Viscous roots of active seismogenic faults revealed by geologic slip rate variations

TLDR: In this paper, the authors measured topography and offset along fault surfaces created during successive episodes of slip on seismically active extensional faults in the Italian Apennines during the Holocene epoch.

Abstract: Viscous flow in the deep crust and uppermost mantle can contribute to the accumulation of strain along seismogenic faults in the shallower crust1. It is difficult to evaluate this contribution to fault loading because it is unclear whether the viscous deformation occurs in localized shear zones or is more broadly distributed2. Furthermore, the rate of strain accumulation by viscous flow has a power law dependence on the stress applied, yet there are few direct estimates of what the power law exponent is, over the long term, for active faults. Here we measure topography and the offset along fault surfaces created during successive episodes of slip on seismically active extensional faults in the Italian Apennines during the Holocene epoch. We show that these data can be used to derive a relationship between the stress driving deformation and the fault strain rate, averaged over about 15 thousand years (kyr). We find that this relationship follows a well-defined power law with an exponent in the range of 3.0–3.3 (1σ). This exponent is consistent with nonlinear viscous deformation in the deep crust and, crucially, strain localization promoted by seismogenic faulting at shallower depths. Although we cannot rule out some distributed deformation, we suggest that fault strain and thus earthquake recurrence in the Apennines is largely controlled by viscous flow in deep, localized shear zones, over many earthquake cycles.

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Viscous roots of active seismogenic faults revealed by
geologic slip rate variations
P.A. Cowie, C.H. Scholz, G.P. Roberts, G.P. Faure Walker, Philippe Steer
To cite this version:
P.A. Cowie, C.H. Scholz, G.P. Roberts, G.P. Faure Walker, Philippe Steer. Viscous roots of active
seismogenic faults revealed by geologic slip rate variations. Nature Geoscience, Nature Publishing
Group, 2013, 6, pp.1036-1040. �10.1038/NGEO1991�. �insu-00913173�

1
Viscous roots of active seismogenic faults revealed by geologic slip rate 1
variations 2
P. A. Cowie
1
, C. H. Scholz
2
, G. P. Roberts
3
, J. P. Faure Walker
4
and P. Steer
1,5
3
1. Department of Earth Science, University of Bergen, Bergen 5002, Norway 4
2. Lamont Doherty Earth Observatory of Columbia University, Palisades, NY 10964-8000, USA 5
3. School of Earth Sciences, Birkbeck College, University of London, WC1E 7HX, UK 6
4. Institute for Risk and Disaster Reduction, University College London, London, WC1E 6BT, UK 7
5. Géosciences Rennes, Université de Rennes 1, CNRS, Rennes Cedex CS 35042, France. 8
During the earthquake cycle viscous flow at depth contributes to elastic strain 9
accumulation along seismogenic faults
1
. Evaluating the importance of this contribution 10
to fault loading is hampered by uncertainty about whether viscous deformation mainly 11
occurs in shear zones or by distributed flow. Furthermore, viscous strain rate has a 12
power-law dependence on applied stress
2
but few estimates exist for the power-law 13
exponent applicable to the long term in situ behaviour of active faults. Here we show 14
that measurements of topography and whole-Holocene offsets along seismically active 15
normal faults in the Italian Apennines can be used to derive a relationship between 16
stress and strain rate (averaged over 15±3 kyrs). This relationship, which follows a well-17
defined power-law with an exponent in the range 3.0-3.3 (1
σ), is used to infer the 18
rheological structure of the crust and constrain the width of active extension across the 19
Apennines. Our result supports the idea that the irregular, stick-slip movement of 20
upper crustal faults, and hence earthquake recurrence, are controlled by down-dip 21
viscous flow in shear zones over multiple earthquake cycles. 22

2
Earthquakes in the crust occur down to depths of approximately 15km in most regions 23
because below this depth temperature- and time-dependent creep (aseismic) deformation 24
processes become progressively more important. It is therefore generally accepted that the 25
upper crustal, seismogenic, portion of a fault is rooted down dip into a ductile (mylonitic) 26
shear zone and that the transition from frictional stick-slip to viscous flow is temperature and 27
strain rate dependent. At sufficiently high temperatures, distributed ductile deformation may 28
also occur in the lower crust and upper mantle. Both localised flow in shear zones and 29
distributed flow lead to elastic strain accumulation in the upper crust and thus loading of 30
faults to failure but currently there is disagreement as to which dominates
3,4
. Experimental 31
work, field data and theory indicate the flow law for the lithosphere at tectonic strain rates 32
should be that of dislocation creep in which strain rate, ė, is proportional to stress raised to an 33
exponent n, where n is typically in the range 2 to 4
5,6
: 34






−=
RT
Q
Ae
n
exp
σ

Equation 1 35
Here
σ
is driving stress, A is a material property, Q is activation energy, R is the molar gas 36
constant and T is absolute temperature. Geodetic observations of post-seismic relaxation 37
reveal temporal and spatial variations in effective viscosity that are most easily explained by 38
power law creep with n ≈ 3
7
. However geodetic data generally do not permit discrimination 39
between contributions of bulk flow of the upper mantle, of the lower crust, or plastic creep 40
within a shear zone
2
. Moreover, it is not clear that the rheological properties indicated by 41
postseismic transients are applicable to longer term behaviour of the coupled frictional-42
viscous fault system
8
. 43
Here we show that extensional strain rates derived from slip on seismogenic normal 44
faults in the actively uplifting and extending central and southern Italian Apennines can be 45

3
used to address this issue. The strain rates are measured at the surface using published 46
structural data
9,11
(Fig. 1, 2; see Methods) along active normal faults, characterised by 47
bedrock scarps that exhibit striated fault planes and offset dated Holocene sediments and 48
geomorphic surfaces
11
. These faults have developed in the last 2-3 My since thrusting in this 49
region diminished as westward subduction of the Adriatic plate beneath the Italian peninsula 50
slowed and slab tearing/detachment initiated ~6 Ma
10,12
. Present day topographic elevation 51
increases inland reaching elevations up to 2900 m locally along the footwall crests of major 52
extensional faults. Short wavelength (10-20 km) topographic variations due to faulting are 53
superimposed on long wavelength (100-150 km) topography aligned NW-SE along the axis 54
of the Italian Peninsula
12
(Fig. 2a). Gravity admittance data indicate that the long wavelength 55
topography is supported by buoyancy variations in the uppermost mantle
12
. Regional surface 56
uplift rates
13
increase in magnitude inwards from the Adriatic and Tyrrhenian coasts, 57
mimicking in shape the long wavelength topography
13
. 58
The extensional strain rates, averaged over the whole Holocene (15±3 kyrs), correlate 59
with average topographic elevation along the length of the central and southern Apennines
10
60
(Fig. 1c). This observation is confirmed by the map view distribution of active faults relative 61
to topographic contours (e.g., Fig. 2a). Geodetic data
also show that the highest contemporary 62
strain rates coincide with the highest elevation area in the central Apennines
14
. A power law 63
regression between the strain rate, ė, and elevations, h, (in transects 90 km across strike by 30 64
km wide along strike) reveals a well-defined relationship with power law exponents in the 65
range 3.0-3.3 (1σ) (see Methods and Supplementary material). Data from two independent 66
sets of 30km transects show that the result is not location dependent (Fig. 1d). Varying 67
transect width (from 5 km to 60 km) shows that over all scales the exponent lies within the 68
range 2.7-3.4 and 2.3-4.0 at 95% and 99% confidence intervals respectively. These variations 69

4
in strain rate cannot be attributed to thermal structure as heat flow increases gradually from < 70
40 mWm
-2
along the Adriatic coast to > 60 mWm
-2
along the Tyrrhenian coast, independent 71
of elevation and distance along strike
15
. 72
To interpret our data (Fig. 1d) in terms of Equation 1 we need to demonstrate that h 73
and
σ
are directly proportional. Previous workers (e.g., ref 16) made the connection by 74
approximating the lithosphere as a homogeneous thin viscous sheet. However, where thicker 75
than average crust (40 – 50km) overlies thinned mantle lithosphere, as it does in the central 76
and southern Apennines, the vertical velocity field is unlikely to be continuous at the scale of 77
the entire lithosphere
17
. Furthermore, the topography varies by 100’s of meters over 78
wavelengths < 100 km in which case approximations made in the thin sheet model break 79
down
18
. To avoid making these approximations we use observational constraints to relate h to 80
σ
by noting that (1) the upper crust is at or close to the threshold for brittle failure, i.e., “at 81
yield”
19
and (2) earthquake focal mechanisms and fault kinematic data along active faults
9,11
82
indicate that the maximum compressive stress,
σ
1
, is vertical and the least compressive 83
stress
σ
3
is parallel to the principal extensional strain orientation (NE-SW in Fig. 2). In an 84
elastic-brittle upper crust at yield,
σ
3
, is directly proportional to
σ
1
, compatible with incipient 85
frictional failure on optimally oriented planes
20
(Fig. 3). Thus the differential stress is also 86
proportional to
σ
1
, e.g., (
σ
1
-
σ
3
) ≈ 2
σ
1
/3 if Byerlee friction constants are assumed. Below the 87
base of the seismogenic zone (~14-17 km depth in this region
19,21
), where viscous flow 88
dominates, differential stress is less but we assume there is no stress discontinuity across this 89
transition over long time scales (Fig. 3). Additional topographic loads that result from surface 90
uplift relative to sea level increase
σ
1
, and hence (
σ
1
-
σ
3
), driving deformation (by a depth 91
and temperature dependent combination of frictional slip and viscous flow; Fig. 3) such that 92
differential stress in the upper crust is relaxed to re-establish the “at yield” condition (Fig. 93

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