Table Of ContentComputational
Seismology and
Geodynamics
Volume 5
ISSN 0733-5792
ISBN 0-87590-974-4
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Printed in the United States of America.
Computational
Seismology and
Geodynamics
Volume 5
Editor.
Dipak K. Chowdhury
Associate Editors:
Jean-Claude De Bremaecker
Kashhaiar Lashgari
Edo Nyland
Robert Odom
Mrinal Sen
M. M. Vishik
Russian Editors:
V. I. Keilis-Borok
A. L. Levshin
G. M. Molchan
B. M. Naimark
Selected papers from volume 30 of
VychisliteVnaya Seysmologiya
AMERICAN GEOPHYSICAL UNION
Washington, D.C. 2003
Computational
Seismology and
Geodynamics
Contents
Preface
Geodynamics
Modeling of the Ionian basin formation: Deep processes and tectonic evolution
A. T. Ismail-Zadeh, R. Nicolich, and L. Chernobory 1
Seismicity on mid-oceanic ridges: A global geodynamic analysis.
P. A. Sobolev and D. V. Rundquist 13
Forward Problems in Mathematical Physics
On reducing the order of the Rayleigh system. I. General theory
A. N. Kuznetsov 20
On reducing the order of Rayleigh system. II. Cases of reduction
A. N. Kuznetsov and V. M. Markushevich 28
On free oscillations of a rotating viscous liquid outer core of
the Earth
L M. Rozenknop and E. L. Reznikov 36
Variational approach to the problem of free oscillations of the Earth
L. M. Rozenknop, E. N. Bessonova, and E. L. Reznikov 43
Steady solutions to tj the Navier-Stokes equations
O. M. Podvigina 60
Inverse Problems in Geophysics
On reconstructing density distribution of horizontally homogeneous
liquid through wavenumbers and amplitudes of progressing surface waves.
N. N. Novikova and G. M. Henkin. 66
Advances in the classical travel-time inversion problem.
M. L. Gerver 74
On an Algorithm for solving the inverse problem of ray seismics
B. V. Digas, V. I. Maksimov, B. G Bukchin, and A. V. Lander
Vibrosounding of the uppermost sea bottom by ship noise.
V. E. Fedorov
Seismicity Models
Probabilities and information gain for earthquake forecasting
D. Vere-Jones
Strange attractor and clustering of shocks in the spring-block model
with healing
V. M. Gertzik
PREFACE
The Editorial Board of Computational Seismology and Geodynamics and the American Geophysical
Union are again pleased to publish the fifth volume in this series. For a variety of reasons, the
publication of this volume is somewhat delayed. The Editorial Board regrets this delay.
The American Geophysical Union has been publishing selected and edited English translations of
articles published in the well-known Russian journal Vychislitel 'naya Seysmolgiya in Computational
Seismology and Geodynamics since 1994. These volumes have made significant contributions in
enhancing our knowledge in the geosciences. It is hoped this volume will play an equally significant
role. Articles in the areas of Geodynamics, Forward Problems in Mathematical Physics, Inverse
Problems and Seismicity models are presented in this volume. The Editorial Board thanks the
reviewers of the manuscripts, and the Russian Editorial Board for their help and cooperation.
Computational Seismology and Geodynamics accepts research manuscripts from international
scientists in the fields of Seismology, Tectonics and Tectonphysics, Geodynamics and other related
fields. Manuscripts may be sent to any of the members of the Editorial Board of Computational
Seismology and Geodynamics.
Dipak K. Chowdhury
Editor, Computational Seismology and Geodynamics
COMPUTATIONAL SEISMOLOGY AND GEODYNAMICS VOL. 5
Modeling of the Ionian basin formation:
Deep processes and tectonic evolution
A. T. Ismail-Zadeh
International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian
Academy of Sciences, Moscow
R. Nicolich and L. Cernobori
Department of Naval Architecture, Ocean and Environmental Engineering, University of Trieste,
Italy
Abstract. We present evolutionary models (both conceptual and quantitative) for
the Ionian basin formation based on vast geological and geophysical datasets. The
tectonic analysis of the region revealed three phases of rapid subsidence of southern
Sicily and adjacent northwestern Ionian basin: in Middle-Late Triassic, Late
Jurassic-Early Cretaceous, and Neogene. On the basis of recent seismostratigraphic
data we assume that the basin started to form in the Late Jurassic due to extension
of continental lithosphere. During the active rifting phase, accompanied by thinning
of the crust and of the lower part of the lithosphere, the underlain asthenosphere
moved upward. The mantle material rose and partially melted when the geotherm
moved up crossing the solidus. A part of the magmatic melt moved upward, partially
crystallized within the lower crust and partially reached the surface through active
volcanism . We assume that the extension in the Late Jurassic did not lead to
the formation of oceanic crust, but significantly attenuated the continental crust
and the lithosphere. We also assume that another part of the melt remained at
the lithosphere/asthenosphere boundary and formed a magmatic lens. The basaltic
melt in the lens crystallized owing to changed temperature-pressure conditions and
then turned into dense rocks (eclogites). Gravitational anomalies and increased P
wave velocities in this zone confirm the existence of anomalously dense bodies in
the upper mantle. The eclogite lens sank in the asthenosphere causing a viscous
flow that resulted in the evolution of the Ionian basin since the Early Cretaceous.
We analyze numerical models of the flow induced by the uplift of the anomalous
mantle and by the subsidence of the heavy lens. By combining results of subsidence
analysis and of numerical modeling, we conclude that the processes in the upper
mantle leading to the Ionian basin formation can be explained by the upwelling
mantle stream, phase transition and sinking of the eclogite lens. It is believed
that the extension in the Late Jurassic, the rapid basin subsidence in the Early
Cretaceous, and the subsequent shortening in the Late Cretaceous and Tertiary
constitute the tectonic expression of these processes.
Introduction 1981]. The difficulty in understanding the evolution of
the Ionian basin can be partly attributed to the lack
The Ionian Sea basin and adjacent areas of the East of well data within the basin. However, both reflection
ern Mediterranean have a complex geological history and refraction seismic data and their stratigraphic in
[e.g., Udias and Buforn, 1995]. The basin has an isomet terpretations indicate that the basin is filled with about
ric shape, its sea bottom is more than 4 km deep. The 8 km of sediments ranging from Jurassic to Quaternary
geodynamic evolution of the region since the Mesozoic [Makris et al., 1986; Ferrucci et al., 1991; de Voogd et
time results directly from the relative motions and inter al., 1992; Truffert et al, 1993; Cernobori et al, 1996].
actions between the African and European plates and Several detailed reconstructions of tectonic evolution
is closely associated with the Tethys evolution. Various of the Mediterranean region were proposed on the ba
hypotheses have been suggested for the Ionian basin sis of geological and paleomagnetic data [Biju-Duval et
evolution. The basin was considered as a possible relic al, 1977; Dercourt et al, 1986; Gealey, 1988; Dewey et
of the PaleoTethys and as a relic of the Neo-Tethys [Hsu al, 1989]. However, due to complex collision processes
and Bernoulli, 1975]; as a Jurassic-Cretaceous basin including block rotations, paleoreconstructions are not
and as a Tertiary foundered basin [Scandone et al, always reliable enough and leave room for alternative
1
Copyright American Geophysical Union
2 1SMAIL-ZADEH: MODELING IONIAN BASIN FORMATION
models. Moreover, reconstructions of tectonic evolution
are rarely combined with associated deep-seated pro
cesses. We believe that tectonic processes, occurring on
the earth's surface, have to be considered together with
processes in I he underlying upper mantle, since surface
tectonic activities are an expression of dynamics of 1 he
lithosphere/asthenosphere system.
According to the model of Dercourt et al. [1986] for
the Mesozoic-Cenozoic plate tectonic evolution of the
Eastern Mediterranean, the extension within the Io
nian basin started in the Late Jurassic. Dercourt et al.
[1986] supposed that a rotation of Apulia with respect
to Africa caused a rapid subsidence of the Ionian basin
in the Aptian time. The basin was still expanding in the
Late Cretaceous and ceased its extension in the Early
Paleocene. Within the framework of this reconstruc 14' 00' 14" 30' 15'00' 15'30' 16'00'
tion, the reason of rapid subsidence of the Ionian basin
Figure 1. Map of Sicily and the northwestern part of
remains unclear: Why did the rotation of Apulia result the Ionian basin showing well sites (dots) and profiles
in the rapid subsidence of the adjacent basin? It is also AB and MS-112 (solid lines). The numbers on the pro
unclear what is the cause of positive gravity anomalies file MS-112 indicate the positions of backstripped sites
in the Ionian basin area and increased P wave velocities (prepared by using GMT [Wessel and Smith, 1991]).
in ilie uppermost mantle beneath this area.
In this paper, we present quantitative models of the pirically for each lithological unit [Carmtchael, 1989].
subsidence history of southern Sicily and northwestern Sediment ages, derived from the micropaleontological
Ionian basin, propose a possible mechanism for the Io analysis, were reported using the geological time scale
nian basin formation in the Mesozoic-Tertiary, and con [Harland et. at., 1990]. We did not consider eustatic sea-
struct numerical models permitting to analyze the re level changes because no specific paleobathymetric data
gional evolution. The numerical models are based on were available for the wells used in this study. Errors
the extension of the lithosphere and the crust, on the related to variations in adopted porosity-depth relation
phase transition to eclogites in the uppermost mantle, ships are not indicated. Variations of these parameters
and on induced viscous flows in the asthenosphere. The could result in errors in the range of 100 m in the com
suggested model for the basin formation is not contra putation of the tectonic subsidence.
dictory to the model of Dercourt et al. [1986], but inte
Southern Sicily
grates it with vertical movements of the crust beneath
the Ionian Sea.
The southern Sicily (Hyblean Plateau) and the Sicily
Channel platform are a slightly deformed area of the
Subsidence History of the Crust African continental margin. During the Mesozoic, this
region was a typical subsiding passive continental mar
We considered geological and geophysical data in the gin [Patacca et al., 1979]; its paleogeographic domains
subsidence analysis: well data in the southern Sicily and preserved their shapes and sizes to the present day.
its offshore [Temperature sotterranee, 1977: Palacca et This region had been extensively investigated by oil ex
nl., 1979], geological cross-sections within the Ilyblean ploration; hence there are numerous wells crossing the
Plateau (southeastern Sicily) and the northwestern pari thick Mesozoic-Tertiary sequences down to Upper Tri-
of the Ionian Sea [Casero et al., 1984; Bianchi et al., assic dolomites. Models of subsidence considered here
1987], and regional geophysical investigations [Makrts are based on t he analysis of 53 wells drilled in this region
et al., 1986]. Let us point out that the southern Sicily (Figure 1).
is elevated above sea level at present and so it is not The two-dimensional subsidence history along the
a part of the Ionian basin. However, we associate the profile AB (see Figure 1) through the Hyblean Plateau
evolution of the southern Sicily with the development is presented in Figure 2. During the Middle Triassic
of the basin in Mesozoic time. (Figure 2a), the region was characterized by slow subsi
The subsidence analysis is based on the backstripping dence and sedimentation, predominantly of carbonates.
method [e.g., Sclater and Christie, 1980]. This tech In the Late Triassic, rapid subsidence occurred in this
nique allows to separate isostatic effects of sediments region; the thickness of accumulated sediments ranged
from those of tectonic subsidence. Porosity-depth dis from A to 6 km (Figure 2b). From the Jurassic time,
tribution was calculated on the basis of the observed the whole region underwent moderate subsidence and
average lithologies using the standard exponential re sedimentation (Figure 2c).
lation: ifi(z) = <p<jexp(—cz), where ip is the porosity Since most of the wells drilled in the region do not
as a function of depth Both <po, the surface poros reach the basement, we studied the three-dimensional
ity (z — 0), and c, a constant, are determined em- tectonic subsidence for the Late Triassic surface. Figure
Copyright American Geophysical Union
ISMAIL-ZADEH: MODELING IONIAN BASIN FORMATION 3
profile was reconstructed down to the basement for the
N
western portion of the Ionian basin [Makris et al., 1986].
i 1 1 1 I —i 1 i
A B The ages of the stratigraphic horizons were taken from
E 0
•t - ,». ... the map of the paleoenvironmental evolution and vol-
S 4 canism [Longaretti and Rocchi, 1990].
a. The tectonic subsidence curves for different locations
Q 8 .. 4 j. \ , i f
are shown in Figure 4. We can distinguish three phases
1:
10 20 30 40 50 60 70 80 of the tectonic activity. The first phase extends from the
Late Jurassic until the Late Cretaceous and is marked
by a very rapid subsidence. The second phase (from
the Late Cretaceous to the Miocene) is characterized
by a relatively slow continuous subsidence. The third
phase shows Neogene active tectonic subsidence toward
the center of the Ionian basin. We believe that this
active subsidence correlates with the Alpine-Apennine
deformation events.
Geodynamic Model of the Basin
Evolution
Q
The results of the tectonic analysis show the rapid
0 10 20 30 40 50 60 70 80 subsidence of the southern Sicily toward the Ionian Sea
in the Late Triassic. Some authors [e.g., Knipper, 1975]
Length, km
suggest that the Triassic extension in the Alpine folded
Figure 2. Computed subsidence evolution along the region and the attenuation of the crust resulted in the
profile AB (see Figure 1) through the central part of the formation of deep sea basins. However, there is not
southern Sicily for successive ages: Middle Triassic (a),
enough evidence for the strict timing of the Triassic
Late Triassic (b), and Quaternary (c). Sediments: Qua
subsidence.
ternary (1), Cretaceous (2), Jurassic (3), Late Triassic
(4), and Early Triassic (5); (6) marks the basement. On the basis of seismic and stratigraphic data [Makris
et al., 1986; Ferrucci et al., 1991; Cernobori et al., 1996]
and of the results of the tectonic analysis, we assume
3 shows the temporal/spatial evolution of this surface that the Ionian basin started to form in the Late Juras
in Early Jurassic (a), Middle Jurassic (b), Late Creta sic in consequence of the opening of Neo-Tethys and of
ceous (c), and present day (d). We see that the sub the Central Atlantic ocean. Upwelling mantle flows re
sidence started in the Middle Jurassic time in the off sulted in the uplift of the underlain asthenosphere and
shore zone and was active till the Late Cretaceous. In the extension and thinning of the crust and the litho
the Tertiary time, rapid downwarping occurred in the sphere (Figure 5a). Seismic data indicate a substan
northwestern portion of the region. We interpret this tial thinning of the crust in the central part of the Io
stage of subsidence as the result of thrust loading dur nian basin, down to 15 km [Makris et al., 1986]. When
ing the Maghrebian-Apennine Late Neogene collision. the geotherm rose high enough to cross the solidus, the
The analysis of the subsidence of the southern Sicily mantle material partially melted [McKenzie and Bickle,
indicated local regional subsidence values which differ 1988]; the low-density melt could filter upward [Karakin
from the maximum subsidence of the Ionian basin. and Lobkovsky, 1979; McKenzie, 1984].
Thus, basing on the subsidence models and on the re It is likely that a minor amount of the melt flowed
gional paleotectonic evolution, we can distinguish three up, partially crystallized within the lower crust and
main phases of the subsidence activity: the first phase partially reached the sea floor, as indicated by the
is marked by a sudden sinking of the southern Sicily in Late Jurassic basaltic volcanism [Longaretti and Roc
the Late Triassic; the second phase is characterized by chi, 1990] (see Figure 5b). Recent multichannel reflec
a moderate subsidence of the Sicilian offshore since the tion studies beneath the Ionian basin [Cernobori et al.,
Middle Jurassic; whereas the third one is marked by a 1996] reveal a highly reflective discontinuities within the
rapid subsidence of the northwestern Hyblean Plateau lower crust. It could be explained by the action of the
in the Tertiary. basaltic intrusions on the lower part of the crust chang
ing its petrologic and physical properties, as well as by
Subsidence of the Ionian Sea Basin
phase transitions of basalts to garnet granulites.
The regional tectonic analysis is based on the seimostrati We assume that a large portion of the non-effusive
graphic cross section [Casero et al., 1984] along the pro melt remained in the lithospheric/asthenospheric trap,
file MS-112 (see Figure 1) crossing the main tectonic forming a magmatic lens. Subsequently, the melt crys
boundary of the basin, the Malta Escarpment. This tallized under low temperature and high lithospheric
Copyright American Geophysical Union
ISMAIL-ZADEH: MODELING IONIAN BASIN FORMATION
a b
37.25 37.25
37.00
36.75
36.50 36.50
14.25 14.50 14.75 15.00 14.25 14.50 14.75 15.00
37.25
37.00
36.75
36.50 36.50
14.25 14.50 14.75 15.00 14.25 14.50 14.75 15.00
Longitude Longitude
Figure 3. Three-dimensional tectonic subsidence of the Late Triassic surface of the southern
Sicily and its offshore at ages: (a) Early Jurassic; (b) Middle Jurassic; (c) Late Cretaceous; (d)
present day. The contour lines mark tectonic subsidence in meters. The present coast line is
shown by solid line.
pressure and then turned into anomalously dense eclogitic caused the rapid subsidence of the basement. It should
rocks (Figure 5c) that sank in the surrounding less dense be noted that recent experimental studies [Carswell,
mantle material, resulting in a viscous flow and lead 1990] showed a nonlinear behavior of phase diagrams for
ing to the Ionian basin evolution in the Late Jurassic- gabbro-garnet-amphibolite-eclogite transitions. This
Cretaceous. means that the pressure remains high (typical of the
Yanshin et al. [1980] assumed that phase transi subcrustal upper mantle) when the temperature of the
tions in the crystalline crust beneath the Ionian Sea phase transition is low. Hence it is very unlikely that
Copyright American Geophysical Union
