# Possible orthopyroxene enrichment in the upper mantle below the Mississippi
Embayment

###### Abstract

A high-resolution tomography study for the mantle beneath the New Madrid
Seismic Zone (NMSZ), a major intraplate earthquake zone in the Central and
Eastern US, reveals 3 - 5 % low Vp and Vs anomalies in the upper mantle in the
depth range 100 to 250 km. When attributed only to temperature variations,
such low velocities lead to temperatures higher than the olivine solidus, for
which consistent observational support is lacking. Similar magnitudes of the
Vp and Vs anomalies also suggest that temperature anomalies are unlikely to be
the sole factor because Vs is more sensitive to temperature than Vp. In this
study, we attribute the velocity anomalies to elevated water and orthopyroxene
(Opx) contents as well as temperature variations. We then compute differential
stresses using three-dimensional numerical models subjected to a loading
similar to the regional stresses. The models assume a Maxwell viscoelastic
crust and mantle with viscosities based on the temperature, water and Opx
content converted from the tomography. We find that the presence of water
allows for sub-solidus variations in temperature. However, any combination of
water content and temperature anomalies fails to yield Vp and Vs anomalies of
a similar magnitude. Thus, we consider Opx enrichment in place of water
content. Our calculations show that reasonable Opx content and sub-solidus
temperatures can explain both Vp and Vs anomalies. We speculate that the Opx
enrichment could have been produced by fluids released from a stagnant piece
of the Farallon slab imaged at around 670 km beneath the NMSZ.

EC AS Geochemistry, Geophysics, Geosystems

Center for Earthquake Research and Information, The University of Memphis

Arushi<EMAIL_ADDRESS>
Possible origins of similar-magnitude and negative ($-$ 5 to 6%) Vp and Vs
anomalies at depths 100 to 250 km beneath the NMSZ are explored

A combination of elevated temperature and water content cannot explain Vp and
Vs anomalies

The Vp and Vs anomalies can be explained by an orthopyroxene content of upto
40% along with temperature variations

##  1 Introduction

The New Madrid Seismic Zone (NMSZ), located in the Northern Mississippi
Embayment, is a seismically active region as indicated by paleoseismic
evidence (e.g., Tuttle, 2002) and three historic large (Mw $>$ 7) earthquakes
in 1811- 1812 (Johnston, 1996; Bakun Hopper, 2004). Numerous small-magnitude
earthquakes (Mw $<$ 5) are still being recorded (Fig. 1) posing a potential
risk of seismic hazard in and around this zone.

Figure 1: Earthquake epicenters (>Mw2.0) in the New Madrid Seismic Zone (NMSZ)
from May, 2002 to May, 2017. The color and size of symbols represent the depth
and magnitude, respectively. The black line marks the boundary of the
Mississippi Embayment and the Reelfoot Rift is contained within the blue
dashed line. The inset shows a part of the North American and the U.S. state
borders providing a geographic reference for the location of the NMSZ (black
square). The earthquake catalogue is obtained from the United States
Geological Survey at https://earthquake.usgs.gov/earthquakes/search/. This
figure is available under CC-BY powell2018b.

Geodetic strain rates observed in this region are less than 3 $\times$ 10-9/yr
(Boyd ., 2015). This value is much lower than the strain rate loading of
active plate boundaries suggesting that the earthquake generation is not
entirely associated with plate tectonics. This has puzzled researchers,
invoking them to come up with alternative mechanisms to explain the seismicity
of NMSZ that are compatible with the field observations.

The existing models for the NMSZ seismicity cannot explain all of the existing
seismic and other geophysical observations, calling for an improved model.
Previous studies that proposed lower lithospheric strength (Liu Zoback, 1997),
weaker lower crust (Kenner, 2000), deglaciation of the Laurentide ice sheet
(Grollimund Zoback, 2001), sinking of a denser heterogeneous lower crust
(Pollitz, 2001), and higher mantle temperatures (Zhan ., 2016) in the NMSZ
than in the surrounding region would elevate the stress level and therefore
promote seismicity. However, although required to be weak by some models (Liu
Zoback, 1997; Kenner, 2000), the lower crust in the NMSZ is strong due to the
presence of a dense mafic intrusion (commonly called a pillow) (Mooney .,
1983; Rabak ., 2011) possibly created by the passage of the Bermuda hotspot
during mid-Cretaceous (R. Cox Arsdale, 1997; RT. Cox Arsdale, 2002; Chu .,
2013). Attributing the seismic speed variations in the region’s upper mantle
only to anomalous temperature (Zhan ., 2016) also seems inconsistent with more
recent high resolution tomographic observations (Chen ., 2016, 2014;
Nyamwandha ., 2016). Chen . (2014) and Chen . (2016) found 5 % Vp and 7 % Vs
decrease at depths of 75-150 km beneath the NMSZ, respectively. When converted
to temperature variations only, seismic velocity anomalies of this magnitude
would mean partial melting in the upper mantle. This is not supported by
surface heatflow observations. Since Vs is more sensitive to temperature
(e.g., Goes ., 2000; Cammarano ., 2003) and the presence of melt alters Vs
more than Vp (Karato, 2003), Vs and Vp anomalies of a similar magnitude (3%
-5%) observed by Nyamwandha . (2016) cannot be explained by temperature
variations alone.

We note that two recent regional tomographic studies in the Central and
Eastern United States (CEUS) (Nyamwandha ., 2016; Chen ., 2016) independently
attributed their observed low velocity anomalies not only to elevated
temperature but also to other factors such as the presence of water and
compositional variations. The presence of orthopyroxene (Opx) lowers Vp more
than Vs (Schutt Lesher, 2010) and provides a possible explanation for the
similar magnitudes of the Vp and Vs anomalies in the presence of elevated
temperature. Previous studies have reported Opx enrichment over flat subducted
slabs (e.g., Wagner ., 2008; Tang ., 2012).

We propose that Opx enrichment occurs from the flat Laramide slab below the
NMSZ (Sigloch . 2008) at mantle transition depths , altering the composition
and hydrating the above lying lithosphere. Similar reasoning is invoked to
explain the tomographic and geochemical observations in the North China Craton
(NCC) (e.g., Zhang ., 2009; Santosh ., 2010; Q. Wang ., 2014) in which
asthenospheric upwellings from the stagnant pacific slab altered the
lithosphiere.

To address this idea in our study, we constrain the upper mantle viscosity
beneath the NMSZ assuming that the low velocity anomalies found in the
Nyamwandha . (2016) tomography results come from temperature, water and Opx.
We compute differential stresses at seismogenic depths using the viscosity
distributions as an input for geodynamic numerical models and include the
effects of compositional variations accounting for possible enrichment in Opx.

##  2 Modeling Methods

###  2.1 Viscosity Calculations

####  2.1.1 Case I: Temperature only

Effective viscosity for power law creep is given as (Kirby Kronenberg, 1987):

$\eta_{eff}=\dot{\varepsilon}^{\frac{1-n}{n}}A^{-1/n}\exp\left(-\frac{H}{nRT}\right),$
(1)

where $\dot{\varepsilon}$ is the effective strain rate taken as $3.25\times
10^{-17}s^{-1}$ for our calculations Calais . (2006), $R$ is the gas constant,
$A$ is the pre-exponential factor, $n$ is the power law exponent, $H$ is the
activation energy and $T$ is the temperature. The values of $A$, $n$ and $H$
as well as density for each layer are listed in Table 1. .

Table 1: Rheological constants used in our model simulations

Layer | Composition | Density (kg/m3) | A (MPa-ns-1) | n | H (kJ mol-1)
---|---|---|---|---|---
Upper crusta | Quartzite | 2750 | 1.1 $e^{-4}$ | 4.0 | 223
Lower crusta | Granulite | 2900 | 1.4 $e^{4}$ | 4.2 | 445
Mantleb | Olivine | 3200 | 1.1 $e^{5}$ | 3.5 | 530

$a:$ Burov (2010), $b:$ Dixon . (2004)

We calculate temperature anomalies using the Vp and Vs anomalies, denoted as
$\partial Vp$ and $\partial Vs$ hereafter, determined by Nyamwandha . (2016).
The sensitivities of Vp and Vs to temperature are based on the anelastic and
anharmonic effects in olivine (Ol) and are originally given in Goes . (2000)
as follows:

$\displaystyle\frac{\partial Vp}{\partial T}$ $\displaystyle=$
$\displaystyle\frac{1}{2Vp_{0}\ \rho}\frac{\partial K}{\partial
T}+\frac{2}{3Vp_{0}\ \rho}\frac{\partial\mu}{\partial
T}+Q_{p}^{-1}\frac{aH}{2RT_{0}^{2}\tan(\pi a/2)},$ $\displaystyle Q_{p}$
$\displaystyle=$ $\displaystyle
A\omega^{a}\exp\left[\frac{a(H+PV)}{RT_{0}}\right]\frac{3Vp_{0}^{2}}{4Vs_{0}^{2}},$
$\displaystyle\frac{\partial Vs}{\partial T}$ $\displaystyle=$
$\displaystyle\frac{1}{2Vs_{0}\,\rho}\frac{\partial\mu}{\partial
T}+Q_{s}^{-1}\frac{aH}{2\,R\,T_{0}^{2}\tan(\pi a/2)},$ $\displaystyle Q_{s}$
$\displaystyle=$ $\displaystyle
A\omega^{a}\exp\left[\frac{a(H+PV)}{RT_{0}}\right].$

Density is assumed to be constant as its sensitivity to temperature is about 4
orders of magnitude smaller than those of the elastic moduli when the standard
value of volume expansion coefficient (10-5/K) is assumed. Table 2 lists the
values of parameters and relevant quantities. The reference velocities (Vp0,
Vs0) and the reference temperature (T0) are depth-dependent (Fig. 2). We use
the velocity model from Pujol . (1997) for the crustal depths ($<$ 40 km) and
IASP91 (Kennett Engdahl, 1991) for the mantle ($>$ 40 km). The reference
temperatures are taken from Table 2 in Zhan . (2016), which are originally
from Liu Zoback (1997) for depths shallower than 100 km and from Goes van der
Lee (2002) for greater depths.

Figure 2: Reference P and S wave velocities ($Vp_{0}$ and $Vs_{0}$) used by
Nyamwandha . (2016) for their tomography results and reference temperature
($T_{0}$) from Liu Zoback (1997) and Goes van der Lee (2002) based on which
the temperature anomalies are calculated. This figure is available under CC-BY
powell2018b.  Table 2: Elastic moduli, their temperature derivatives and
anelasticity parameters

Variable | Symbol | Unit | Value
---|---|---|---
Bulk modulusa | $K$ | GPa | 129
Shear modulusa | $\mu$ | GPa | 82
Derivative with temperaturea | $\partial K/\partial T$ | MPa/K |  $-$16
| $\partial\mu/\partial T$ | MPa/K |  $-$14
Angular frequencyb | $\omega$ | rad/s | 2$\pi$
Frequency exponenta,c | $a$ | N/A | 0.15
Gas constant | $R$ | J/mol$\cdot$K | 8.314
Activation energya,c | $H$ | kJ/mol | 500
Volumea,c | $V$ |  $cm^{3}$/mol | 20

$a$: Goes . (2000), $b$: based on the frequency range of the tomography by
Nyamwandha . (2016), $c$: Sobolev . (1996).

####  2.1.2 Case II: Temperature and water

Velocity anomalies are assumed to be a function of water content as well as
temperature in this case. For simplicity, we assume uniform distributions of
water that are completely independent of velocity and temperature variations.
The effective viscosity is derived from the power law creep under the constant
strain rate assumption (Dixon ., 2004):

$\eta_{eff}=\dot{\varepsilon}^{\frac{1-n}{n}}C_{OH}^{-\frac{r}{n}}A^{-\frac{1}{n}}\exp\left(-\frac{H}{nRT}\right).$
(2)

where $r$ is the fugacity exponent, assumed to be 1.2 (Hirth Kohlstedt, 2003),
$C_{OH}$ is water content in Ol given in the unit of H/106 Si. Under the
current assumption, the temperature $T$ for (2) is the reference temperature,
$T_{0}$ from Fig. 2. Parameters for the upper and lower crust are listed in
Table 1 and those for the mantle are taken from Hirth Kohlstedt (2003).

We consider two possible scenarios for water concentration in olivine
following Dixon . (2004): Damp (50 ppm H2O) and wet (fully saturated with
water). Although it is not realistic to assume that the water distributions
are uniform throughout our model domain, we explore these scenarios to assess
the viscosity-lowering effects of the water content.

####  2.1.3 Case III: Temperature and water added selectively

We assume that mantle temperatures are likely to be lower than the olivine
solidus ($T_{m}$) everywhere in the study area. This is because the presence
of melt would alter Vs more than Vp (Karato, 2003) but the region’s tomography
results show similar magnitudes of $\partial Vp$ and $\partial Vs$. If
computed as in Case I, temperatures ($T_{I}$) would exceed $T_{m}$ at some
locations (Fig. 3). Only at those locations, we attribute the excess
temperature ($T_{ex}=T_{I}-T_{m}$) to the presence of water such that
$\partial Vp=\partial Vp^{T_{m}}+\partial Vp^{OH}$, where $\partial
Vp^{T_{m}}$ is the Vp anomaly due to $T_{m}-T_{0}$ and $\partial V{p}^{OH}$ is
contribution to the Vp anomaly from the water. We use the following
relationship between fluid content and velocity anomaly (Karato Jung, 1998):

$\delta C_{OH}=-\frac{\partial
V^{OH}}{V_{o}(T,P)}\left(2\tan\frac{\pi\alpha}{2}\right)\frac{\omega}{\alpha
B}\left(\frac{A}{\omega}\right)^{1-\alpha}\exp\left(\alpha\beta\frac{T_{m}}{T_{0}}\right),$
(3)

where $\partial V^{OH}$ is $\partial Vp-\partial Vp^{T_{m}}=\partial
Vp-\partial V{p}/\partial T(T_{m}-T_{0})$ , $T_{m}$ is the Ol solidus and
$T_{0}$ is the reference temperature. $V_{0}(T,P)$ is the reference velocity,
$\omega=2\pi$ rad/s (Table 2), $\beta$ is related to enthalpy $H$ (in Table 1)
as $H=\beta RT_{m}$ (Karato Jung, 1998), $A=B=8.8\times 10^{6}$ and
$\alpha=0.3$, which corresponds to the half space cooling model from Karato
Jung (1998). $\delta C_{OH}$ is calculated in ppm H/Si assuming that the
reference state has no water content i.e. $C_{OH}=0$.

Figure 3: Minimum and maximum temperatures (blue lines) calculated from P wave
anomalies as in Case I; and the solidus (red line) from Herzberg (1983). This
figure is available under CC-BY powell2018b.

####  2.1.4 Case IV: Temperature and Opx

Opx enrichment, together with temperature variations, may explain the
$\partial Vp$ and $\partial Vs$ of similar magnitudes because Vp is known to
be more sensitive to Opx concentration than Vs (Schutt Lesher, 2010) while Vs
is more sensitive to temperature than Vp. We therefore consider the combined
effects of Opx and temperature on Vp and Vs anomalies as follows:

$\partial V_{k}=\frac{\partial V_{k}}{\partial T}\,\delta
T(X_{Opx})+\frac{\partial V_{k}}{\partial X_{Opx}}\,\delta X_{Opx},$ (4)

where $V_{k}$ denotes Vs or Vp, $X_{Opx}$ is the Opx volume fraction in vol %
and $T$ is temperature (K). The coefficients are defined by the Voigt scheme:
i.e. in case of Vs,

$\frac{\partial V_{s}}{\partial T}=\frac{\partial
V_{s}}{\partial\mu}\frac{\partial\mu}{\partial
T}=\frac{1}{2V_{s}\,\rho}\frac{\partial}{\partial
T}\left[(1-X_{Opx})\,\mu_{Ol}+X_{Opx}\,\mu_{Opx}\right],$

where $\rho$ is the reference density, $\mu$, $\mu_{Ol}$ and $\mu_{Opx}$ are
shear moduli for the bulk composition, pure Ol and pure Opx, respectively. The
sensitivities of elastic moduli to temperature for Ol and Opx are taken from
Goes . (2000) and the sensitivities of Vp and Vs to Opx content from Schutt
Lesher (2010). We invert the above equations for $X_{Opx}$ and $\delta T$
simultaneously using the Newton-Raphson scheme assuming that Opx concentration
is zero in the reference state.

There is no wide consensus on whether the presence of Opx would generally
strengthen or weaken the mantle (e.g., McDonnell ., 2000; Ji ., 2001; Sundberg
Cooper, 2008; Tikoff ., 2010; Tasaka ., 2013; Hansen Warren, 2015)). We
calculate bulk viscosity in the presence of Opx using a constant strain scheme
as $\eta=(1-X_{Opx})\eta_{ol}+X_{Opx}\eta_{opx}$ (e.g., Ji ., 2001). In one
model, we assume that Opx viscosity is 3.3 times that of Ol (Hansen Warren,
2015) for strengthening effects and in another we construct a model in which
Opx viscosity is one eighth of Ol viscosity (Ji ., 2001) to account for
weakening effects of Opx.

###  2.2 Differential Stress Calculations

We construct three-dimensional (3D) models with Maxwell linear viscoelastic
rheology to compute differential stresses. Each model has three layers: upper
crust (0-20 km), lower crust (20-40 km,) and mantle (40-200 km) (Fig. 4a). The
lateral extent of our model is 2665 $\times$ 2554 km. The central region (gray
box) is constrained by the Nyamwandha . (2016) tomography results(Fig. 4a) but
the overall domain is set to be much greater than that of the tomography in
order to reduce boundary effects.

To simulate northeast-trending regional compressional principal stress
($\sigma_{1}$) (ML. Zoback Zoback, 1989), horizontal velocities with a
magnitude of 10 cm/yr are applied on the X- and Y-axis-perpendicular faces
(Fig. 4b) until the differential stress ($|\sigma_{1}-\sigma_{3}|$) of 200 MPa
is achieved at the depth of 10 km (MD. Zoback ., 1993; Baird ., 2010). After
that, the boundary velocity magnitude is reduced to avoid further increasing
the differential stress but is set to a non-zero value, 0.1 cm/yr, to maintain
this stress state without complete viscous relaxation. The top surface is free
(i.e., zero-traction) and the bottom has a no-slip condition.

We discretize the domain into a mesh with 227448 hexahedral tri-linear
elements using Trelis 15.0. The mesh has lateral and vertical resolutions of
25 and 5 km, respectively. We use Pylith (Aagaard ., 2013), an open source
finite element code for crustal dynamics developed and distributed by
Computational Infrastructure for Geodynamics, to calculate stresses and
displacements under the loading conditions described above. Differential
stresses are derived from stress solutions at one location in the NMSZ marked
by the purple line in Fig. 4a.

Figure 4: (a) Model domain and the P wave anomalies from Nyamwandha . (2016).
The domain has 3 layers: 20 km-thick upper crust, 20 km-thick lower crust and
mantle. The purple vertical line through the NMSZ marks the location of
vertical profiles of model results shown in the subsequent figures. The
rectangle on the surface represent the spatial extent of the tomography model.
(b) Cross-section of the model domain and S wave anomalies from Nyamwandha .
(2016) at 100 km depth. Arrows denote the velocity boundary conditions applied
on the side walls. This figure is available under CC-BY powell2018b.

###  2.3 Caveats regarding model setup

We assume that the reference state for the tomography has uniformly zero Opx
concentration. When a non-zero initial Opx concentration is assumed, the Opx
change calculated from inversion is reduced by the initial amount assumed,
keeping the total Opx concentration the same. The inverted temperatures are
also reduced by 20 K if we assume an initial Opx concentration of 20 %,
although we do not show the results with different initial opx concentration.

Also, although the magnitude of the temperature anomaly is reduced when water
is present, the temperature due to our maximum calculated water content in
Case III ($\sim$40 ppm H/Si) changes by $\sim$1 % from the original value
(Karato, 2003), which we neglect in our calculations. We explore Case II only
to observe the weakening effects on viscosity due to the presence of water,
therefore, it is acceptable to consider temperature independently from water
content.

Our model setup does not include the effects of gravity and it is assumed that
the density of all 3 layers, upper crust, lower crust, and mantle, is constant
within each layer. Since we are interested only in the effects of local mantle
heterogeneity on the overlying crust, gravity in our model setup can be
neglected. Additionally, ignoring density contrasts due to temperature
anomalies is justifiable as the volumetric expansion coefficient for common
rocks is $\sim$ $10^{-5}$/K and for maximum temperatures calculated here, 600
K, this amounts to 0.6% change in the density. We also ignore the effects of
density on composition in Eq. 6 and take the bulk density as 3220 kg/m3 using
the average of the densities of Ol (3222 kg/m3) and Opx (3218 kg/m3). This
assumption is reasonable as the densities of Ol and Opx (taken from Goes .
(2000)) are similar and using average density introduces a maximum change of
0.06 % compared to the case where density is calculated by the weighted
average.

We also assess the effects of the Reelfoot Rift (Fig. 1) by imposing $-$6 % Vp
and Vs anomalies in the rift (Pollitz Mooney, 2014) modeled as $\sim$70 km
wide on the surface, narrowing to $\sim$35 km at the depth of 10 km (Marshak
Paulsen, 1996). With the imposed low velocity anomalies, viscosities within
the rift are lower than the surrounding areas and therefore, the resultant
differential stresses from the model with the rift are lower than the models
without rifts. This observation is consistent with the effects of rift zones
found by Zhan . (2016). We do not show the model results with the rift as we
are interested in explaining the cause of the low-velocity anomaly ($>$50 km
depths) and it’s impact on the NMSZ seismicity. The presence of rifts lowers
the absolute differential stress in the upper crust by $\sim$10 MPa but does
not change the relative impact on differential stress among the cases
investigated in this study.

##  3 Model Results

###  3.1 Case 1: Temperature only

We convert $\partial Vp$ and $\partial Vs$ to temperature variations using
(2.1.1) and (2.1.1). Temperature anomalies are plotted in Fig. 5 at different
depths with best-fitting linear trends (black solid lines, Fig. 5). If both
$\partial Vp$ and $\partial Vs$ are simultaneously explained by temperature
only, the converted temperatures should be equal falling on a line with the
slope equal to 1 (red lines, Fig. 5) and the magnitudes of $\partial Vs$ would
be greater than those of $\partial Vp$ because Vs has greater sensitivity to
temperature than Vp. However, slopes of the best-fitting lines are in the
range 0.5 to 0.7 at all depths, consistently smaller than one because
$\partial Vp$ and $\partial Vs$ have similar magnitudes in the tomography by
Nyamwandha . (2016).

Figure 5: Scatter plots of temperature anomalies calculated from P wave
($\Delta T_{p}$) and S wave ($\Delta T_{s}$) anomalies with the best-fitting
lines (black). The red line has a slope equal to 1, representing the case
where both Vp and Vs anomalies are due to temperature only. This figure is
available under CC-BY powell2018b.

We show one of the viscosity calculations based on the $\partial Vp$-converted
temperature anomalies at cross-section C-C′ (see Fig. 4) in Fig. 6. The Vp
anomalies from Nyamwandha . (2016) along this cross-section are shown in Fig.
6a. According to the Vp sensitivity to temperature, (2.1.1), and parameters in
Table 2, the temperature variations are in the range $\pm$600 K (Fig. 6b). We
compute the viscosity using (1) and the total temperature, which is the sum of
the reference geotherm (Fig. 2) and the temperature variations. The viscosity
distribution (Fig. 6c) follows the pattern of velocity and temperature
variations and the minimum is about 1020 Pa$\cdot$s where Vp is the smallest.

Figure 6: Conversion of the velocity anomalies into model viscosities at
cross-section CC’ in Fig. 4a. Thin vertical gray lines mark the boundaries of
the tomography domain of Nyamwandha . (2016) (see Fig. 4a). Vertical axis is
exaggerated by a factor of 3. (a) P-wave velocity anomalies ($\partial V_{p}$)
from Nyamwandha . (2016). (b) Temperature anomalies calculated based on
$\partial V_{p}$. (c) Viscosities computed based on the temperatures anomalies
in (b) and the reference temperature shown in Fig. 2. This figure is available
under CC-BY powell2018b.

###  3.2 Case II: Temperature and uniform water content

We compute differential stresses within the NMSZ based on the reference
temperature (Fig. 2) and a spatially-uniform concentration of $H_{2}O$ in
olivine: 50 ppm (damp) and water saturated concentration (wet) (Fig. 7a). We
compare our calculations with the viscosity computed from $\partial
Vp$-converted temperatures as in Case I and no water content, referred as the
dry case ($C_{OH}=0$ ppm) subsequently. Given the same temperature, water can
reduce differential stress in the upper mantle (depths $\geq$ 40 km) by orders
of magnitude but in the upper crust, differential stress increases with water
content by about 2 MPa (Fig. 7b). The same effect of water content on
differential stress level in the upper crust is seen in the models based on Vs
anomalies (not shown here).

Figure 7: Depth profiles of (a) viscosity (b) differential stresses within the
NMSZ (purple line in Fig. 4) for the model computed from Vp-based temperatures
calculated in Case I (black), reference temperatures from Fig. 2 with uniform
COH concentration of 50 ppm (cyan), reference temperatures from Fig. 2 with
water-saturated olivine concentration (blue). Differential stresses (b) are
zoomed into to observe the concentration in upper crust on the right. This
figure is available under CC-BY powell2018b.

###  3.3 Case III: Temperature and selectively-added water

We compute water content in the super-solidus regions identified in Case I
(Fig. 3) using (3) and plot the contours of the calculated water contents on
the Vp anomalies calculated from the temperatures in the super-solidus region,
$\partial V_{p}^{ex}$, at a depth 150 km and in the cross section (marked in
Fig. 4) in Fig. 8. The correlation between the calculated water content and
low $\partial V_{p}$ is clearly seen in the cross section and the depth
section (Fig. 8). For our calculations from the velocity anomalies (3), water
contents reach up to 50 ppm in low-Vp regions.

Figure 8: Selectively-added water contents based on the velocity anomalies
converted from the temperatures in the super-solidus region shown on a cross-
section along the latitude of 36.2∘ (left), which approximately coincides with
CC’ in Fig. 4 and on a depth section at 150 km (right). The lower velocities
correspond to higher calculated water contents. This figure is available under
CC-BY powell2018b.

Based on the water content only in the supersolidus regions, we calculate the
viscosity distribution using (2) and the parameters in Table 1 within the NMSZ
(Fig. 4). The resultant differential stresses in the NMSZ upper crust are
compared with the dry model (Case I) in Fig. 9b. A minor decrease in viscosity
due to the weakening effect of the water is seen only in the depth range from
120 to 160 km, where significant water content is calculated (Fig. 9a) .
Differential stresses also show only minor differences between the dry model
and the present model over the same depth range (Fig. 9b).

Figure 9: Same as Fig. 7 but for the model with selectively-added water in
blue and the dry model described in Case I in black. This figure is available
under CC-BY powell2018b.

###  3.4 Case IV: Temperature and Opx content

We compute Opx volume fraction ($X_{Opx}$) and temperature anomalies ($\Delta
T$) that simultaneously satisfy $\partial Vs$ and $\partial Vp$ by solving the
system of equations (4). Two depth slices at 100 and 160 km displaying
$X_{Opx}$ and $\Delta T$ are plotted in Fig.10. Since $X_{Opx}$ is more
sensitive to Vp and $\Delta T$ is more sensitive to Vs, we plot $X_{Opx}$ and
Vp together in the left panels and $\Delta T$ and Vs together in the right
panels in Fig.10. $X_{Opx}$ values show correlation with negative Vp
anomalies, reaching a maximum of 0.2 at 100 km depth and 0.3 at 160 km.
Temperature anomalies vary between $\pm$450 K. This magnitude of temperature
anomalies is 10-20 % smaller than that of the dry, Opx-free case (Case I),
which exhibited temperature anomalies of $\pm$600 and $\pm$500 K at the
corresponding depths (Fig.6).

Figure 10: Inverted Opx contents and temperature anomalies at depths of 100
and 160 km. (left) Vp anomalies overlain by the contours of the Opx volume
fraction. (right) Vs anomalies overlain by the contours of the temperature
variations. This figure is available under CC-BY powell2018b.

Differential stresses are computed under various assumptions on the effects of
Opx enrichment on viscosity (Fig. 11). We consider three possibilities: Opx
enrichment increases viscosity Hansen Warren (2015), decreases it Ji . (2001),
or has no effect on viscosity. Estimates for the sensitivity of viscosity to
Opx contents are only loosely constrained (e.g., McDonnell ., 2000; Ji .,
2001; Tikoff ., 2010; Tasaka ., 2013; Hansen Warren, 2015). Hansen Warren
(2015) suggest a factor of 1.2 to 3.3 increase in viscosity for a pyroxene
fraction upto 30 %. Conversely, Ji . (2001) indicate a factor of 3 to 8
decrease in the strength of enstatite, the Mg end member of Opx, relative to
fosterite, the Mg end member of Ol, for samples containing 0.4-0.6 volume
fraction of fosterite. We choose a factor of 3.3 for increase and 8 for the
decrease in Opx viscosity relative to Ol as end member cases. Our calculations
for these three cases show that the strengthening and weakening effects by Opx
enrichment are insignificant (Fig. 11a). Differential stresses also show only
about 1 % of variation at all depths (Fig. 11b).

Figure 11: Same as Fig. 7 but for the models corresponding to the three
possible effects of Opx enrichment on viscosity: Viscosity strengthening
(light blue), viscosity weakening (brown) and the same viscosity as olivine
(purple). This figure is available under CC-BY powell2018b.

##  4 Discussion

Differential stress calculated in all the cases described in the study is most
sensitive to the temperature and less so to the Opx content and water content.
Low differential stresses in the mantle in all the models (cases I-IV) are
consistent with the high-temperature anomalies and low mantle viscosity
values. Relatively strong crust (depths $>$ 40 km) concentrates the
differential stress from the deeper mantle. Differential stress in the upper
crust calculated from the Opx-enriched cases (case IV) appears to be smaller
than values computed using forward calculated temperatures (case I and II).
This trend is the result of lower temperatures (Fig. 10) observed after
inversion in case IV than the calculated temperatures in case I (Fig. 5),
implying that the mantle in case I is weaker and concentrates higher
differential stress in the upper crust (Fig. 12). It can also be observed from
Fig. 12 that the effects of Opx on differential stress are minor. Capping the
maximum temperatures computed from P wave anomalies ($\Delta T_{p}$) with the
olivine solidus and attributing the excess anomalies to water content (case
III) has minor effect on the differential stress compared to case I. On the
other hand, the differential stress calculated using uniform water content
(case II) and the reference temperature (Tref) differs appreciably from all
the other cases (I, III) using the $\partial V_{p}$-calculated temperatures.
Therefore it can be inferred from Fig.12 that the differential stress is most
sensitive to the temperature.

Figure 12: Depth profiles of differential stress from all the cases (Case I to
IV) presented in this study. Case I: temperatures converted from the $\partial
V_{p}$ (purple); Case II: water added in the whole domain with the reference
temperature (cyan and blue); Case III: selective addition of water in super-
solidus region and temperature calculated from Case I using $\partial V_{p}$
(black); Case IV: temperatures inverted using $\partial V_{p}$ and $\partial
V_{s}$ and Opx for its strengthening (red), weakening (green) and no (yellow)
viscosity effects on Opx. This figure is available under CC-BY powell2018b.

Nonetheless, we favor the differential stress calculations with the inverted
temperatures and the presence of Opx (Case IV) because only they can explain
the similar magnitudes of the upper mantle Vp and Vs anomalies determined by
Nyamwandha . (2016). The velocity anomalies cannot be attributed to elevated
temperature alone, a more fertile mantle, or to the presence of fluids
combined with elevated temperatures; the presence of elevated amounts of Opx
is a necessary condition. The inverted values of Opx in the range of 5-45 %
(Fig. 10) are similar to those found previously for the Kaapvaal Craton
(Wagner ., 2008) and the Colorado Plateau (Li ., 2008). Metasomatism by Si
rich fluids derived from a subducting slab is the preferred mechanism for Opx
enrichment in these regions as documented by the texture and composition of
mantle xenoliths (Smith ., 1999; Bell ., 2005; Li ., 2008).

The need for Opx enrichment to provide a reasonable explanation of the similar
Vp and Vs anomalies argues for the presence of a slab below the Mississippi
Embayment at some point in time. Flat subduction of the Farallon slab is
usually invoked to explain deformation and magmatism during the Laramide
orogeny (ca. 80 to 35 Ma) in the western U.S. (e.g., Humphreys, 2009) and
several studies suggest that flat slab segments are present at depths above
1000 km in the central U.S. (Sigloch ., 2008; Liu ., 2008; Sigloch, 2011;
Schmandt Lin, 2014; Gao Liu, 2014; Porritt ., 2014). Flattening of the
Farallon slab can be attributed to the subduction of oceanic plateaus (the
Shatsky and Hess plateaus) located on an old ($>$50 My) slab (e.g., English
Johnston, 2004; Liu ., 2010). This situation would result in cold slab
subduction, facilitating transport of hydrous minerals to transition zone
depths (Maruyama Okamoto, 2007; Kusky ., 2014; Z. Wang ., 2018). Geodynamic
modeling by Liu . (2010) indicates that the top of the Hess plateau is located
at a depth of about 660 km below the Mississippi Embayment (Figure 4 in (Liu
., 2010)).

Seismic velocity models determined by tomographic inversion of teleseismic
body waves also indicate the presence of high velocity regions at or below the
transition zone in the central U.S. that are interpreted as fragments of the
Farallon slab (e.g., Sigloch ., 2008; Sigloch, 2011; Schmandt Lin, 2014;
Porritt ., 2014). All of these models indicate the presence of a high velocity
region in the vicinity of the Mississippi Embayment with, in general,
shallower high velocities to the east of the NMSZ. The P and S wave velocity
models determined by Porritt . (2014) indicate the presence of high velocities
in the depth range 200 to 800 km below the Embayment and surrounding area. In
the depth range 400 to 600 km, the high velocity region is split by a band of
low velocities that trends NNE, roughly along the western boundary of the
Embayment. The low velocity band is either not present or cannot be resolved
below 600 km. The low velocity band corresponds to the low velocity region
imaged in the depth range 100 to 250 km below the Embayment in the higher
resolution study by using TA and NELE FlexArray stations.

Biryol . (2016) attribute the high velocity upper mantle region located to the
east of the NMSZ to the presence of a dense, partially removed, lithospheric
drip. The down-going drip may result in upward, return flow of the
asthenosphere below the Reelfoot rift (Figure 9 in (Biryol ., 2016)). Our
analysis indicates that the Vp and Vs anomalies determined by Nyamwandha .
(2016) cannot be attributed to the presence of asthenosphere devoid of Opx
enrichment. One possibility that may be compatible with the concept put forth
by Biryol . (2016) is that the upwelling asthenosphere was enriched in Opx by
the presence of a slab fragment that has subsequently dropped to depths just
below the transition zone. A deeper slab fragment is suggested by the
tomography results of Schmandt Lin (2014) and by the present location of the
Hess oceanic plateau determined by Liu . (2010).

##  5 Conclusions

In this study, we explore possible explanations for the upper mantle Vp and Vs
anomalies ($\partial V_{p}$ and $\partial V_{s}$), negative and of similar
magnitudes, found below the Mississippi Embayment in the tomographic study by
Nyamwandha . (2016) and suggest Opx enrichment as the most plausible one. When
inverted for Opx volume fraction and temperature anomalies, these low velocity
anomalies correspond to positive temperature anomalies up to 450 K and Opx
contents of up to 40 %. The presence of Opx reduces the range of temperature
variations, which is $\pm$ 600 K when converted from $\partial V_{p}$ only.
The estimated Opx fraction is in the range of estimates made for the Kaapvaal
Craton (Wagner ., 2008) and the Colorado Plateau (Li ., 2008), which are
associated with the water-rock interactions from the Chile–Argentina and
Farallon flat slab, respectively. In NMSZ, olivine alteration to Opx might
have been induced by fluids released from the flat-subducted Laramide slab.

We set up numerical viscoelastic models based on the tomography by Nyamwandha
. (2016) to assess how variations in temperature, water and Opx contents
affect the regional stress field in three dimensions. The concentration of
stress from the weaker mantle into the stronger overlying crust has been
indicated previously to explain the seismicity of the NMSZ (e.g., Kenner,
2000; Zhan ., 2016). We observe similar stress-concentrating effects due to
warm upper mantle indicated by the low velocity anomalies.

###### Acknowledgements.

We thank C. Nyamwandha for access to the tomography data.

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