Computing the Sensitivity Kernels for 2.5-D Seismic Waveform Inversion in Heterogeneous,Anisotropic Media

2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity of the seismograms to changes in the model parameters. This paper applies two methods, called ‘the perturbation method’ and ‘the matrix method’, to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green’s function vectors and their gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The two Green’s function vectors are the responses of the displacement vector to the two directed unit vectors located at the source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green’s function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic (TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen parameters) plus one angle defining the symmetry axis.     

Microseismicity and tectonics of Sinai

Five microearthquake seismographs were used at 11 sites in northern Sinai in the period February 1987 to February 1988 to study the microseismicity of the area around the Maghara coal mine for mine-development studies. A total of 270 events were recorded on 850 records. The magnitude, epicenter and depth of each event were calculated using suitable software for an Egyptian Geological Survey and Mining Authority's (EGSMA) XT computer. The interpretation of the seismic activity in the area is given in view of plate tectonics, the Sinai subplate boundary follows the Gulf of Aqaba and the Dead Sea. The plate and subplate boundaries are presently active, and there seems to be a diffuse zone of deformation between “NW Africa” and “Nubia” affecting the Cairo-Suez district.     

Implications of the saltation–abrasion bedrock incision model for steady‐state river longitudinal profile relief and concavity

The saltation–abrasion model predicts rates of river incision into bedrock as an explicit function of sediment supply, grain size, boundary shear stress and rock strength. Here we use this experimentally calibrated model to explore the controls on river longitudinal profile concavity and relief for the simple but illustrative case of steady‐state topography. Over a wide range of rock uplift rates we find a characteristic downstream trend, in which upstream reaches are close to the threshold of sediment motion with large extents of bedrock exposure in the channel bed, while downstream reaches have higher excess shear stresses and lesser extents of bedrock exposure. Profile concavity is most sensitive to spatial gradients in runoff and the rate of downstream sediment fining. Concavity is also sensitive to the supply rate of coarse sediment, which varies with rock uplift rate and with the fraction of the total sediment load in the bedload size class. Variations in rock strength have little influence on profile concavity. Profile relief is most sensitive to grain size and amount of runoff. Rock uplift rate and rock strength influence relief most strongly for high rates of rock uplift. Analysis of potential covariation of grain size with rock uplift rate and rock strength suggests that the influence of these variables on profile form could occur in large part through their influence on grain size. Similarly, covariation between grain size and the fraction of sediment load in the bedload size class provides another indirect avenue for rock uplift and strength to influence profile form. Copyright © 2008 John Wiley & Sons, Ltd.     

Applications of the random model of drainage basin composition

The random model of drainage basin composition is founded on the assumptions that (a) natural channels are topologically random in the absence of geological controls and (b) for channel networks developed in similar environments, the exterior and interior link lengths are independent random variables with a common distribution for each type. The effectiveness of this model in estimating the values of geomorphic variables and in explaining and predicting geomorphic relationships is illustrated by several examples. The data required for these examples were obtained from map studies of 30 channel networks, comprising a total of about 8700 links, in eastern Kentucky. A common factor in the success of all three applications of the model is the way in which the planimetric features of drainage basins are determined by their underlying topologic structure.     

Problems in the calibration of an acoustic device for the observation of bedload transport

Developments in theoretical and empirical modelling of bedload transport processes are hindered by the lack of an adequate data base for testing or establishing the models. Conventional methods of measuring bedload transport rates fail to provide the necessary continuous or frequent record of variations at a single section. Acoustic techniques have the potential to overcome this deficiency, but their application has been very limited. Some of the problems of calibrating an acoustic device in the field and in a laboratory flume are discussed, and a possible circuit design described which might minimize calibration difficulties by automatically subtracting the noise generated by flow turbulence.     

Equations of kinetic and available potential energy evolution in wave-number frequency space

The equations of kinetic and available potential energy for the analysis of the growth and decay of atmospheric waves in wave-number-frequency space are derived. The effects of linear and nonlinear interactions of waves in the velocity and temperature fields, the conversions between the available potential and kinetic energies, and the Reynolds and molecular stresses on wave growth and decay are discussed.     

Mortality,growth and fecundity of transplanted mussel and barnacle populations near a pulp mill outfall

The mortality, growth and fecundity of transplanted adult mussel (Mytilus edulis) and barnacle (Balanus glandula) populations near a kraft pulp mill outfall at Port Mellon, British Columbia, were determined. The results indicated that adults of both species were tolerant of bleached kraft pulp mill effluent and survived near the pulp mill outfall. However, the growth rates of both species were retarded when compared with those at the control station. The reproductive activities of the transplanted barnacles were also impaired.     

Steady, annual, and monthly recharge implied by deep unconfined aquifer flow

We consider the response of a deep unconfined horizontal aquifer to steady, annual, and monthly recharge. A groundwater divide and a zero head reservoir constrain the aquifer, so that sinusoidal monthly and aperiodic annual recharge fluctuations create transient specific discharge near the reservoir and an unsteady water table elevation inland. One existing and two new long-term data sets from the Plymouth-Carver Aquifer in southeastern Massachusetts calibrate and confirm hydraulic properties in a set of analytical models. [Geohydrology and simulated groundwater flow, 1992] data and a new power law for tritiugenic helium to tritium ratios calibrate the steady recharge that drives the classical parabolic model of steady hydraulics [Applied Hydrogeology, 2001]. Observed water table and gradient fluctuations calibrate the transient recharge models. In the latter regard, monitoring wells within 1 km of Buttermilk Bay exhibit appreciable specific discharge and reduced water table fluctuations. We apply [Trans Am Geophys Union 32(1951)238] periodic model to the monthly hydraulics and a recharge convolution integral [J Hydrol 126(1991)315] to annual flow. An infiltration fraction of 0.79 and a consumptive use coefficient of 1.08×10⁻⁸ m/s °C relate recharge to precipitation and daylight weighted temperature across all three time scales. Errors associated with this recharge relation decrease with increasing time scale.     

Predicting copper toxicity in estuarine and marine waters using the Biotic Ligand Model

The Biotic Ligand Model (BLM) has proven efficient in predicting the toxicity of a variety of metals to freshwater organisms. Consequently, the US EPA has proposed its use for calculating freshwater copper criteria. This study evaluates the BLM for use in estuarine and marine waters. Studies were conducted using the bivalve, Mytilus sp. and 48-h embryo-larval development chronic estimator test methods. These are the most sensitive taxa and test in the US EPA saltwater copper criteria database. Samples from five locations around the USA were tested. There is a strong relationship between measured and BLM predicted copper EC50s (log transformed data, r² = 0.76, p < 0.001, n = 44). The BLM predicted within a factor ±2 of measured EC50s in 41 of 44 cases. However, the BLM tends to predict lower EC50s when measured EC50s are approximately 10 μg Cu/L. This may be due to limitations of the metal-dissolved organic matter interaction model.     

Transboundary aquifers: a global program to assess, evaluate, and develop policy

Transboundary aquifers are as important a component of global water resource systems as are transboundary rivers; yet, their recognition in international water policy and legislation is very limited. Existing international conventions and agreements barely address aquifers and their resources. To rectify this deficiency, the International Association of Hydrogeologists and UNESCO's International Hydrological Programme have established the Internationally Shared (transboundary) Aquifer Resource Management (ISARM) Programme. This multiagency cooperative program has launched a number of global and regional initiatives. These are designed to delineate and analyze transboundary aquifer systems and to encourage riparian states to work cooperatively toward mutually beneficial and sustainable aquifer development. The agencies participating in ISARM include international and regional organizations (e.g., Organization of American States, United Nations Environment Programme, United Nations Economic Commission for Europe, Food and Agriculture Organization, and South African Development Community). Using outputs of case studies, the ISARM Programme is building scientific, legal, environmental, socioeconomic, and institutional guidelines and recommendations to aid sharing nations in the management of their transboundary aquifers. Since its start in 2000, the program has completed inventories of transboundary aquifers in the Americas and Africa, and several ISARM case studies have commenced.