Effect of micro‐inhomogeneity on the effective stress coefficients and undrained bulk modulus of a poroelastic medium: a double spherical shell model

Although most rocks are complex multi‐mineralic aggregates, quantitative interpretation workflows usually ignore this complexity and employ Gassmann equation and effective stress laws that assume a micro‐homogeneous (mono‐mineralic) rock. Even though the Gassmann theory and effective stress concepts have been generalized to micro‐inhomogeneous rocks, they are seldom if at all used in practice because they require a greater number of parameters, which are difficult to measure or infer from data. Furthermore, the magnitude of the effect of micro‐heterogeneity on fluid substitution and on effective stress coefficients is poorly understood. In particular, it is an open question whether deviations of the experimentally measurements of the effective stress coefficients for drained and undrained elastic moduli from theoretical predictions can be explained by the effect of micro‐heterogeneity. In an attempt to bridge this gap, we consider an idealized model of a micro‐inhomogeneous medium: a Hashin assemblage of double spherical shells. Each shell consists of a spherical pore surrounded by two concentric spherical layers of two different isotropic minerals. By analyzing the exact solution of this problem, we show that the results are exactly consistent with the equations of Brown and Korringa (which represent an extension of Gassmann's equation to micro‐inhomogeneous media). We also show that the effective stress coefficients for bulk volume α, for porosity n_? and for drained and undrained moduli are quite sensitive to the degree of heterogeneity (contrast between the moduli of the two mineral components). For instance, while for micro‐homogeneous rocks the theory gives n_? = 1, for strongly micro‐inhomogenous rocks, n_? may span a range of values from –∞ to ∞ (depending on the contrast between moduli of inner and outer shells). Furthermore, the effective stress coefficient for pore volume (Biot–Willis coefficient) α can be smaller than the porosity ?. Further studies are required to understand the applicability of the results to realistic rock geometries.     

Propagating PZ 90 to WGS 84 Transformation Parameters

The 29^th Research Institute recently published its latest transformation parameters for WGS and PZ 90. Because these tranformation parameter estimates were derived from stations located within Russia, variance-covariance propagation was carried out to study the benefits of a better global distribution of stations. An example that includes two stations in North America is presented. The transformation improves significantly. ? 1999 John Wiley & Sons, Inc.     

Tracing suspended organic nitrogen from the Yangtze River catchment into the East China Sea

Total suspended matter was collected along the Yangtze River (Changjiang) and in the East China Sea in April to May and in September 2003, respectively, to study origin and fate of particulate organic nitrogen. Concentrations of particulate organic carbon (POC), nitrogen (PN) and hydrolyzable particulate amino acids (PAA; d- and l-enantiomers) were higher in the Yangtze Estuary than in the river and decreased offshore towards the shelf edge. In the coastal area, higher values of PAA were observed in the surface layer than in the bottom water. Stable carbon isotope ratios (δ¹³C) of POC increased from − 24.4‰ in the river to values around − 21‰ on the East China Sea Shelf. Dominant amino acids were aspartic acid + aspartine (Asx), glutamic acid + glutamine (Glx), glycine, alanine and serine. The proportions of Asx, Glx and isoleucine were higher in the marine than in the riverine samples contrary to the distributions of glycine, alanine, threonine and arginine. The proportions of d-amino acids were highest in the riverine suspended organic matter (6% of PAA) decreasing towards the shelf edge (1.5% of PAA). d-arginine, not reported in natural aquatic samples so far, was the most abundant d-amino acid in the river. The amino acid composition of the particulate organic matter (POM) in the Yangtze River indicates an advanced stage of degradation of POM. Highly degraded organic matter from soils is probably a main source of POM in the Yangtze River, but the relatively high δ¹³C values and low C/N ratios (7.7 ± 1.6) also indicate contribution from anthropogenic sources. The degraded riverine material was a dominant organic matter source in the estuary, where aquatic primary production had only a small overall contribution. In the East China Sea, gradual settling of riverine organic matter and the addition of fresher phytoplankton impacted the amino acid composition and δ¹³C values, and on the outer shelf relatively fresh phytoplankton-derived organic matter dominated.     

Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification

The quasi-normal scale elimination (QNSE) is an analytical spectral theory of turbulence based upon a successive ensemble averaging of the velocity and temperature modes over the smallest scales of motion and calculating corresponding eddy viscosity and eddy diffusivity. By extending the process of successive ensemble averaging to the turbulence macroscale one eliminates all fluctuating scales and arrives at models analogous to the conventional Reynolds stress closures. The scale dependency embedded in the QNSE method reflects contributions from different processes on different scales. Two of the most important processes in stably stratified turbulence, internal wave propagation and flow anisotropization, are explicitly accounted for in the QNSE formalism. For relatively weak stratification, the theory becomes amenable to analytical processing revealing just how increasing stratification modifies the flow field via growing anisotropy and gravity wave radiation. The QNSE theory yields the dispersion relation for internal waves in the presence of turbulence and provides a theoretical reasoning for the Gargett et al. (J Phys Oceanogr 11:1258–1271, 1981) scaling of the vertical shear spectrum. In addition, it shows that the internal wave breaking and flow anisotropization void the notion of the critical Richardson number at which turbulence is fully suppressed. The isopycnal and diapycnal viscosities and diffusivities can be expressed in the form of the Richardson diffusion laws thus providing a theoretical framework for the Okubo dispersion diagrams. Transitions in the spectral slopes can be associated with the turbulence- and wave-dominated ranges and have direct implications for the transport processes. We show that only quasi-isotropic, turbulence-dominated scales contribute to the diapycnal diffusivity. On larger, buoyancy dominated scales, the diapycnal diffusivity becomes scale independent. This result underscores the well-known fact that waves can only transfer momentum but not a scalar and sheds a new light upon the Ellison–Britter–Osborn mixing model. It also provides a general framework for separation of the effects of turbulence and waves even if they act on the same spatial and temporal scales. The QNSE theory-based turbulence models have been tested in various applications and demonstrated reliable performance. It is suggested that these models present a viable alternative to conventional Reynolds stress closures.     

Origin and emplacement of the impact formations at Chicxulub,Mexico, as revealed by the ICDP deep drilling at Yaxcopoil‐1 and by numerical modeling

We present and interpret results of petrographic, mineralogical, and chemical analyses of the 1511 m deep ICDP Yaxcopoil‐1 (Yax‐1) drill core, with special emphasis on the impactite units. Using numerical model calculations of the formation, excavation, and dynamic modification of the Chicxulub crater, constrained by laboratory data, a model of the origin and emplacement of the impact formations of Yax‐1 and of the impact structure as a whole is derived. The lower part of Yax‐1 is formed by displaced Cretaceous target rocks (610 m thick), while the upper part comprises six suevite‐type allochthonous breccia units (100 m thick). From the texture and composition of these lithological units and from numerical model calculations, we were able to link the seven distinct impact‐induced units of Yax‐1 to the corresponding successive phases of the crater formation and modification, which are as follows: 1) transient cavity formation including displacement and deposition of Cretaceous “megablocks;” 2) ground surging and mixing of impact melt and lithic clasts at the base of the ejecta curtain and deposition of the lower suevite right after the formation of the transient cavity; 3) deposition of a thin veneer of melt on top of the lower suevite and lateral transport and brecciation of this melt toward the end of the collapse of the transient cavity (brecciated impact melt rock); 4) collapse of the ejecta plume and deposition of fall‐back material from the lower part of the ejecta plume to form the middle suevite near the end of the dynamic crater modification; 5) continued collapse of the ejecta plume and deposition of the upper suevite; 6) late phase of the collapse and deposition of the lower sorted suevite after interaction with the inward flowing atmosphere; 7) final phase of fall‐back from the highest part of the ejecta plume and settling of melt and solid particles through the reestablished atmosphere to form the upper sorted suevite; and 8) return of the ocean into the crater after some time and minor reworking of the uppermost suevite under aquatic conditions. Our results are compatible with: a) 180 km and 100 km for the diameters of the final crater and the transient cavity of Chicxulub, respectively, as previously proposed by several authors, and b) the interpretation of Chicxulub as a peak‐ring impact basin that is at the transition to a multi‐ring basin.     

Simulations of the mean solar magnetic field during sunspot cycle 21

Regarding new bipolar magnetic regions as sources of flux, we have computed the evolution of the photospheric magnetic field during 1976–1984 and derived the corresponding evolution of the mean line-of-sight field as seen from Earth. We obtained a good, but imperfect, agreement between the observed mean field and the field computed for a nominal choice of flux transport parameters. Also, we determined the response of the computed mean field to variations in the transport parameters and the source properties. The results lead us to regard the mean-field evolution as a random-walk process with dissipation. New eruptions of flux produce the random walk, and together differential rotation, meridional flow (if present), and diffusion provide the dissipation. The net effect of each new source depends on its strength and orientation (relative to the strength and orientation of the mean field) and on the time elapsed before the next eruption (relative to the decay time of the field). Thus the mean field evolves principally due to the contributions of the larger sources, which produce a strong, gradually evolving field near sunspot maximum but a weak, sporadically evolving field near sunspot minimum.E. O. Hulburt Center for Space Research.Laboratory for Computational Physics.     

Theory of the Trojan asteroids

In the previously published Parts I and II of the paper, the author has constructed a formal long-periodic solution for the case of 11 resonance in the restricted problem of three bodies to 0(m ^3/2), wherem is the small mass parameter of the system. The time-dependencet(, ,m), where is the mean synodic longitude and is related to the Jacobi constant, has been expressed by ahyperelliptic integral. It is shown here that with the approximationm=0 in the integrand, the functiont(, , 0) can be expanded in a series involving standardelliptic functions. Then the problem of inversion can be formally solved, yielding the function (t, , 0).Similarly, the normalized period (,m) of the motion can be approximated by theHagihara hyperelliptic integral (, 0), corresponding tom=0. This integral is also expanded into elliptic functions. Asymptotic forms for (, 0) are derived for 0 and for 1, corresponding to the extreme members of thetadpole branch of the family of orbits.     

Multiple prediction using the homeomorphic-imaging technique

A new method for predicting different kinds of multiples and peg-leg reflections in unstacked seismic data is discussed. The basis for this method is the fact that kinematic properties of multiples can be represented as a combination of kinematic properties of primary reflections. The prediction is made using a two-step process. In the first step, the values for the angle of emergence and radius of curvature of the wavefront for primary reflections from ‘multiple-generating’ interfaces are obtained. These parameters are estimated directly from unstacked data for every source point using the homeomorphic-imaging technique. The second step consists of prediction of multiples from primary reflections that satisfy a so-called ‘multiple condition’. This condition is the equality of the absolute values of the angles of emergence calculated from the first step. This method is effective even in complex media and information on the subsurface geology is not required. The parameters are estimated directly from the unstacked data and do not require any computational efforts such as in wavefield extrapolation of data.     

An extended Ideal Resonance Problem

An Extended Resonance Problem is defined by the Hamiltonian, $$F = B(y) + 2\mu ^2 A(y)[\sin x + \lambda (y)]^2 \mu<< 1,\lambda = O(\mu ).$$ It is noted here that the phase-plane trajectories exhibit adouble libration, enclosing two centers, for the initial conditions of motion satisfying the inequality $$1 - |\lambda |< |\alpha |< 1 + |\lambda |,$$ where α is the usualresonance parameter. A first order solution for the case of double libration is constructed here by a generalization of the procedure previously used in solving the Ideal Resonance Problem with λ=0. The solution furnishes a reference orbit for a Perturbed Ideal Problem if a double libration occurs as a result of perturbations.     

Theory of the Trojan asteroids Part II

In the previously published (1977a) Part I of the paper, the author has constructed a formal long-periodic solution for the case of 1:1 resonance in the restricted problem of three bodies. Here the accuracy of the solution is carried fromO(m) toO(m ^3/2), wherem is the mass parameter of the system.Asymptotic approximations for the period of the motion are obtained for the case of small oscillations about the Lagrangian pointL ₄, in agreement with the classical theory, and for the vicinity of a logarithmic singularity on themean separatrix, passing throughL ₃. The regularizing function (), which removes the singularities of the Poincaré type, is extended to all orders, and the result is used to prove the periodicity of the solution.