ON THE BREMMER SERIES DECOMPOSITION: EQUIVALENCE BETWEEN TWO DIFFERENT APPROACHES*

A Bremmer Series decomposition of the solution y(t) to the lossless wave equation in layered media is where the y_j(t) are physically meaningful constituents (i.e., y₁(t) are primaries, y₂(t) are secondaries, etc.). This paper reviews Mendel's state space models for generating the constituents; reviews Bremmer's integral equation models for generating the constituents; and demonstrates how Mendel's state space models can be obtained by a careful decomposition of Bremmer's integral equation models. It shows that Mendel's equations can be viewed as approximate numerical solutions of Bremmer's integral equations. In a lossless homogeneous medium, the approximations become exact.     

Author Index 1991

Abstract

Evapotranspiration (ET) is an important process in the hydrological cycle and needs to be accurately quantified for proper irrigation scheduling and optimal water resources systems operation. The time variant characteristics of ET necessitate the need for forecasting ET. In this paper, two techniques, namely a seasonal ARIMA model and Winter's exponential smoothing model, have been investigated for their applicability for forecasting weekly reference crop ET. A seasonal ARIMA model with one autoregressive and one moving average process and with a seasonality of 52 weeks was found to be an appropriate stochastic model. The ARIMA and Winter's models were compared with a simple ET model to assess their performance in forecasting. The forecast errors produced by these models were very small and the models would be promisingly of great use in real-time irrigation management.     

Spatial Periodic Boundary Condition for MODFLOW

Small‐scale hyporheic zone (HZ) models often use a spatial periodic boundary (SPB) pair to simulate an infinite repetition of bedforms. SPB's are common features of commercially available multiphysics modeling packages. MODFLOW's lack of this boundary type has precluded it from being effectively utilized in this area of HZ research. We present a method to implement the SPB in MODFLOW by development of the appropriate block‐centered finite‐difference expressions. The implementation is analogous to MODFLOW's general head boundary package. The difference is that the terms on the right hand side of the solution equations must be updated with each iteration. Consequently, models that implement the SPB converge best with solvers that perform both inner and outer iterations. The correct functioning of the SPB condition in MODFLOW is verified by two examples. This boundary condition allows users to build HZ‐bedform models in MODFLOW, facilitating further research using related codes such as MT3DMS and PHT3D.     

Ocean tidal effects on Earth rotation

Tidal forces due to the tide-raising potential deform the solid and fluid regions of the Earth, causing the Earth's inertia tensor to change, and hence causing the Earth's rate of rotation and length-of-day to change. Because both the tide-raising potential and the solid Earth's elastic response to the tidal forces caused by this potential are well-known, accurate models for the effects of the elastic solid body tides on the Earth's rotation are available. However, models for the effect of the ocean tides on the Earth's rotation are more problematic because of the need to model the dynamic response of the oceans to the tidal forces. Hydrodynamic ocean tide models that have recently become available are evaluated here for their ability to account for long-period ocean tidal signals in length-of-day observations. Of the models tested here, the older altimetric data-constrained model of Kantha et al. (1998) is shown to still do the best job of accounting for ocean tidal effects in length-of-day, particularly at the fortnightly tidal frequency. The model currently recommended by the IERS is shown to do the worst job.     

Comment on Fofonoff's mode

Abstract

Recently Merkine, Mo and Kalnay (1985) have re-examined the possible existence of Fofonoff's (1954) steady free inertial solution and the role of Fofonoff's mode in numerical circulation models after Veronis (1966). Merkine et al. conclude that the Fofonoff mode does not occur, that such a mode would be barotropically unstable and that resemblances between numerical circulations and Fofonoff's mode are more dependent upon the natures of forcing and dissipation. On the contrary, I suggest that Fofonoff's mode very naturally does emerge and that forcing and dissipation only impede the full realization of Fofonoff's mode. Moreover, statistical mechanical arguments from Salmon, Holloway and Hendershott (1976) show that the Fofonoff mode is expected to co-exist with a transient eddy field whose statistics are in equilibrium with the mode; thus bartotropic instability does not argue for non-realization of Fofonoff's mode.     

Cone models for nearly incompressible soil

Cones can be used to model soil in a unified strength-of-materials approach. For the vertical and rocking motions involving predominantly compressional-extensional deformation, the corresponding dilatational wave velocity tends to infinity for Poisson's ratio approaching 1/2. Based on the rigorous solution for the dynamic stiffness of a rigid disk for all frequencies, whereby the partition of the power among P-, S- and Rayleigh waves is also discussed, two special features are necessary for the vertical and rocking motions for nearly incompressible soil with Poisson's ratio between 1/3 and 1/2: (1) The appropriate wave velocity is selected as twice the shear wave velocity and not as the dilatational wave velocity; (2) A trapped mass which increases linearly with Poisson's ratio is introduced. The trapped mass can be assigned to the base mat, allowing the cone model to be constructed in the same way for all Poisson's ratios. The realization of cone models for surface foundations on a homogeneous half-space and on a layer on a flexible half-space and for embedded and pile foundations is addressed.     

A STUDY ON THE POLES AND ZEROES OF STEFANESCU'S RAISED KERNEL FUNCTION

The theory of geoelectric sounding exploration is based on Stefanescu's kernel. In order to study the analytic properties of the kernel, necessary and sufficient conditions on it's poles and zeroes are developed. A distinction is made between “physical” and “perfect” models. It is shown that a physical model may be determined from either the set of poles or the set of zeroes of the raised kernel function at the top of the model. These roots may be of desired multiplicities. For determining a perfect model, both sets of poles and zeroes are required and they all have to be simple ones.     

利用Lg波谱特征估计地下核爆炸装置的埋深

Lg波同时携带地球介质结构信息和爆炸源引起的二次源信息,是研究地下爆炸震源机制及检测、识别手段的重要震相。基于对某一区域介质结构的了解,将实测Lg波谱特征形态与理论波谱形态进行比对,利用Lg波频谱曲线的低谷点随震源深度"左移"的特征,作为辅助识别手段估计地下核爆炸装置的埋深。研究结果对深入地理解地下核爆炸震源机制有重要的参考意义。     

Shallow Unconfined Flow on a Sloping Base Redux

When is the impact of a sloping base large enough to justify more complex models for an unconfined aquifer? The intuitive answer that “it depends on the magnitude of the slope” is not wholly correct. Using recent mathematical results (the Lambert W function), we explicitly solve the simple sloping base problem. This explicit solution offers insights beyond those possible using Dupuit's, Polubarinov‐Kochina's, Harr's, Child's, and others' implicit solutions. Specifically, it shows that the impact of the sloping base is best characterized by the saturated thickness divided by the change in base elevation, not by the slope.     

Occam's inversion of magnetic resonance sounding on a layered electrically conductive earth

The magnitudes of the initial amplitude of the magnetic resonance sounding (MRS) signals from an aquifer located in a layered electrically conductive earth, are nonlinear functions of water content distribution. Occam's inversion method is adapted to the nonlinear inversion problem. In the case of an electrically conductive medium, the Jacobian matrix is analytically evaluated at the beginning of the inversion. And the uniqueness of the inversion can be partially solved by imposing the flattest and smoothest model constraints on the optimization problem. Synthetic MRS signals from resistive and conductive earth, as well as field data, have been inverted by Occam's method. The results indicate that with the help of Occam's inversion, a true model can be obtained from an initial model of homogeneous water content. Furthermore, for noise-free MRS signals, both the flattest and smoothest models reveal correct water content distributions. When signals are contaminated by noises, the case is different; and the smoothest model might have a lower water content distributing in a larger range than that of the true model, while which might be obtained by utilizing the flattest model Occam's inversion.     

Initial velocity model construction of seismic tomography in near-surface applications

The impact of initial velocity models on final image reconstruction results and how to construct a proper initial velocity model in near-surface tomography studies are investigated on a two-layer synthetic model with gradually increasing velocity with depth. Refraction initial velocity models and linear velocity function models are tested on both synthetic and field data to obtain images close to reality. It is concluded that velocity function type initial models should be preferred in soft alluvial deposits that exist within the investigated depths, whereas refraction initial models should be preferred in the groundwater table or with strong refractors' existence within the investigated depths to obtain optimum subsurface images in refraction–diving wave seismic tomography.     

Radiation belt modelling in the framework of space weather effects and forecasting

The Earth's trapped radiation belts were discovered at the beginning of the space age and were immediately recognised as a considerable hazard to space missions. Consequently, considerable effort was invested in building models of the trapped proton and electron populations, culminating in the NASA AP-8 and AE-8 models which have been de facto standards since the 1970s. The CRRES mission has demonstrated that the trapped radiation environment is much more complex than the static environment described by the old models. Spatial and especially temporal variations were shown to be much more important than previously thought, and to require more complex models than those in use at that time. Such models are now becoming available, but they are as yet limited in spatial and temporal coverage. It is vital to coordinate future modelling efforts in order to develop new standard models.The lack of standardisation of radiation belt models complicates their use in engineering applications where particle fluxes are needed as input to radiation effects models. ESA's SPace ENVironment Information System (SPENVIS) provides standardised access to models of the hazardous space environment, including but not limited to radiation effects, through a user-friendly World Wide Web interface. The interface includes parameter input with extensive defaulting, definition of user environments, streamlined production of results (both in graphical and textual form), background information, and on-line help. The system can be accessed at the WWW site http://www.spenvis.oma.be/spenvis/. SPENVIS Is designed to help spacecraft engineers perform rapid analyses of environmental problems and, with extensive documentation and tutorial information, allows engineers with relatively little familiarity to produce reliable results. It has been developed in response to the increasing pressure for rapid-response tools for system engineering, especially in low-cost commercial and educational programmes.     

Earth tides

The main geometrical characteristics and mechanical properties of bodily tides are described, using the convenient elastic parameters of Love. The problem of the Earth's deformation is a problem of spherical elasticity of the sixth order. The importance of Earth tides in astronomy and geophysics is emphasized by their relation to the precession-nutation and tesseral tidal problems, the secular retardation of the Earth's speed of rotation due to the dissipation of energy in sectorial tides, the periodic variations of the speed of rotation due to zonal tides, the satellite orbit perturbations due to the Earth's potential variation, and the radial deformations in laser distance measurements. The possibility that dynamical effects would be produced in the Earth's liquid core was pointed out by Poincaré and developed by Jeffreys, Vicente, and Molodensky. An experimental confirmation is presented here. The role of the Earth tide phenomenon in gravimetry and oceanography is also described, as are the perturbing effects due to regional tectonic features. Instrumental developments are critical in the acquisition of precise data; the calibration problem is fundamental for a correct comparison with Earth models.     

P- and S-wave anisotropy of a synthetic sandstone with controlled crack geometryl1

A method is reported for the production of synthetic porous sandstones containing cracks of known dimensions and geometry with respect to the matrix. A synthetic sandstone was manufactured from Sand cemented with an epoxy glue. The cracks of known geometry were introduced into the material in the manufacturing stage, by emplacing thin metallic discs in the Sand-epoxy matrix. These discs were chemically leached out of the consolidated porous sandstone. Acoustic anisotropy. and shear-wave splitting were observed in the synthetic sandstones. For the dry sample the observed angular dependence of the P- and S- wave velocities (at 100 kHz) compares well, qualitatively, with the theoretical models of Hudson and of Thomsen. Quantitatively, however, the experimental data fits Hudson's model better. For the case of a saturated sample the experimental results are in excellent agreement with Thomsen's model. Hudson's model, on the other hand, predicts a different angular dependence for P-waves. This demonstrates that the concept of fluid transfer between cracks and the ambient porosity can be a significant process. The results reported here are from the first successful experiment in which the theoretical models were tested on a porous material containing a known crack geometry.     

HYPOSAT – An Enhanced Routine to Locate Seismic Events

—?A program package, called HYPOSAT, has been under development that attempts to use the maximum information possible to estimate the hypocenter of a seismic source. The standard input parameters can be used: arrival times of first and later onsets with backazimuths and ray parameters (or apparent velocities). In addition, travel-time differences between different phases observed at the same station can be optionally used. The observed standard deviations are used to weight all input parameters and the inversion is done with a generalized matrix inversion code.¶A starting solution with a priori uncertainties can be calculated as the intersection of all backazimuth observations. If S observations are also available, a preliminary origin time is estimated using Wadati's approach to estimate a source time.¶Global earth models and user-defined horizontally layered local or regional models can be used alone or together to locate seismic events. To gain the best result from all input data, observations of all seismic phases as defined in the IASPEI91 tables can be inverted. Station corrections and corrections for phases with reflection points at the earth's surface can be applied by using local velocity structures.     

Indirect Boundary Element Method applied to fluid–solid interfaces

In this paper scattering of elastic waves in fluid–solid interfaces is investigated. We use the Indirect Boundary Element Method to study this wave propagation phenomenon in 2D models. Three models are analyzed: a first one with an interface between two half-spaces, one fluid on the top part and the other solid in the bottom; a second model including a fluid half-space above a layered solid; and finally, a third model with a fluid layer bounded by two solid half-spaces. The source, represented by Hankel's function of the second kind, is always applied in the fluid. This indirect formulation can give to the analyst a deep physical insight on the generated diffracted waves because it is closer to the physical reality and can be regarded as a realization of Huygens' principle. In any event, mathematically it is fully equivalent to the classical Somigliana's representation theorem. In order to gauge accuracy we test our method by comparing with an analytical solution known as Discrete Wave Number. A near interface pulse generates scattered waves that can be registered by receivers located in the fluid and it is possible to infer wave velocities of solids. Results are presented in both time and frequency domain, where several aspects related to the different wave types that emerge from this kind of problems are pointed out.     

时间相依的地震危险性概率分析

阐述了基于泊松模型以及时间相依的特征地震模型的地震危险性概率分析的基本原理与方法 .以祁连山中东段为例 ,对 2种不同模型的地震危险性概率分析结果做了对比研究 ,指出时间相依的地震危险性概率分析在理论上可能更为合理 ,并且可以应用于强震的短临预测研究 .     

Improving evapotranspiration estimation models through quantitative watershed parameter analysis and remote sensing applications

Numerous models had been developed to predict the annual evapotranspiration (ET) in vegetated lands across various spatial scales. Fu's (Scientia Atmospherica Sinica, 5, 23–31) and Zhang's (Water Resources Research, 37, 701–708) ET simulation models have emerged as highly effective and have been widely used. However, both formulas have the non-quantitative parameters (m in Fu's model and w in Zhang's model). Based on the collected 1789 samples from global long-term hydrological studies, this study discovered significant relations between m (or w) and vegetation coverage or greenness in collected catchments. Then, we used these relations to qualify the parameters in both Zhang's and Fu's models. Results show that the ET estimation accuracies of Fu's (or Zhang's) model are significantly improved by about 13.49 mm (or 6.74 mm) for grassland and cropland, 38.52 mm (or 29.84 mm) for forest and shrub land (coverage<40%), 19.74 mm (or 16.17 mm) for mixed land (coverage<40%), respectively. However, Zhang's model shows higher errors compared with Fu's model, especially in regions with high m (or w) values, such as those with dense vegetations or P/E₀ (annual precipitation to annual potential ET) smaller than 1.0. Additionally, this study also reveals that for regions with vegetation cover less than 40%, the annual ET is not only determined by vegetation types, but also relates to the sizes of vegetation-covered areas. Conversely, for regions with vegetation cover more than 40%, the annual ET is mainly determined by the vegetation density rather than vegetation types or vegetation coverage. Thus, linking m (or w) parameters with vegetation greenness allows leveraging remote sensing for forest management in data-scarce areas, safeguarding regional water resources. This study pioneers integrating vegetation-related indices with basin parameters, advocating for their crucial role in more effective hydrological modelling.     

Validation of classical density-dependent solute transport theory for stable,high-concentration-gradient brine displacements in coarse and medium sands

A series of careful laboratory soil column experiments was carried out for the purpose of providing data for testing recently presented theories of miscible density-dependent flow and transport. In particular, modifications to the standard theory involve extensions to both Darcy's (for flow) and Fick's laws (for diffusive/dispersive solute flux). Both coarse- and medium-grained sands were used in the experiments. All experiments concerned upward (i.e., stable) displacement of fresh water within the soil by a brine solution, under either constant head or constant volume flux conditions. The experimental data were analysed using accurate numerical solutions of the standard governing flow and transport model, as well as models with modified Darcy's and Fick's laws. Model parameters were determined by a step-wise fitting procedure based on the least-squares criterion. The results show clearly that, for large density contrasts, an extended Darcy's law was not necessary. On the other hand, an extension to Fick's Law was needed to model the experimental data accurately.