Ari Ben-Menahem

Tectonics, seismicity and structure of the Afro-Eurasian junction — the breaking of an incoherent plate

Abstract The purpose of this study was to unveil the tectonics and seismicity, S-wave velocity structure and inelastic behaviour with depth of the earths crust in the continental Near East. To this end, we have analyzed body wave phases and surface-wave signals from 47 earthquakes in the magnitude range 3.5–6.5 that were originated and recorded in (or close to the margins of) the Near East during 1927–1974. First motions, P- and S-wave forms, radiation patterns of crustal Love and Rayleigh waves, spectral amplitudes, dispersion and travel-time data as well as geologic, morphologic and historical data were used in unison to provide information on tectonic patterns, slip rates and the inelastic properties of the crust. Most of the numerical algorithms and inversion routines that have been generated during the computer era were utilized. In this sense, this is the first experimental effort in which both amplitude and phase data were simultaneously inverted over a broad frequency range to yield information on both source and structural parameters in one stroke. We found a rather sharp Moho discontinuity with average thickness of 32–35 km underlying the continental crust. The crust contains cracks and pressurized water to a depth of about 20 km. Below this depth the rock becomes ductile. This accounts for a confinement of seismic activity in the upper crust, the low values of the Poisson ratio (0.18–0.21) at 20–25 km and the low Q values there. Crustal shear velocities in Sinai and the Levant fracture zone are significantly higher than the corresponding velocities in the eastbound section Elat-Zagros foothills. Fault-plane solutions and kinematic source parameters of 15 earthquakes since 1927 together with a critical examination of historical seismicity during the last 4,000 years, were used to unveil the major tectonic features of the junction zone. The main results are: 1. (1) The fault systems in the Afro-Eurasian junction (apart from its northern end) have a dominantly left-lateral strike-slip component, transforming the opening motion of the ridge-like Red Sea into a collision zone of the Alpine mountain belt. In this region the edges of the coherent Arabia and Africa plates break up in the neighbourhood of their boundary as they approach the region of continental collision with the Eurasian plate. This breakup consists of gradual loss of coherency and deterioration of its rigidity as more and more deformation is taken up by the branching faults. 2. (2) The Sinai region should not be considered a separate plate, but rather a splinter of the Africa plate, which is breaking up incoherently as it approaches the zone of collision. It is probably useless to try to find its western boundary. 3. (3) The Dead Sea fault — a source for many biblical and post-biblical earthquakes in the last four millenia — was definitely outlined. It has an estimated mean rate of activity of two events per century at magnitudes from 6 to 7. An aseismic slip rate of at least 3 mm/year is taking place along this fault.

Source parameters of the siberian explosion of June 30, 1908, from analysis and synthesis of seismic signals at four stations

Abstract Old seismograms of the Tungus event of June 30, 1908, are analysed and compared with contemporary records of air explosions from Novaya Zemlya and Lop-Nor. Observed arrival times and absolute amplitudes of Rayleigh waves, infrasonic-coupled ground-motion and SH crustal shear waves at Jena, Tiflis, Tashkent and Irkutsk, support a source model which consists of a combined action of an atmospheric-explosion equivalent to a vertical point impulse of magnitude 7 · 10 18 dyn sec and a ballistic-wave equivalent to a horizontal point impulse of magnitude 1.4 · 10 18 dyn sec striking S65°E toward the northwest. All the accumulated knowledge in earthquake and explosion seismology since the beginning of the century is harnessed to the effort of interpreting the observed seismograms. The agreement between the observations in the epicentral area and the ensuing signals in the far seismic and acoustic field support the hypothesis that the Siberian UFO explosion had the effects of an Extraterrestrial Nuclear Missile of yield 12.5 ± 2.5 Mt.

Variation of slip and creep along the levant rift over the past 4500 years

Frequency—magnitude relations were established for a fault system embedded in a shear zone with dimensions 1000 km × 200 km that extends from the Gulf of Elat to the East-Anatolian fault. The resulting frequency—magnitude relations were found to be in good agreement with both the documented instrumental earthquake statistics for ML ⩾ 4.5 in the present century and microearthquake activity for ML ⩾ 1.5 recorded in Israel and some adjacent territories during 1976–1979. When these frequency—magnitude relations are extended to 2500 B.C., one can account for the maximal magnitude earthquakes that echo in the Bible and are manifested in archaeological excavations. It is found that seismic slip-rates increase significantly from south toward north in such a way that in north-central Israel and Lebanon, seismic slip constitutes only 13 of the motion, the rest being attributed to visco-elastic processes. Further north, as one approaches the collision zone with the Turkish plate, aseismicity tends to disappear and the slip is purely seismic.

Elastic wave scattering by anisotropic obstacles: Application to fractured volumes

The Born approximation is frequently applied to isotropic media to determine wave fields scattered from heterogeneous regions. We extend this theory to the general case of an anisotropic obstacle embedded within an anisotropic matrix and show that a perturbation to any of the 21 independent elastic constants acts as a secondary moment tensor source which radiates energy as it is encountered by the incident wave. We consider the case of an anisotropic obstacle in an isotropic background medium in more detail, since the well-known Greens tensor for isotropic, homogeneous media and the Born approximation allow an expression of the radiation patterns, P and S wave, of Rayleigh scattering due to a perturbation to any elastic constants. The wave fields scattered from an anisotropic obstacle differ significantly from the isotropic case in dependence on both the direction of observation and the direction of the incident wave. In order to provide a concrete example of these results, we examine the case of a small fractured volume. If the fractures within the volume are randomly oriented, the resulting material is isotropic, but if the cracks are aligned, the material is anisotropic with five independent elastic constants. In the latter case, the value of C44, analogous to the isotropic rigidity, is unchanged from the background value (δC44 = 0) when the cracks are aligned perpendicular to the x; axis. We present the P, SV and SH radiation patterns for the two scatterers and discuss the implications for observation of fractured volumes. The most important result is that the the zero perturbation δC44 in the aligned crack case causes the scattered displacement field to vanish completely for incident shear waves polarized parallel to the crack plane. Determination of this direction for observations of a fractured zone would allow important insights into the nature of the fracturing.

Rate of seismicity of the dead sea region over the past 4000 years

Abstract The results of two millennia of earthquake documentation, a few decades of macroseismic and instrumental routine seismological observations and five months of microearthquake monitoring, are used to estimate the rate of seismic activity of the Dead Sea fault. It is found that these vastly diverse data which combine long- and short-term tectonic processes, are in good accord with the formula: log 10 N=2.54 − 0.86M L where N is the annual number of events of local magnitude M L or greater. If this equation is extrapolated to ca. 2000 B.C., it yields a Richter magnitude M s = 7 for the event of Sodom and Gomorrah which is believed to be associated with the strongest earthquake in the region during historical times. Comparing our findings with the results of other investigators in Turkey, Greece, Aegean Sea and Iran, we note that the b values along the Syrian-African rift zone (0.78–0.86) are smaller than those in Greece and its surrounding seas (0.94–1.16).

Source mechanism of the Alaskan earthquake of 1964 from amplitudes of free oscillations and surface waves

Abstract Spectral amplitudes of Love and Rayleigh waves in the period range 100–300 s and line spectra of toroidal and spheroidal eigenvibrations with periods of 450–800 s (l = 7 to 17) were used to derive the source mechanism of the Alaskan earthquake of March 28, 1964. It was found that the data are consistent with a dominant dip-slip motion (λ = 77°–95°) on a steeply dipping fault (δ = 70°–88°) with a depth dependent source dislocation U0(h) that extends to a depth of some 125 km [U0(0) = 5 m, U0 (65 km) = 40 m, U0 (125 km) = 0]. Other source parameters are b = 650 ± 50 km , ν = 3 ± 0.25 km/s , Ω = 3000 μ m and = 1600 unit faults.

Source mechanism of the 1906 San Francisco earthquake

Abstract Surface-wave amplitudes in the period range 50–100 s at eight European and North American stations, horizontal slip profiles along the rupture zone and the timing of certain events along the fault during rupture time are all engaged in unison to reconstruct the motion at the source. A modified source model is used to accommodate a moving rupture with variable dislocation in the direction of propagation. It is inferred that the rupture started at about 13 h 11 m 55 s GMT near San Juan Bautista and propagated unilaterally northwestward along N35°W over 400 km with an average rupture velocity of 3.5 km/s. At 13 h 12 m 12 s, the dynamic shear front, moving with the rupture speed, hit the Lick Observatory. Then, at 13 h 12 m 18 s, the rupture arrived to the vicinity of the epicenter in the Santa Cruz Mountains given by B. Bolt. There the slip changed sharply from an average of 0.5 m to a high value of 3 m causing extensive landslides and avalanches. At 13 h 12 m 32.5 s two railroad clocks at San Rafael were stopped. Finally, at 13 h 12 m 36 s the offset front hit the Naval Observatory at Mare Island and stopped the astronomical clocks there. Conspicuous surface waves, visible on Wiechert seismograms in Europe in the period range 55–65 s, reflect the true rupture time. The seismic data inversion yields an effective radiation source some 240 km long with an average vertical extent of some 34 km over a total fault length of 400 km ( U d S ⋍ 29,000 m km 2 or μ U d S ⋍ 9 · 10 27 dyn cm ). It began at the Santa Cruz Mountains and ended some 20 km off coast Point Arena. Thus, due to the nonuniform slip profile, only 3 5 of the total fracture length contributed to the far radiation field. Although the product of the average source displacement (over the entire fault) and the vertical extent appears to be fairly well determined from the surface-wave spectrums, the separate values of these entities cannot be uniquely determined. If the average surface displacements (∼ 3.2 m) are diagnostic of the entire fault, a vertical extent of H = 34 km is required. Finally, a new analysis of surface waves from the Alaska earthquake of July 10, 1958, the Queen Charlotte Islands earthquake of August 22, 1949 and the Kern County shock of July 21, 1952, enables us to draw parallels between the three biggest major events which occurred along the NE Pacific coast during 1906–1958. A common feature of all of these earthquakes is that vertical failure extents of 30–40 km are implied.

Scattering of elastic waves by localized anisotropic inclusions

The existence of Rayleigh scattering of elastic plane waves by anisotropic homogeneous inclusions is theoretically demonstrated. The case of transverse isotropy is studied in detail. It is shown that a scattered longitudinal wave creates radial‐longitudinal (P), collatitudinal‐shear (SV), and azimuthal shear waves (SH). Likewise, scattered SV and SH waves, each generate radial P waves and SV and SH shear waves. All scattered amplitudes are proportional to the square of the frequency and have radiation pattern signatures as those of equivalent dipoles, center of compression, and double couples. It is shown that observations of spatial patterns of scattered amplitudes can yield, through inversion, the elastic constants of the anisotropic inclusion. The results obtained can serve as a theoretical basis for the observed short‐period SH and SV waves from underground explosions at teleseismic distances.

Decoupling of the Vector Wave Equation of Elasticity for Radially Heterogeneous Media

The potential representation of the vector fields is employed to effect the decoupling of the vector wave equation of elasticity for radially heterogeneous isotropic media. Two types of decoupling are considered: decoupling for all values of the frequency and decoupling for high frequencies, which is useful in the ray‐theory treatment. In the case of decoupling for all frequencies, the three constitutive parameters of the medium should satisfy a pair of nonlinear differential equations. For high‐frequency decoupling, one of these equations becomes unnecessary. A few useful examples of the media that satisfy the conditions of decoupling are given.

The equivalent force system of a monopole source in a fluid‐filled open borehole

One of the major contributors to the complexity of boundary-value problems pertaining to theoretical modeling of exploration elastodynamics is the presence of both vertical and horizontal discontinuities. It has been known for a long time that it is sometimes possible to replace certain boundaries by a system of images, provided the extra stresses and displacements induced by these images could indeed mimic the discontinuities caused by the said boundaries (e.g., Ben-Menahem and Singh, 1981). In this vein, we show that part of the field created by a monopole source acting on the axis of a fluid-filled open borehole surrounded by a homogeneous and isotropic formation, can be reconstructed with the aid of an equivalent force system (EFS) that mimics the geometrodynamic effects of the borehole. The advantages of the EFS are twofold. In the first place, it simplifies the physical setup and brings many seemingly different problems into a common denominator in a sense that they are reduced to fields of known basic force systems. Second, and this is not less important, much computer time is saved and numerical complexities are avoided.