Princeton, New Jersey.
Segall, P., and S. Lu (2015). Injection induced seismicity: Poroelastic and
earthquake nucleation effects, J. Geophys. Res. 120, no. 7, 5082–
5103, doi: 10.1002/2015JB012060.
Sibson, R. H. (1994). Crustal stress, faulting and fluid flow, Geol.
Soc. Lond. Spec. Publ. 78,69–84, doi: 10.1144/GSL.SP.1994.078.
01.07.
Townend, J., and M. D. Zoback (2000). How faulting keeps the crust
strong, Geology 28, no. 5, 399–402, doi: 10.1130/0091-7613
(2000)28<399:HFKTCS>2.0.CO;2.
Walsh, F. R., and M. D. Zoback (2015). Oklahoma’srecentearth-
quakes and saltwater disposal, Sci. Adv. 1, no.5,doi:10.1126/
sciadv.1500195.
Walsh, F. R., and M. D. Zoback (2016). Probabilistic assessment of
potential fault slip related to injection-induced earthquakes: Appli-
cation to north-central Oklahoma, USA, Geology 44, no. 12, 991–
994, doi: 10.1130/G38275.1.
Walter, J. I., J. C. Chang, and P. J. Dotray (2017). Foreshock seismicity
suggests gradual differential stress increase in the months prior to
the 3 September 2016 Mw5.8 Pawnee earthquake, Seismol. Res.
Lett. 88, no. 4, doi: 10.1785/0220170007.
Wang, H. F. (2000). Theory of Linear Poroelasticity with Applications to
Geomechanics and Hydrogeology, Princeton Series in Geophysics,
Princeton University Press, Princeton, New Jersey.
Wang, R., and H. J. Kümpel (2003). Poroelasticity: Efficient modeling
of strongly coupled, slow deformation processes in a multilayered
half-space, Geophysics 68, no. 2, 705–717, doi: 10.1190/1.1567241.
Weingarten, M., S. Ge, J. W. Godt, B. A. Bekins, and J. L. Rubinstein
(2015). High-rate injection is associated with the increase in U.S.
mid-continent seismicity, Science 348, no. 6241, 1336–1340, doi:
10.1126/science.aab1345.
Wolff, R. G. (1970). Relationship between horizontal strain near a well
and reverse water level fluctuation, Water Resour. Res. 6, no. 6,
1721–1728, doi: 10.1029/wr006i006p01721.
Xue, L., E. E. Brodsky, J. Erskine, P. M. Fulton, and R. Carter (2016). A
permeability and compliance contrast measured hydrogeologically
on the San Andreas fault, Geochem. Geophys. Geosys. 17, no. 3,
858–871, doi: 10.1002/2015GC006167.
Yeck, W. L., G. P. Hayes, D. E. McNamara, J. L. Rubinstein, W. D. Barn-
hart, P. S. Earle, and H. M. Benz (2016). Oklahoma experiences
largest earthquake during ongoing regional wastewater injection
hazard mitigation efforts, Geophys. Res. Lett. 44, no. 2, 711–717,
doi: 10.1002/2016GL071685.
Yeck, W. L., M. Weingarten, H. M. Benz, D. E. McNamara, E. A. Berg-
man, R. B. Herrmann, J. L. Rubinstein, and P. S. Earle (2016). Far-
field pressurization likely caused one of the largest injection induced
earthquakes by reactivating a large preexisting basement fault struc-
ture, Geophys. Res. Lett. 43, no. 19, 10,198–10,207, doi: 10.1002/
2016gl070861.
Zhang, Y., M. Person, J. Rupp, K. Ellett, M. A. Celia, C. W. Gable, B.
Bowen, J. Evans, K. Bandilla, P. Mozley, et al. (2013). Hydrogeologic
1052 Seismological Research Letters Volume 88, Number 4 July/August 2017
controls on induced seismicity in crystalline basement rocks due to
fluid injection into basal reservoirs, Groundwater 51, no. 4, 525–
538, doi: 10.1111/gwat.12071.
APPENDIX
SIMULATION PARAMETERS
In Table A1, we give the layered poroelastic parameters used in
simulations of injection. Simulation A represents the case of
variable elasticity parameters within each layer based on repre-
sentative bulk properties (Wang, 2000;Jaeger et al., 2007),
whereas simulation B represents the limiting case in which elas-
ticity parameters are fixed for the entire domain based on
parameters for granitic basement. In both simulations, the hy-
draulic diffusivities are variable, but equivalent; thus, the effec-
tive permeabilities are different between the two simulations,
except in the basement rock.
In Table A2, we give the parameters used in the seismicity
rate calculations, including the state parameter, background
stressing rate, and effective normal stress.
Andrew J. Barbour
Jack H. Norbeck1
Justin L. Rubinstein
Earthquake Science Center
U.S. Geological Survey
345 Middlefield Road
Menlo Park, California 94025 U.S.A.
abarbour@usgs.gov
Published Online 3 May 2017
1Also at Department of Energy Resources Engineering, Stanford Uni-
versity, Stanford, California U.S.A.
Table A2
Rate-and-State Frictional Properties Used in Seismicity
Rate Calculations
Parameter Value
A0.003
_τ010−4(MPa/yr)
¯σ10 (MPa)
Table A1
Layered Poroelastic Parameters Used in Simulations of Wastewater Injection
Layer Thickness (m) μ(GPa) νν
uBD(m2=s)
Simulation A: Variable elasticity parameters
Sedimentary 1100 10 0.3 0.4 0.75 0.1
Confining (post-Simpson, e.g., Sylvan shale) 200 15 0.3 0.4 0.75 0.005
Injection (Arbuckle-Simpson) 600 15 0.25 0.4 0.75 1.0
Basement (granitic) ∞30 0.25 0.38 0.75 (1.0, 0.002)*
Simulation B: Fixed elasticity parameters
Sedimentary 1100 30 0.25 0.38 0.75 0.1
Confining 200 30 0.25 0.38 0.75 0.005
Injection 600 30 0.25 0.38 0.75 1.0
Basement ∞30 0.25 0.38 0.75 (1.0, 0.002)*
μ, elastic shear modulus; ν,νu, drained and undrained Poisson’s ratio, respectively; B, Skempton’s coefficient; D, hydraulic
diffusivity.
*Range from top of basement unit to 8 km; the values decrease logarithmically with relative depth.
Seismological Research Letters Volume 88, Number 4 July/August 2017 1053
