PRENLAB (Earthquake-Prediction Research in a Natural Laboratory)
Subproject 7 Theoretical analysis of faulting and earthquake processes
Maurizio Bonafede E-mail: bonafede@ibogfs.df.unibo.it
tel: +39-51-630.5001 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
Report no. 1 (task no. 1)
Title: Inferences on the regional stress field from the study of secondary
earthquake fractures
Maurizio Bonafede E-mail: bonafede@ibogfs.df.unibo.it
tel: +39-51-630.5001 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
Maria Elina Belardinelli E-mail: belardinelli@ingrm.it
tel: +39-6-51860.352 fax: +39-6-5041.181
I.N.G., Via Vigna Murata 605, 00143 Roma, Italy.
Agust Gudmundsson E-mail: agust@norvol.hi.is
tel: +354-1-694.488 fax: +354-1-629.767
Nordic Volcanological Institute, 101 Reykjavik, Iceland
The appearance of tension gashes at the earth surface, following an
earthquake, can provide constraints on the regional stress field which
produced the earthquake. Such fissures can be often observed when the seismic
fault does not reach the surface and are called secondary earthquake
fractures. This study is applied to the South Iceland Seismic Zone, located
between the Reykjanes Ridge and the eastern volcanic zone, in South Iceland.
This zone is characterized by North and North-East trending arrays of
en-enchelon tension fractures which are the most prominent surface features.
The arrays are globally oriented in the direction of dextral strike-slip
faults, buried under Holocene lava flows, but the orientations (alpha) of
individual fissures generally deviate 10-20 degrees from the strike direction
(see figure 1.1).
In order to understand the relationships between fissure arrays and the stress
field producing them, the earthquake-induced stress field is computed by means
of a dislocation model in a layered half-space and is superposed onto a
regional stress field with principal axes sigma1 and sigma2 (figure 1.2.a).
The angle between the seismic
fault and individual fissures cannot be less than 22.5 degrees, if the latter
open as pure tensile cracks, whatever the orientation (theta) of the regional
stress field (figure 1.2.b). Fissure angles less than 22.5 degrees can be
explained if
the fissures break at depth as shear cracks,
with strike direction alpha' dictated by the Coulomb-Navier
criterion (figure 1.2.c),
and open in mixed tensile mode from the surface down to a few tens
of meters, where the tensile stress produced by the earthquake
overcomes the lithostatic pressure (figure 1.3).
Accordingly, the presence of open fissures
striking a few degrees away from the direction inferred for the fault strike
can be employed to draw inferences on the frictional regime prevailing in the
brittle seismogenic layer and on the orientation and intensity of the regional
stress field.
Compared to anticipated milestones in work program, the previous
report is a contribution to task 1. Further contributions to task 1 to be
completed in the next months include: a more detailed description of the
stress induced by strike slip earthquakes in the near-field, employing crack
models and the inclusion of variable stress drop patterns compatible with
frictional laws, surface layering and tectonic loading.
Preliminary results were presented at the Reykjavik meeting, further
advancements have been presented at the GNGTS meeting in Rome, final results
will be presented at the EUG9 meeting in Strasbourg. A paper will be submitted
soon.
Report no. 2 (task no. 2)
Title: Global post-seismic rebound following strike-slip and normal faulting
earthquakes.
Maurizio Bonafede E-mail: bonafede@ibogfs.df.unibo.it
tel: +39-51-630.5001 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
Antonio Piersanti E-mail: piersanti@ing750.ingrm.it
tel: +39-6-51860 fax: +39-6-5041.181
I.N.G., Via Vigna Murata 605, 00143 Roma, Italy.
Giorgio Spada E-mail: giorgio@gea.df.unibo.it
tel: +39-51-630.5013 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
In order to study the post-seismic rebound following large lithospheric
earthquakes we have built a spherical, self-gravitating earth model with
viscoelastic rheology [Piersanti et al. 1996]. This model, which allows to
compute coseismic and postseismic displacements associated to lithosperic
earthquakes, is now employed to predict horizontal and vertical rates of
deformations in Iceland. The results are compared with geodetic data in
order to better constrain the rheological structure of the upper mantle
beneath Iceland. Although motions associated with rift dynamics and postglacial
adjustment are expected to contribute in a dominant way to present-day
velocities in this area, new insights are expected from the application of our
postseismic rebound model to Iceland. The solutions and algorithms developed
under task 2 are meant as working tools for finalizing tasks 3 and 5.
References: A. Piersanti, G. Spada, and R. Sabadini, Global
postseismic rebound of a viscoelastic Earth: Theory for finite faults and
application to the 1964 Alaska earthquake, J. Geophys. Res., in press, 1996.
Report no. 3 (task no. 3)
Title: Comparison between global earth models, including sphericity and
self-gravitation, and plane models.
Andrea Antonioli E-mail: studenti27@ibogfs..df.unibo.it
tel: +39-51-630.5013 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
Maurizio Bonafede E-mail: bonafede@ibogfs.df.unibo.it
tel: +39-51-630.5001 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
Antonio Piersanti E-mail: piersanti@ing750.ingrm.it
tel: +39-6-51860 fax: +39-6-5041.181
I.N.G., Via Vigna Murata 605, 00143 Roma, Italy.
Giorgio Spada E-mail: giorgio@gea.df.unibo.it
tel: +39-51-630.5013 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
We have compared two different approaches to the study of post-seismic
deformations. In the first one, we have considered a flat earth model forced
by a vertical strike-slip fault embedded in an elastic lithosphere [Nur and
Mavko, 1974]. In the second one, we have solved the same problem in spherical
geometry, taking advantage of the results by Piersanti et al. [1996] (see
reference to task no. 2). In both cases, we have computed the coseismic
displacements and the delayed post-seismic displacements associated with the
viscoelastic relaxation of a uniform mantle.
In Figure 3.1 we compare coseismic (left) and postseismic (right)
horizontal
displacements computed according to the spherical model (dashed lines) with
those predicted on the basis of the flat one (solid lines). The two top panels
refer to moderate source-observer distances (i.e., 0 < d < 120 km), whereas the
far-field responses are portrayed in the bottom panels, with 120 < d < 4000 km.
In this case study we have employed a vertical strike-slip fault
source of width W=50 km, which breaks the lithosphere-mantle boundary, located
at a depth of 100 km. As expected, there is a close agreement between the two
models in the coseismic regime for moderate source-observer distances (0 < d <
120 km, top left panel). In the postseismic regime (top, right) the spherical
model predicts a displacement which sensibly differs from the one obtained by
means of a flat model. Differences between spherical and flat models are
particularly large in the far field (bottom panels).
An analysis similar to that performed in Figure 3.1 has also been
carried out on the stress fields induced by a strike-slip earthquake.
Significant corrections to both the time-evolution and the spatial pattern of
the stress field have been found even at distances from the ridge much less
than the radius of the Earth. We have observed that stresses due to
lithospheric earthquakes in a spherical Earth decay slowly with increasing
distance from the fault, in contrast with predictions based on flat models.
These findings may have an impact in the study of stress diffusion along the
opposite margins of lithospheric plates, and corroborate recent findings
by Piersanti et al. [1996] on the relevance of post-seismic deformations and
stresses even at very large distances from the fault.
Further contributions to task no. 3 to be completed in the next months
include a more detailed study of the spatial and temporal pattern of the
stress field, and applications to the seismicity of Iceland.
The results of this study have been presented at the 1996 GNGTS
meeting in Rome. They are contained in the dissertation by A. Antonioli:
Deformazione post-sismica globale: confronto fra modelli piani e sferici ed
analisi del campo si sforzi generato da grandi eventi sismici, Thesis,
University of Bologna, 82 pp., 1995. Further results on the stress field will
be presented at the EUG9 meeting in Strasbourg (Antonioli, A., A. Piersanti,
G. Spada, and M. Bonafede, Time-Dependent Stress Field Associated with Rift
Dynamics, EUG Abstract, submitted, 1996). A paper is in preparation.
References: Nur, A., and G., Mavko, Postseismic viscoelastic
rebound, Science, 183, 204-206, 1974.
Report no. 4 (task no. 4)
Title: Modeling of a spreading ridge.
Andrea Antonioli E-mail: studenti27@ibogfs..df.unibo.it
tel: +39-51-630.5013 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
Maurizio Bonafede E-mail: bonafede@ibogfs.df.unibo.it
tel: +39-51-630.5001 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
Antonio Piersanti E-mail: piersanti@ing750.ingrm.it
tel: +39-6-51860 fax: +39-6-5041.181
I.N.G., Via Vigna Murata 605, 00143 Roma, Italy.
Giorgio Spada E-mail: giorgio@gea.df.unibo.it
tel: +39-51-630.5013 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
By means of a viscoelastic model we have computed the deformations associated
with the dynamics of a spreading ridge in a spherical, rheologically
stratified Earth. The purpose is to apply this model to a study of the
tectonics of the Iceland ridge. The method of solution is based on a
quasi-analytical spectral approach to the general equations which govern the
deformations of a spherical Earth due to seismic sources.
Figures 4.1 and 4.2 illustrates the results obtained by means of the
technique outlined above. In this case study, we have employed a simple Earth
model which includes a 100-km thick elastic lithosphere, a uniform mantle with
Maxwell rheology, and a fluid inviscid core. The source of deformation
consists of a 200-km long tensile fault buried at a depth of 50 km. The
response of the Earth to this finite fault has been retrieved by summation of
the effects of n=51 point sources, each characterized by a Burgers vector b =
15 m and by an Heaviside time-history. The more realistic case of a slowly
opening tensile fault can be dealt in a simple way. Figure 4.1 portrays the
coseismic surface displacement u (in centimeters) observed at a given distance
from the fault along different azimuths alpha (namely, 0, 45 and 90 degrees
from top to bottom). The surface displacement is decomposed along the spherical
unit vectors r, theta, and phi (dash-dotted, solid, and dotted curves,
respectively).
To appreciate the effects of mantle relaxation upon surface
observables, we show in Figure 4.2 the long-term response of the Earth to the
same excitation source considered in Figure 4.1. The time-scales governing the
transition from coseismic to postseismic displacements depends essentially
from the viscosity stratification of the mantle. For an upper mantle
characterized by a relatively low viscosity (such as the mantle beneath
Iceland) these time-scales amount to a few years [Piersanti et al., 1996]. A
comparison between Figures 4.1 and 4.2 indicates that relatively large amounts
of relaxation may affect all of the components of the displacement field. In
particular, we observe amplifications of a factor of 2 for the theta and r
components of displacements along alfa = 90 degrees (bottom panels). Another
interesting feature of Figure 4.2 is the large spatial scale of the region
experiencing horizontal motions in the postseismic regime. A first
comparison with results based on a homogeneous half-space model
have revealed a few unexpected results which are currently under
investigation.
Preliminary results on this topic have been presented at the 1996 GNGTS
meeting in Rome, final results will be presented at the EUG9 meeting in
Strasbourg (Antonioli, A., A. Piersanti, G. Spada, and M. Bonafede,
Time-Dependent Stress Field Associated with Rift Dynamics, EUG Abstract,
submitted, 1996).
Report no. 5 (task no. 5)
Title: Modeling of accelerated plate tectonics on a ridge following a major
earthquake in a transform shear zone: inferences on the rheological structure
below Iceland.
Andrea Antonioli E-mail: studenti27@ibogfs..df.unibo.it
tel: +39-51-630.5013 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
Maurizio Bonafede E-mail: bonafede@ibogfs.df.unibo.it
tel: +39-51-630.5001 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
Antonio Piersanti E-mail: piersanti@ing750.ingrm.it
tel: +39-6-51860 fax: +39-6-5041.181
I.N.G., Via Vigna Murata 605, 00143 Roma, Italy.
Giorgio Spada E-mail: giorgio@gea.df.unibo.it
tel: +39-51-630.5013 fax: +39-51-630.5058
Dipartimento di Fisica, Viale Berti-Pichat 8, 40127 Bologna, Italy
The episodic uprise of magma along the Iceland rift is expected to induce
time-dependent stress accumulation in the surrounding regions, which may be
associated to seismic activity along transform faults. In turn, seismic
activity may affect significantly the evolution of Mid-atlantic ridge. In
order to model these complex interacting processes, we will employ the Earth
model described above (tasks no. 2 e 4), which allows to compute the
deformation and stress fields associated with major earthquakes and the
time-dependent opening of the Iceland rift. Task 5 can not be finalized within
Phase 1, though preliminary results might be available during Phase 1.
Suggestion for proposed research topics to be included in the next
application (Phase 2 of PRENLAB).
A complete modeling of the interaction mentioned under task 5 requires
the use of numerical methods, powerful computers and adequate economic and
human resources. This study can only start after full achievement of tasks
1-4, which will be finalized by the end of Phase 1 of this project. Task
number 5 constitutes the main objective of this research program but can only
be completed within phase 2.