Range of validity of seismic ray and beam methods in general inhomogeneous media – II. A canonical problem

Summary. The Green's function, in a constant gradient medium, is derived for an explosive point source, in the frequency and the time domains. The analytical dynamic ray tracing (DRT) solution is rederived with conditions stated in Part I. The Gaussian beam (GB) solution is investigated. New beam parameters and conditions are defined. Comparisons between exact and approximate solutions are undertaken.
For both methods, DRT and GB, conditions of validity are explicit and quantitative. An accuracy criterion is defined in the time domain, and measures a global relative error. The range of validity is expressed in the form of two inequalities for the dynamic ray tracing method and of five inequalities for the Gaussian beam method. Results remain accurate at ray turning points. For the types of medium considered, the breakdown of the dynamic ray tracing method is smoother and better behaved than that of Gaussian beams. As examples, a vertical seismic profiling configuration, and a shallow earthquake are modelled, using Gaussian beams.     

Early angiosperm diversification: evidence from southern South America

In this report, we analyze the angiosperm fossil record (micro- and megafossil) from the central and southern basins of Argentina, southern South America, deposited between the late Barremian (128.3 Ma) to the end of the Coniacian (85.8 Ma). Based on this analysis, three major stages in the evolution of the angiosperms in the southernmost region of South America are established as follows: the late Barremian–Aptian, the latest Aptian-earliest Albian, and the middle Albian- Coniacian. The comparison between our fossil data set and those from Australia, North America, Asia and Europe suggest that the evolution and diversification of the angiosperms at mid and high latitudes in both hemispheres occurred roughly synchronously.     

Modeling environmental effects on the size-structured energy flow through marine ecosystems. Part 2: Simulations

Numerical simulations using a physiologically-based model of marine ecosystem size spectrum are conducted to study the influence of primary production and temperature on energy flux through marine ecosystems. In stable environmental conditions, the model converges toward a stationary linear log–log size-spectrum. In very productive ecosystems, the model predicts that small size classes are depleted by predation, leading to a curved size-spectrum.It is shown that the absolute level of primary production does not affect the slope of the stationary size-spectrum but has a nonlinear effect on its intercept and hence on the total biomass of consumer organisms (the carrying capacity). Three domains are distinguished: at low primary production, total biomass is independent from production changes because loss processes dominate dissipative processes (biological work); at high production, ecosystem biomass is proportional to primary production because dissipation dominates losses; an intermediate transition domain characterizes mid-production ecosystems. Our results enlighten the paradox of the very high ecosystem biomass/primary production ratios which are observed in poor oceanic regions. Thus, maximal dissipation (least action and low ecosystem biomass/primary production ratios) is reached at high primary production levels when the ecosystem is efficient in transferring energy from small sizes to large sizes. Conversely, least dissipation (most action and high ecosystem biomass/primary production ratios) characterizes the simulated ecosystem at low primary production levels when it is not efficient in dissipating energy.Increasing temperature causes enhanced predation mortality and decreases the intercept of the stationary size spectrum, i.e., the total ecosystem biomass. Total biomass varies as the inverse of the Arrhenius coefficient in the loss domain. This approximation is no longer true in the dissipation domain where nonlinear dissipation processes dominate over linear loss processes. Our results suggest that in a global warming context, at constant primary production, a 2–4 °C warming would lead to a 20–43% decrease of ecosystem biomass in oligotrophic regions and to a 15–32% decrease of biomass in eutrophic regions.Oscillations of primary production or temperature induce waves which propagate along the size-spectrum and which amplify until a “resonant range” which depends on the period of the environmental oscillations. Small organisms oscillate in phase with producers and are bottom-up controlled by primary production oscillations. In the “resonant range”, prey and predators oscillate out of phase with alternating periods of top-down and bottom-up controls. Large organisms are not influenced by bottom-up effects of high frequency phytoplankton variability or by oscillations of temperature.     

A new derivation of the ratio Q(wobble)/Qμ (mantle)

Summary An extension of the Love-Larmor theory to a low-loss unelastic earth model, leads to the surprisingly simple approximation
   
where τ_s= 447.4 sidereal day is the static wobble period, τ_R= 306 sidereal day is the rigid-earth wobble period and τ_w= 433 sidereal day is the observed Chandler period. Q _W, Q _μ are the respective average Q values of the wobble and the Earth's mantle at τ_W. The known numerical factor F is only slightly dependent on the Earth structure.     

Vector-scattering of elastic waves by directional structural space gradients

A nonstochastic and noniterative theory of vector scattering in inhomogeneous media is presented. The elastodynamic vector wave-equation for 3D inhomogeneous media is solved for a weak heterogeneity at the high-frequency region. It is shown that there exists a forward scattered field which decays slowly along the source-receiver path. Its rate of attenuation depends on the azimuth of the path relative to the direction of the inhomogeneity, but is independent of frequency. The Green's tensor for the above regime is derived in closed form and leads to the quantification of fields of dipolar sources in weak inhomogeneous media. The inhomogeneity at the source creates a source-induced scattering (in addition to path-scattering) having a radiation-pattern that bears the signature of the source. The availability of the analytic Green's tensor, in conjunction with the Huygens-Kirchhoff-Helmholtz formalism, opens new ways to calculate the scattered fields due to various structural inhomogeneities applicable to exploration and earthquake seismology. The theoretical results of this study point to the conclusion that the scalar wave approximation may not always be valid for the propagation of seismic waves in the earth's lithosphere.