Accounting for uncertain fault geometry in earthquake source
inversions
– Application to the Mw 6.2 Amatrice earthquake, central Italy
Théa Ragon Anthony Sladen Mark Simons
Geophysical Journal International, Volume 218, Issue 1, July
2019, Pages 689–707, https://doi.org/10.1093/gji/ggz180
Published: 13 April 2019 Article history
SUMMARY
Our understanding of earthquake sources is limited by the
availability and the quality of observations and the fidelity of our physical
models. Uncertainties in our physical models will naturally bias our inferences
of subsurface fault slip. These uncertainties will always persist to some level
as we will never have a perfect knowledge of the Earth’s interior. The choice
of the forward physics is thus ambiguous, with the frequent need to fix the
value of several parameters such as crustal properties or fault geometry. Here,
we explore the impact of uncertainties related to the choice of both fault
geometry and elastic structure, as applied to the 2016 Mw 6.2 Amatrice
earthquake, central Italy. This event, well instrumented and characterized by a
relatively simple fault morphology, allows us to explore the role of
uncertainty in basic fault parameters, such as fault dip and position. We show
that introducing uncertainties in fault geometry in a static inversion reduces
the sensitivity of inferred models to different geometric assumptions.
Accounting for uncertainties thus helps infer more realistic and robust slip
models. We also show that uncertainties in fault geometry and Earth’s elastic
structure significantly impact estimated source models, particularly if
near-fault observations are available.
Inverse theory, Probability distributions, Earthquake source
observations
SubjectSeismology
Issue Section: Seismology
1 INTRODUCTION
With scarce observations mainly limited to the surface of the
Earth, our estimates of crustal properties and fault geometry are always
uncertain. This imperfect knowledge is usually not accounted for in inferences
of subsurface fault slip, with only observational errors considered. When
imaging the slip on a fault, we often assume minimum complexity as a
recognition of our inherent ignorance and to simplify the computation of the
forward problem. For instance, we often assume the Earth is flat, that it can
be approximated as a homogeneous elastic medium and that the causative fault
geometry is simple and known. Uncertainties related to these approximations
will affect the calculated response of the Earth and lead to different source
models (e.g. Simons et al.2002; Beresnev 2003; Hartzell et al.2007; Dettmer et
al.2014; Diao et al.2016; Ragon et al.2018). These so-called epistemic
uncertainties can be many orders of magnitude greater than observational
uncertainties for large earthquakes (Ragon et al.2018). In this study, we
investigate uncertainties related to our poor knowledge of the geometry of the
causative fault and elastic structure.
Fault geometry for a given earthquake is generally deduced
from a variety of observations including surface rupture, centroid moment
tensor solutions, previous earthquakes, aftershocks distributions or
tomography. Because of observational inaccuracies or simply a lack of data, it
is usual to describe the causative fault by a reduced set of fixed parameters
(location, strike, dip, length, width) to define one or several planar, or at least
smoothly varying, fault segments. Yet, we know from field investigations and
modelling that seismogenic faults are complex systems, at least at the surface
(e.g. Segall & Pollard 1980; Okubo & Aki 1987; Peacock 1991; Walsh et
al.2003; Manighetti et al.2015). At depth, fault complexity is still an open
question (Graymer et al.2007; Wei et al.2011; Ross et al.2017). Though, faults
are thought to be non-planar at all scales (e.g. Power et al.1987; Candela et
al.2012). The variability of proposed fault morphology for many events, such as
the 2009 Mw 6.3 L’Aquila (Lavecchia et al.2012), the October 2016 Norcia
(Bonini et al.2019), the 2011 Mw 9.0 Tohoku–Oki (e.g. Lay 2018), the 1999 Mw
7.4 Izmit (e.g. Duputel et al.2014) or the 2015 Mw 7.8 Gorkha events (e.g. Wang
& Fialko 2015; Elliott et al.2016; Yue et al.2017), suggests that even with
a large amount of observations and prior seismotectonic knowledge of the area,
it is not possible to robustly determine fault geometry, and neither to choose
the most realistic architecture. In the following, we only address
uncertainties in basic fault geometry parameters, such as fault dip and
position, and the fault we assume for inversion (planar, not rough) thus
remains different than the structures we observe (complex and rough).
To address our uncertain assumptions on the causative fault
geometry, we previously proposed a practical framework based on a sensitivity
analysis (Ragon et al.2018, hereafter referred to as RSS18). There we described
a methodology to account for uncertainties of the fault geometry parameters,
such as fault dip, position, strike or curvature, following the framework
described in Duputel et al. (2014). This methodology has been validated through
a toy model, but it remains to be explored in the case of a real earthquake.
The impact of uncertainties in fault geometry is particularly striking for a
simple 2-D case (as in RSS18). Yet, for a real event, the information brought
by laterally extensive observations could potentially minimize the influence of
epistemic uncertainties. Here, as with the toy model study, we focus on the
effect of fault dip and position as they cover two primary sources of fault
geometry uncertainties. To analyse and illustrate the impact of these
first-order parameters independently of other geometric characteristics
(curvature, variation in strike,...), we consider an earthquake that ruptured a
relatively simple fault geometry, the Mw6.2 earthquake that struck central
Italy in August 2016. This event is characterized by a clear surface rupture
and a well-observed causative fault geometry (EMERGEO Working Group 2016a;
Cheloni et al.2017; Pucci et al.2017). The choice of the Amatrice event is also
motivated by the large density of available near-field observations, the good
coverage of geodetic data and the overall quality of the instrumentation. The
availability of near-field data is important since RSS18 showed that far-field
observations are less sensitive to a change in fault geometry, and tend to
induce less bias in the inferred source model. As an intermediate magnitude
earthquake, epistemic uncertainties will not be as influential as they could be
for a large event (e.g. Mw≥8). But the observational errors are limited,
allowing us to emphasize the effect of epistemic uncertainties.
We begin by quantifying the uncertainties in the fault
geometry (for fault dip and position) and in crustal structure for the 2016 Mw
6.2 Amatrice earthquake, using available observations and published studies. We
then compare co-seismic slip models inferred assuming different fault
geometries. Accounting for uncertainties in both fault dip and position, we
explore the influence of uncertainties in the fault geometry in the
distribution of co-seismic subsurface fault slip. Finally, we describe our
preferred model, as constrained by geodetic data, for the August 2016
earthquake.
2 THE 2016 AUGUST 24 Mw6.2 EARTHQUAKE
2.1 The 2016 seismic sequence of central Italy
The Mw 6.2 2016 August 24 earthquake was the first of a
series of moderate to large events, with five events of more than Mw 5.0, all
of which activated a normal fault system located in the central Apennines. In
the following, we refer to the 2016 August 24 event as the Amatrice earthquake.
On October 26th and 30th, 2 months after the onset of the Amatrice sequence, Mw
5.9 and Mw 6.5 earthquakes occurred a few tenth of kilometres to the north,
near the town of Norcia (Fig. 1). Overall, this sequence mainly ruptured the Mt
Bove-Mt Vettore-Mt Gorzano fault system, as evidenced by co-seismic surface
ruptures (EMERGEO Working Group 2016a,b; Pucci et al.2017). The Amatrice event
ruptured to the surface over more than 5 km along the southern part of the Mt
Vettore fault, with an estimated maximal vertical offset of 30 cm (Fig. 1;
EMERGEO Working Group 2016a; Pucci et al.2017). The ruptured geometry of the
Amatrice event appears to be a lot simpler than for the October 2016 shocks,
which may have ruptured several fault segments and antithetic faults (EMERGEO
Working Group 2016b; Cheloni et al.2017; Chiaraluce et al.2017).
Figure 1.
Seismotectonic framework of the area involved in the 2016 seismic sequence (top), and assumed forward model and associated uncertainties (bottom). In the map (top), the solid grey lines are the major seismogenic faults of the area (Boncio et al.2004a), while assumed causative faults for the published finite-fault studies (Lavecchia et al.2016; Tinti et al.2016; Cheloni et al.2017; Chiaraluce et al.2017; Huang et al.2017b; Liu et al.2017) are shown as the dashed grey lines. Identified surface rupture areas of the August 24 earthquake are plotted with the blue dots (Pucci et al.2017). Beach balls are the focal mechanisms of the two mainshocks and three main aftershocks (moment tensor solutions from the INGV Time Domain Moment Tensor catalog available at http://cnt.rm.ingv.it/en/tdmt), with their respective epicentres located by the black and white stars. Our preferred fault geometry (fault geometry A) is delineated with the dark blue line, while the fault geometry B is in orange. This colours are the same for the elevation profile (bottom), where uncertainties in each fault geometry are also represented. The assumed elastic modulus μ and associated uncertainties are also illustrated for the 12 first kilometres below the Earth surface. For a more complete view of assumed crustal properties, refer to Supporting Information Fig. S1.
2.2 Geometry of the causative fault
Numerous observations are available to constrain the fault
geometry of the Amatrice earthquake, including ground surface deformation
derived from surface rupture (Fig. 1) and satellite imagery, distribution of
aftershocks and aftershocks focal mechanisms. The continuous part of the
surface rupture delineates a curved path with an average strike of 155° (e.g.
EMERGEO Working Group 2016a; Pucci et al.2017), consistent with the strike of
seismogenic faults identified from previous earthquakes and geological data
(Fig. 1, e.g. Boncio et al.2004b). The fault geometry is constrained at depth
by the distribution of relocated aftershocks that occurred after the 24 August
event (e.g. Bonini et al.2016; Michele et al.2016; Chiaraluce et al.2017).
Vertical sections orthogonally oriented to the fault trend show that the
causative fault can be well described by a main segment dipping 35–40° (Bonini
et al.2016; Cheloni et al.2017). However, the aftershock cluster is too
scattered to determine a clear fault geometry, and possible structures could
dip from 30° to 55° with an uncertainty on fault surface trace location of more
than 5 km.
This uncertainty in fault geometry is also in published
focal mechanisms or fault geometries. Dip and strike parameters of available
focal mechanisms vary by more than 12° and 30°, respectively (Liu et al.2017).
Most published analyses of the Amatrice earthquake agree on modelling the
causative fault as one main segment. But assumed fault parameters differ
significantly from one model to another. Strike and fault position have
generally been determined from nodal planes and/or interferometric synthetic
aperture radar (InSAR) frames (Tinti et al.2016; Huang et al.2017b; Liu et
al.2017), giving strike values ranging from N155° (Liu et al.2017) to N167°
(Huang et al.2017b). When the fault strike is inverted from GPS or InSAR data,
inferred value is around N161° (respectively, Cheloni et al.2016; Lavecchia et
al.2016). The fault dip is also generally solved for, and inferred dip values range
between 34° and 51° (Bonini et al.2016; Cheloni et al.2016; Lavecchia et
al.2016; Tinti et al.2016; Huang et al.2017b; Liu et al.2017; Pizzi et al.2017;
Tung & Masterlark 2018). Fault position and length are also highly
variable, resulting in up to 3 km offset between published fault traces. Tung
& Masterlark (2018) also show that the variability of solved fault geometry
parameters is highly influenced by the assumed earth model.
Fault morphologies used for the Amatrice event are, as for
the 2009 Mw 6.3 L’Aquila (Lavecchia et al.2012) or the Mw 9.0, 2011, Tohoku–Oki
events (Lay 2018), extremely variable. For the Amatrice earthquake, uncertainty
of dip and strike parameters reaches 10–15°, and uncertainty of fault surface
position is of 2–5 km (Fig. 1).(…)
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