Crustal structure of the Levant Basin, eastern Mediterranean

A seismic refraction/wide-angle reflection experiment was undertaken in the Levant Basin, eastern Mediterranean. Two roughly east–west profiles extend from the continental shelf of Israel toward the Levant Basin. The northern profile crosses the Eratosthenes Seamount and the southern profile crosses several distinct magnetic anomalies. The marine operation used 16 ocean bottom seismometers deployed along the profiles with an air gun array and explosive charges as energy sources. The results of this study strongly suggest the existence of oceanic crust under portions of the Levant Basin and continental crust under the Eratosthenes Seamount. The seismic refraction data also indicate a large sedimentary sequence, 10–14 km thick, in the Levant Basin and below the Levant continental margin. Assuming the crust is of Cretaceous age, this gives a fairly high sedimentation rate. The sequence can be divided into several units. A prominent unit is the 4.2 km/s layer, which is probably composed of the Messinian evaporites. Overlying the evaporitic layer are layers composed of Plio–Pleistocene sediments, whose velocity is 2.0 km/s. The refraction profiles and gravity and magnetic models indicate that a transition from a two layer continental to a single-layer oceanic crust takes place along the Levant margin. The transition in the structure along the southern profile is located beyond the continental margin and it is quite gradual. The northern profile, north of the Carmel structure, presents a different structure. The continental crust is much thinner there and the transition in the crustal structure is more rapid. The crustal thinning begins under western Galilee and terminates at the continental slope. The results of the present study indicate that the Levant Basin is composed of distinct crustal units and that the Levant continental margin is divided into at least two provinces of different crustal structure.     

Slowness domain offset and traveltime approximations in layered vertical transversely isotropic media

Considering horizontally layered transversely isotropic media with vertical symmetry axis and all types of pure‐mode and converted waves we present a new wide‐angle series approximation for the kinematical characteristics of reflected waves: horizontal offset, intercept time, and total reflection traveltime as functions of horizontal slowness. The method is based on combining (gluing) both zero‐offset and (large) finite‐offset series coefficients. The horizontal slowness is bounded by the critical value, characterised by nearly horizontal propagation within the layer with the highest horizontal velocity. The suggested approximation uses five parameters to approximate the offset, six parameters to approximate the intercept time or the traveltime, and seven parameters to approximate any two or all three kinematical characteristics. Overall, the method is very accurate for pure‐mode compressional waves and shear waves polarised in the horizontal plane and for converted waves. The application of the method to pure‐mode shear waves polarised in the vertical plane is limited due to cusps and triplications. To demonstrate the high accuracy of the method, we consider a synthetic, multi‐layer model, and we plot the normalised errors with respect to numerical ray tracing.     

Slowness-domain kinematical characteristics for horizontally layered orthorhombic media. Part I: Critical slowness match

Kinematical characteristics of reflected waves in anisotropic elastic media play an important role in the seismic imaging workflow. Considering compressional and converted waves, we derive new, azimuthally dependent, slowness-domain approximations for the kinematical characteristics of reflected waves (radial and transverse offsets, intercept time and traveltime) for layered orthorhombic media with varying azimuth of the vertical symmetry planes. The proposed method can be considered an extension of the well-known ‘generalized moveout approximation’ in the slowness domain, from azimuthally isotropic to azimuthally anisotropic models. For each slowness azimuth, the approximations hold for a wide angle range, combining power series coefficients in the vicinity of both the normal-incidence ray and an additional wide-angle ray. We consider two cases for the wide-angle ray: a ‘critical slowness match’ and a ‘pre-critical slowness match’ studied in Parts I and II of this work, respectively. For the critical slowness match, the approximations are valid within the entire slowness range, up to the critical slowness. For the ‘pre-critical slowness match’, the approximations are valid only within the bounded slowness range; however, the accuracy within the defined range is higher. The critical slowness match is particularly effective when the subsurface model includes a dominant high-velocity layer where, for nearly critical slowness values, the propagation in this layer is almost horizontal. Comparing the approximated kinematical characteristics with those computed by numerical ray tracing, we demonstrate high accuracy.     

Traveltime approximation in vertical transversely isotropic layered media

The well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging.     

Moveout approximation for horizontal transversely isotropic and vertical transversely isotropic layered medium. Part II: effective model‡

We use residual moveouts measured along continuous full azimuth reflection angle gathers, in order to obtain effective horizontal transversely isotropic model parameters. The angle gathers are generated through a special angle domain imaging system, for a wide range of reflection angles and full range of phase velocity azimuths. The estimation of the effective model parameters is performed in two stages. First, the background horizontal transversely isotropic (HTI)/vertical transversely isotropic (VTI) layered model is used, along with the values of reflection angles, for converting the measured residual moveouts (or traveltime errors) into azimuthally dependent normal moveout (NMO) velocities. Then we apply a digital Fourier transform to convert the NMO velocities into azimuthal wavenumber domain, in order to obtain the effective HTI model parameters: vertical time, vertical compression velocity, Thomsen parameter delta and the azimuth of the medium axis of symmetry. The method also provides a reliability criterion of the HTI assumption. The criterion shows whether the medium possesses the HTI type of symmetry, or whether the azimuthal dependence of the residual traveltime indicates to a more complex azimuthal anisotropy. The effective model used in this approach is defined for a 1D structure with a set of HTI, VTI and isotropic layers (with at least one HTI layer). We describe and analyse the reduction of a multi‐layer structure into an equivalent effective HTI model. The equivalent model yields the same NMO velocity and the same offset azimuth on the Earth's surface as the original layered structure, for any azimuth of the phase velocity. The effective model approximates the kinematics of an HTI/VTI layered structure using only a few parameters. Under the hyperbolic approximation, the proposed effective model is exact.     

Low-angle faults above and below a blueschist belt—Tinos Island, Cyclades, Greece

New observations from the Island of Tinos, Greece, allow a better definition of the structural position of the Alpine (Eocene) blueschist belt exposed in the islands of the Aegean Sea. These blueschists, over a significant part of the Aegean sea, are delimited from below by a low-angle thrust fault, while from above they are delimited by a low-angle, normal-type fault which omits a substantial crustal interval. Both underlying and overlying rocks were not affected by the high? metamorphism. The rapid uplift and exhumation of the high? rocks was therefore mainly the result of fault movements rather than erosion and whole-crust uplifting. The low-angle normal fault apparently had a major role in the uplift of the blueschists.     

The structure, isostasy and gravity field of the Levant continental margin and the southeast Mediterranean area

A 3-D layered structure of the Levant and the southeastern Mediterranean lithospheric plates was constructed using interpretations of seismic measurements and borehole data. Structural maps of three principal interfaces, elevation, top basement and the Moho, were constructed for the area studied. This area includes the African, Sinai and Arabian plates, the Herodotus and the Levant marine basins and the Nile sedimentary cone. In addition, an isopach map of the Pliocene sediments, as well as the contemporaneous amount of denuded rock units, was prepared to enable setting up the structural map of the base Pliocene sediment. Variable density distributions are suggested for the sedimentary succession in accord with its composition and compaction. The spatial density distribution in the crystalline crust was calculated by weighting the thicknesses of the lower mafic and the upper felsic crustal layers, with densities of 2.9 g/cm³ and 2.77 g/cm³, respectively. Results of the local (Airy) isostatic modeling with compensation on the Moho interface show significant deviations from the local isostasy and require variable density distribution in the upper mantle. Moving the compensation level to the base of the lithosphere ( 100 km depth) and adopting density variations in the mantle lithosphere yielded isostatic compensation (± 200 m) over most of the area studied. The spatial pattern obtained of a density distribution with a range of ± 0.05 g/cm³ is supported by a regional heat flux. Simulations of the flexure (Vening Meinesz) isostasy related to the Pliocene to Recent sedimentary loading and unloading revealed concentric oscillatory negative and positive anomalies mostly related to the Nile sedimentary cone. Such anomalies may explain the rapid subsidence in the Levant Basin and the arching in central Israel, northern Sinai and Egypt during Pliocene–Recent times. Comparison between the observed (Bouguer) gravity and the calculated gravity for the constructed 3-D lithospheric structure, which has variable density distributions, provided a good match and an independent constraint for the large-scale structure suggested and confirmed an oceanic nature for the Levant Basin lithosphere.     

Physical Controls on Spatial Variability in Decomposition of Organic Matter in Lake Kinneret,Israel

High resolution chemical data collected during summer 2003 indicate that the lower water mass (LWM) of the thermally stratified Lake Kinneret (LK) can be subdivided into three layers: a benthic boundary layer (BBL), overlain by the hypolimnion (HYP), and on top, the lower part of the metalimnion (ME-L). After onset of thermal stratification, the BBL is the first layer that turns anoxic, followed shortly afterward by the ME-L, while the HYP remains oxic and has relatively higher pH until later in summer. Thus, during the early summer, the HYP forms an oxygen-containing layer in-between two DO-deficient layers. Somewhat later, the HYP is characterized by still having significant levels of nitrate NO₃, while in both adjacent layers nitrate is already removed through denitrification. The mechanisms controlling the gradual decline of dissolved oxygen (DO) in the HYP during the summer were studied. The seasonal mean lake-wide vertical eddy diffusion coefficient in this layer, evaluated from heat flux measurements, is approximately 4 × 10⁻⁶ m² s⁻¹. The vertical oxygen flux due to diffusion from within the HYP toward its oxygen-deficient upper and lower boundaries accounts for most of the slow summer decline in DO in this layer. A smaller portion of this decline can be attributed to in-layer respiratory processes. The low turbidity, relatively high pH, and slow accumulation rate of NH₄ in the HYP support the notion that the slower mineralization processes occurring in this layer result from relatively low ambient concentrations of biodegradable organic matter, most probably due to the short residence time of the particles settling through this layer.     

Eigenrays in 3D heterogeneous anisotropic media,Part I: Kinematics

We present a new ray bending approach, referred to as the Eigenray method, for solving two‐point boundary‐value kinematic and dynamic ray tracing problems in 3D smooth heterogeneous general anisotropic elastic media. The proposed Eigenray method is aimed to provide reliable stationary ray path solutions and their dynamic characteristics, in cases where conventional initial‐value ray shooting methods, followed by numerical convergence techniques, become challenging. The kinematic ray bending solution corresponds to the vanishing first traveltime variation, leading to a stationary path between two fixed endpoints (Fermat's principle), and is governed by the nonlinear second‐order Euler–Lagrange equation. The solution is based on a finite‐element approach, applying the weak formulation that reduces the Euler–Lagrange second‐order ordinary differential equation to the first‐order weighted‐residual nonlinear algebraic equation set. For the kinematic finite‐element problem, the degrees of freedom are discretized nodal locations and directions along the ray trajectory, where the values between the nodes are accurately and naturally defined with the Hermite polynomial interpolation. The target function to be minimized includes two essential penalty (constraint) terms, related to the distribution of the nodes along the path and to the normalization of the ray direction. We distinguish between two target functions triggered by the two possible types of stationary rays: a minimum traveltime and a saddle‐point solution (due to caustics). The minimization process involves the computation of the global (all‐node) traveltime gradient vector and the traveltime Hessian matrix. The traveltime Hessian is used for the minimization process, analysing the type of the stationary ray, and for computing the geometric spreading of the entire resolved stationary ray path. The latter, however, is not a replacement for the dynamic ray tracing solution, since it does not deliver the geometric spreading for intermediate points along the ray, nor the analysis of caustics. Finally, we demonstrate the efficiency and accuracy of the proposed method along three canonical examples.