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At least 811 records · Page 45Linked to original sources
USGS2021

Partitioning and transformation of organic and inorganic phosphorus among dissolved, colloidal and particulate phases in a hypereutrophic freshwater estuary

Phosphorus (P) loadings to the Great Lakes have been regulated for decades, but re-eutrophication and seasonal hypoxia have recently been increasingly reported. It is of paramount importance to better understand the fate, transformation, and biogeochemical cycling processes of different P species across the river-lake interface. We report here results on chemical speciation of P in the seasonally hypoxic Fox River-Green Bay system and variations in sources and partitioning of P species along the aquatic continuum. During midsummer when productivity is generally high, phosphate and dissolved organic P (DOP) were the major species in river water while particulate-organic-P predominated in open bay waters, showing a dynamic change in the chemical speciation of P along the river-bay transect with active transformations between inorganic and organic P and between colloidal and particulate phases. Colloidal organic P (COP, >1 kDa) comprised 33‒65% of the bulk DOP, while colloidal inorganic P was generally insignificant and undetectable especially in open bay water. Sources of COP changed from mainly allochthonous in the Fox River, having mostly smaller sized colloids (1–3 kDa) and a lower organic carbon to phosphorus (C/P) ratio, to predominantly autochthonous in open bay waters with larger sized colloids (>10 kDa) and a higher organic C/P ratio. The observed high apparent distribution coefficients ( K d ) of P between dissolved and particulate phases and high-abundant autochthonous colloidal and particulate organic P in the hypereutrophic environment suggest that, in addition to phosphate, colloidal/particulate organic P may play a critical role in the biogeochemical cycling of P and the development of seasonal hypoxia.

Wisconsin↗
USGS2026

Aging of biosolids in fields prolongs the release of biosolid-borne PFAS and promotes the release of select PFCA in water

Land application of biosolids can introduce PFAS into croplands. Biosolids transported to surface waters through runoff may subsequently release PFAS into aquatic environments. The objective was to evaluate the effects of the aging of biosolids and the presence of sediment on the release of biosolid-borne PFAS to water at the water-sediment interface under anaerobic conditions. Through two independent rounds of microcosm experiments, we demonstrate that by day 136, most of the PFAS compounds (e.g., perfluorocarboxylic acids, or PFCAs) released <10 ng per g biosolids dry weight, except for 5:3 FTCA. Kinetically, the aging process substantially delayed the release of some long-chain PFAS (i.e., PFNA, PFDA, and PFOS) to water, due to the collapse of the porous structure of biosolids during aging. After day 136, the amount of long-chain PFAS released from aged biosolids reached levels similar to those released from the fresh biosolids due to the recovery of the pore structure during the release experiment. Mass balance analysis showed considerably higher, final masses of PFPeA, PFHxA, and PFOA than their initial masses, suggesting that precursors were biotransformed into these compounds during the release experiment, and biosolid aging led to elevated biotransformation and release of these three PFCAs. Sediment had little effect on the kinetics or extent of PFAS release from biosolids, except that the extent of FTCA release was reduced in the presence of sediment potentially due to adsorption. Overall, biosolid aging can delay the release of long-chain PFAS and promote the biotransformation to and release of PFCAs.

Water Research↗
USGS2004

Habitat of endangered white abalone, Haliotis sorenseni

Surveys with a submersible at offshore islands and banks in southern California found that white abalone were most abundant at depths between 43 and 60 m. This is deeper than estimates taken when white abalone were more abundant. Densities were highest at sites far from fishing ports. Controlling for depth and site found that white abalone were significantly more abundant in areas with Laminaria farlowii (an alga) but abalone were not associated with areas high in the cover of other algae ( Pelagophycus porra or Eisenia arborea ) or the amount of sand in the habitat (except that abalone always occurred on rock). Within an area with abalone, the particular rock they occurred on was significantly larger than unoccupied neighboring rocks. Occupied rocks were not significantly different in algal cover or in sea urchin density than unoccupied neighboring rocks. The position of abalone on a rock was nearer to the rock–sand interface than would be expected based on a random distribution. More white abalone were feeding when in association with red urchins, perhaps because both grazers capture drift algae to eat. These data may aid future efforts to locate white abalone brood stock and identify locations for outplanting.

Biological Conservation↗
USGS1997

History of water-column anoxia in the Black Sea indicated by pyrite framboid size distributions

A detailed study of size distributions of framboidal pyrite in Holocene Black Sea sediments establishes the timing of a change from deposition under an oxic water column to deposition under an anoxic and sulfidic water column. In the most recent carbonate-rich sediments (Unit I) and in the organic carbon-rich sapropel (Unit II), framboid size distributions are remarkably uniform (mean diameter = 5 μm); over 95% of the framboids in Unit I and Unit II are < 7 μm in diameter. These properties of framboidal pyrite are consistent with framboid nucleation and growth within an anoxic and sulfidic water column, followed by transport to the sediment-water interface, cessation of pyrite growth due to the exhaustion of reactive iron, and subsequent burial. In contrast, the organic carbon-poor sediments of lacustrine Unit III contain pyrite framboids that are generally much larger in size (mean diameter = 10 μm). In Unit III, over 95% of the framboids are < 25 μm in diameter, 40% of framboids are between 7 μm and 25 μm, and framboids up to 50 μm in diameter are present. This distribution of sizes suggests framboid nucleation and growth within anoxic sediment porewaters. These new data on size distributions of framboidal pyrite confirm that the development of water-column anoxia in the Black Sea coincided with the initiation of deposition of laminated Unit II sapropels.

Earth and Planetary Science Letters↗
USGS1997

Kinetics of the coesite to quartz transformation

The survival of coesite in ultrahigh-pressure (UHP) rocks has important implications for the exhumation of subducted crustal rocks. We have conducted experiments to study the mechanism and rate of the coesite→quartz transformation using polycrystalline coesite aggregates, fabricated by devitrifying silica glass cylinders containing 2850 H/10 6 Si at 1000°C and 3.6 GPa for 24 h. Conditions were adjusted following synthesis to transform the samples at 700–1000°C at pressures 190–410 MPa below the quartz–coesite equilibrium boundary. Reaction proceeds via grain-boundary nucleation and interface-controlled growth, with characteristic reaction textures remarkably similar to those seen in natural UHP rocks. We infer that the experimental reaction mechanism is identical to that in nature, a prerequisite for reliable extrapolation of the rate data. Growth rates obtained by direct measurement differ by up to two orders of magnitude from those estimated by fitting a rate equation to the transformation–time data. Fitting the rates to Turnbull's equation for growth therefore yields two distinct sets of parameters with similar activation energies (242 or 269 kJ/mol) but significantly different pre-exponential constants. Extrapolation based on either set of growth rates suggests that coesite should not be preserved on geologic time scales if it reaches the quartz stability field at temperatures above 375–400°C. The survival of coesite has previously been linked to its inclusion in strong phases, such as garnet, that can sustain a high internal pressure during decompression. Other factors that may play a crucial role in preservation are low fluid availability — possibly even less than that of our nominally “dry” experiments — and the development of transformation stress, which inhibits nucleation and growth. These issues are discussed in the context of our experiments as well as recent observations from natural rocks.

Earth and Planetary Science Letters↗
USGS1998

Chemistry, isotopic composition, and origin of a methane-hydrogen sulfide hydrate at the Cascadia subduction zone

Although the presence of extensive gas hydrate on the Cascadia margin, offshore from the western U.S. and Canada, has been inferred from marine seismic records and pore water chemistry, solid gas hydrate has only been found at one location. At Ocean Drilling Program (ODP) Site 892, offshore from central Oregon, gas hydrate was recovered close to the sediment-water interface at 2–19 m below the seafloor (mbsf) at 670 m water depth. The gas hydrate occurs as elongated platy crystals or crystal aggregates, mostly disseminated irregularly, with higher concentrations occurring in discrete zones, thin layers, and/or veinlets parallel or oblique to the bedding. A 2- to 3-cm thick massive gas hydrate layer, parallel to bedding, was recovered at ∼ 17 mbsf. Gas from a sample of this layer was composed of both CH 4 and H 2 S. This sample is the first mixed-gas hydrate of CH 4 H 2 S documented in ODP; it also contains ethane and minor amounts of CO 2 . Measured temperatures of the recovered core ranged from 2 to −1.8°C and are 6 to 8 degrees lower than in-situ temperatures. These temperature anomalies were caused by the partial dissociation of the CH 4 H 2 S hydrate during recovery without a pressure core sampler.During this dissociation, toxic levels of H 2 S (δ 34 S, +27.4‰) were released. The δ 13 C values of the CH 4 in the gas hydrate, −64.5 to −67.5‰ (PDB) , together with δD values of −197 to −199‰ (SMOW) indicate a primarily microbial source for the CH 4 . The δ 18 O value of the hydrate H 2 O is +2.9‰ (SMOW) , comparable with the experimental fractionation factor for sea-ice. The unusual composition (CH 4 H 2 S) and depth distribution (2–19 mbsf) of this gas hydrate indicate mixing between a methane-rich fluid with a pore fluid enriched in sulfide; at this site the former is advecting along an inclined fault into the active sulfate reduction zone. The facts that the CH 4 H 2 S hydrate is primarily confined to the present day active sulfate reduction zone (2–19 mbsf), and that from here down to the BSR depth (19–68 mbsf) the gas hydrate inferred to exist is a ≥99% CH 4 hydrate, suggest that the mixing of CH 4 and H 2 S is a geologically young process. Because the existence of a mixed CH 4 H 2 S hydrate is indicative of moderate to intense advection of a methane-rich fluid into a near surface active sulfate reduction zone, tectonically active (faulted) margins with organic-rich sediments and moderate to high sedimentation rates are the most likely regions of occurrence. The extension of such a mixed hydrate below the sulfate reduction zone should reflect the time-span of methane advection into the sulfate reduction zone.

Earth and Planetary Science Letters↗
USGS2001

NEHRP soil classifications for estimating site-dependent seismic coefficients in the Upper Mississippi Embayment

Local soil conditions have a profound influence on the characteristics of ground shaking during an earthquake. Exceptionally deep soil deposits, on the order of 100-1000 m deep, are found in the Upper Mississippi Embayment of the central United States. Shear waves (SH) from earthquakes in the New Madrid seismic zone are expected to be strongly affected by the sharp impedance contrasts at the bedrock/sediment interface, attenuation of seismic waves in the soil column, and the SH-wave velocities of the more poorly consolidated near-surface (???50 m) soils. SH-wave velocities of the near-surface soils at nearly 400 sites in the Upper Mississippi Embayment were determined using conventional seismic SH-wave refraction and reflection techniques. Based on the average SH-wave velocities of the upper 30 m of the soils, sites in the Mississippi River floodplain portion of the study area are predominantly classified as Site Class D (180-360 m/s) in accordance with the 1997 NEHRP provisions. Sites away from the active floodplains in western Kentucky and western Tennessee, the SH-wave velocities of the upper 30 m of soils typically ranged from mid-200 to mid-300 m/s. Several sites in western Kentucky had averaged SH-wave velocities greater than 360 m/s, thereby qualifying them as Site Class C (360-760 m/s) in accordance with the 1997 NEHRP provisions. One dimensional site effects, including amplification and dynamic site period, were calculated for a representative suite of sites across the Upper Mississippi Embayment at latitude ?? 38.5??. Although seismic attenuation is greater in the Mississippi River floodplain (i.e. thicker, lower velocity material), the site effects tend to be greater than in the uplands of western Tennessee because of larger impedance contrasts within the near-surface soils. ?? 2001 Elsevier Science B.V. All rights reserved.

Engineering Geology↗
USGS2000

Authigenic molybdenum formation in marine sediments: A link to pore water sulfide in the Santa Barbara Basin

Pore water and sediment Mo concentrations were measured in a suite of multicores collected at four sites along the northeastern flank of the Santa Barbara Basin to examine the connection between authigenic Mo formation and pore water sulfide concentration. Only at the deepest site (580 m), where pore water sulfide concentrations rise to >0.1 μM right below the sediment water interface, was there active authigenic Mo formation. At shallower sites (550, 430, and 340 m), where pore water sulfide concentrations were consistently <0.05 μM, Mo precipitation was not occurring at the time of sampling. A sulfide concentration of ∼0.1 μM appears to be a threshold for the onset of Mo-Fe-S co-precipitation. A second threshold sulfide concentration of ∼100 μM is required for Mo precipitation without Fe, possibly as Mo-S or as particle-bound Mo.

Geochimica et Cosmochimica Acta↗
USGS1967

The occurrence and origin of lamellar troilite in iron meteorites

A number of iron meteorites contain elongated inclusions consisting predominantly of troilite, which have been termed Reichenbach lamellae. Two types of inclusions exist, the first up to 6 cm long and 0·2 mm wide, the second up to 2 cm long and 3 mm wide. The first type contains troilite with subordinate daubreelite and is commonly rimmed by schreibersite and swathing kamacite; the second consists largely of troilite with daubreelite and rare graphite and silicate grains. Both types formed from a residual sulfide melt after the solidification of Ni Fe metal. Swatching kamacite surrounding troilite in iron meteorites formed by nucleation at the troilite-metal interface during the formation of the Widmanstätten texture. Meteorites containing troilite inclusions of the second type appear to have cooled more rapidly than most iron meteorites. In view of the confusion surrounding the use of the term Reichenbach lamella, it is suggested that the term be dropped from the literature.

Geochimica et Cosmochimica Acta↗
USGS1998

Chemical weathering in a tropical watershed, Luquillo Mountains, Puerto Rico: I. Long-term versus short-term weathering fluxes

The pristine Rio Icacos watershed in the Luquillo Mountains in eastern Puerto Rico has the fastest documented weathering rate of silicate rocks on the Earth's surface. A regolith propagation rate of 58 m Ma-1 calculated from iso-volumetric saprolite formation from quartz diorite, is comparable to the estimated denudation rate (25-50 Ma-1) but is an order of magnitude faster than the global average weathering rate (6 Ma-1). Weathering occurs in two distinct environments; plagioclase and hornblende react at the saprock interface and biotite and quartz weather in the overlying thick saprolitic regolith. These environments produce distinctly different water chemistries, with K, Mg, and Si increasing linearly with depth in saprolite porewaters and with stream waters dominated by Ca, Na, and Si. Such differences are atypical of less intense weathering in temperate watersheds. Porewater chemistry in the shallow regolith is controlled by closed-system recycling of inorganic nutrients such as K. Long-term elemental fluxes through the regolith (e.g., Si = 1.7 ?? 10-8 moles m-2 s-1) are calculated from mass losses based on changes in porosity and chemistry between the regolith and bedrock and from the age of the regolith surface (200 Ma). Mass losses attributed to solute fluxes are determined using a step-wise infiltration model which calculates mineral inputs to the shallow and deep saprolite porewaters and to stream water. Pressure heads decrease with depth in the shallow regolith (-2.03 m H2O m-1), indicating that both increasing capillary tension and graviometric potential control porewater infiltration. Interpolation of experimental hydraulic conductivities produces an infiltration rate of 1 m yr-1 at average field moisture saturation which is comparable with LiBr tracer tests and with base discharge from the watershed. Short term weathering fluxes calculated from solute chemistries and infiltration rates (e.g., Si = 1.4 ?? 10-8 moles m-2 s-1) are compared to watershed flux rates (e.g., Si = 2.7 ?? 10-8 moles m-2 s-1). Consistency between three independently determined sets of weathering fluxes imply that possible changes in precipitation, temperature, and vegetation over the last several hundred thousand years have not significantly impacted weathering rates in the Luquillo Mountains of Puerto Rico. This has important ramifications for tropical environments and global climate change. Copyright ?? 1998 Elsevier Science Ltd.

Geochimica et Cosmochimica Acta↗
USGS2005

Microbial biogeochemistry of uranium mill tailings

Uranium mill tailings (UMT) are the crushed ore residues from the extraction of uranium (U) from ores. Among the radioactive wastes associated with the nuclear fuel cycle, UMT are unique in terms of their volume and their limited isolation from the surficial environment. For this latter reason, their management and long-term fate has many interfaces with environmental microbial communities and processes. The interactions of microorganisms with UMT have been shown to be diverse and with significant consequences for radionuclide mobility and bioremediation. These radionuclides are associated with the U-decay series. The addition of organic carbon and phosphate is required to initiate the reduction of the U present in the groundwater down gradient of the mills. Investigations on sediment and water from the U-contaminated aquifer, indicates that the addition of a carbon source stimulates the rate of U removal by microbial reduction. Moreover, most attention with respect to passive or engineered removal of U from groundwaters focuses on iron-reducing and sulfate-reducing bacteria.

Advances in Applied Microbiology↗
USGS1961

Paleomagnetism

This chapter highlights the ways in which rocks become magnetized. It also interprets paleomagnetic results in terms of the theories of polar wandering, continental drift, and an expanding Earth. The chapter describes the salient characteristics and trends of the geomagnetic field during the period of direct observation. Several questions are posed concerning the extension of these properties back to earlier times. Some of these questions can now be answered from the results of paleomagnetic research. The intensity of the main dipole component of the geomagnetic field appears to have been decreasing since well before the period of direct observation. Furthermore, two important properties of the geomagnetic field have been established by spherical harmonic analysis. First, the field is derivable from a potential and, hence, contributions to the total field from currents flowing across the Earth–air interface are negligibly small. Secondly, 2–5% of the field is of external origin and is because of movements of charged particles in the space around the Earth.

Advances in Geophysics↗
USGS1999

Toward the use of remote sensing and other data to delineate functional types in terrestrial and aquatic systems

This chapter discusses the role that remotely sensed data play in improving the ability to document the distribution of global land cover types. If the relationships between the cover types and trace gas fluxes can be determined, then the dynamics of these fluxes can be established. The chapter discusses important aquatic systems—such as wetlands—and the land–water interface. Researchers have a wide variety of options available to utilize the remotely sensed data for the scaling of trace gas fluxes between terrestrial and aquatic ecosystems and the atmosphere. An important application of remote sensing for improving the understanding of trace gas fluxes is the classification of land cover types. Remote sensing is a powerful tool for the collection of environmental data. When combined with other more conventional data, they can be analyzed to extract a wide variety of environmental themes. Models can be developed for improving the fundamental understanding of the dynamics of complex interconnected systems that support and sustain life on earth.

Book chapter↗
USGS2002

Evaluation of a local grid refinement method for steady-state block-centered finite-difference groundwater models

A new method of local grid refinement for two-dimensional block-centered finite difference meshes that uses an iteration-based feedback to couple two separate grids has been developed. Its convergence properties have been evaluated and comparisons with alternative methods have been completed (Mehl and Hill, in review a). This work further investigates a difficulty encountered with the traditional telescopic mesh refinement (TMR) methods that lack a feedback. Results indicate: (1) Coupling the coarse grid with the refined grid in a numerically rigorous way that allows for a feedback can improve the coarse grid results; this improvement is not possible using the TMR methods because there is no feedback. (2) The TMR methods work well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 6.8% and errors in cell-to-cell fluxes up to 7.1% for the case presented. (3) For the TMR methods, coupling using flux boundary conditions produces significant inconsistencies in the head distribution at the boundary interface. TMR inaccuracies can substantially effect parameter estimation (Mehl and Hill, in review b).

Developments in Water Science↗
USGS2000

Preface paper to the Semi-Arid Land-Surface-Atmosphere (SALSA) Program special issue

The Semi-Arid Land-Surface-Atmosphere Program (SALSA) is a multi-agency, multi-national research effort that seeks to evaluate the consequences of natural and human-induced environmental change in semi-arid regions. The ultimate goal of SALSA is to advance scientific understanding of the semi-arid portion of the hydrosphere-biosphere interface in order to provide reliable information for environmental decision making. SALSA approaches this goal through a program of long-term, integrated observations, process research, modeling, assessment, and information management that is sustained by cooperation among scientists and information users. In this preface to the SALSA special issue, general program background information and the critical nature of semi-arid regions is presented. A brief description of the Upper San Pedro River Basin, the initial location for focused SALSA research follows. Several overarching research objectives under which much of the interdisciplinary research contained in the special issue was undertaken are discussed. Principal methods, primary research sites and data collection used by numerous investigators during 1997-1999 are then presented. Scientists from about 20 US, five European (four French and one Dutch), and three Mexican agencies and institutions have collaborated closely to make the research leading to this special issue a reality. The SALSA Program has served as a model of interagency cooperation by breaking new ground in the approach to large scale interdisciplinary science with relatively limited resources.

Conference Paper↗
USGS2002

Natural attenuation of chlorinated solvents at Area 6, Dover Air Force Base: Groundwater biogeochemistry

Monitored natural attenuation (MNA) has recently emerged as a viable groundwater remediation technology in the United States. Area 6 at Dover Air Force Base (Dover, DE) was chosen as a test site to examine the potential for MNA of tetrachloroethene (PCE) and trichloroethene (TCE) in groundwater and aquifer sediments. A "lines of evidence" approach was used to document the occurrence of natural attenuation. Chlorinated hydrocarbon and biogeochemical data were used to develop a site-specific conceptual model where both anaerobic and aerobic biological processes are responsible for the destruction of PCE, TCE, and daughter metabolites. An examination of groundwater biogeochemical data showed a region of depleted dissolved oxygen with elevated dissolved methane and hydrogen concentrations. Reductive dechlorination likely dominated in the anaerobic portion of the aquifer where PCE and TCE levels were observed to decrease with a simultaneous increase in cis-1,2-dichloroethene (cis-DCE), vinyl chloride (VC), ethene, and dissolved chloride. Near the anaerobic/aerobic interface, concentrations of cis-DCE and VC decreased to below detection limits, presumably due to aerobic biotransformation processes. Therefore, the contaminant and daughter product plumes present at the site appear to have been naturally attenuated by a combination of active anaerobic and aerobic biotransformation processes. ?? 2002 Elsevier Science B.V. All rights reserved.

Journal of Contaminant Hydrology↗
USGS2003

The saturated zone at Yucca Mountain: An overview of the characterization and assessment of the saturated zone as a barrier to potential radionuclide migration

The US Department of Energy is pursuing Yucca Mountain, Nevada, for the development of a geologic repository for the disposal of spent nuclear fuel and high-level radioactive waste, if the repository is able to meet applicable radiation protection standards established by the US Nuclear Regulatory Commission and the US Environmental Protection Agency (EPA). Effective performance of such a repository would rely on a number of natural and engineered barriers to isolate radioactive waste from the accessible environment. Groundwater beneath Yucca Mountain is the primary medium through which most radionuclides might move away from the potential repository. The saturated zone (SZ) system is expected to act as a natural barrier to this possible movement of radionuclides both by delaying their transport and by reducing their concentration before they reach the accessible environment. Information obtained from Yucca Mountain Site Characterization Project activities is used to estimate groundwater flow rates through the site-scale SZ flow and transport model area and to constrain general conceptual models of groundwater flow in the site-scale area. The site-scale conceptual model is a synthesis of what is known about flow and transport processes at the scale required for total system performance assessment of the site. This knowledge builds on and is consistent with knowledge that has accumulated at the regional scale but is more detailed because more data are available at the site-scale level. The mathematical basis of the site-scale model and the associated numerical approaches are designed to assist in quantifying the uncertainty in the permeability of rocks in the geologic framework model and to represent accurately the flow and transport processes included in the site-scale conceptual model. Confidence in the results of the mathematical model was obtained by comparing calculated to observed hydraulic heads, estimated to measured permeabilities, and lateral flow rates calculated by the site-scale model to those calculated by the regional-scale flow model. In addition, it was confirmed that the flow paths leaving the region of the potential repository are consistent with those inferred from gradients of measured head and those independently inferred from water-chemistry data. The general approach of the site-scale SZ flow and transport model analysis is to calculate unit breakthrough curves for radionuclides at the interface between the SZ and the biosphere using the three-dimensional site-scale SZ flow and transport model. Uncertainties are explicitly incorporated into the site-scale SZ flow and transport abstractions through key parameters and conceptual models. ?? 2002 Elsevier Science B.V. All rights reserved.

Journal of Contaminant Hydrology↗
USGS2000

Characterization of seismic hazard and structural response by energy flux

Seismic safety of structures depends on the structure's ability to absorb the seismic energy that is transmitted from ground to structure. One parameter that can be used to characterize seismic energy is the energy flux. Energy flux is defined as the amount of energy transmitted per unit time through a cross-section of a medium, and is equal to kinetic energy multiplied by the propagation velocity of seismic waves. The peak or the integral of energy flux can be used to characterize ground motions. By definition, energy flux automatically accounts for site amplification. Energy flux in a structure can be studied by formulating the problem as a wave propagation problem. For buildings founded on layered soil media and subjected to vertically incident plane shear waves, energy flux equations are derived by modeling the buildings as an extension of the layered soil medium, and considering each story as another layer. The propagation of energy flux in the layers is described in terms of the upgoing and downgoing energy flux in each layer, and the energy reflection and transmission coefficients at each interface. The formulation results in a pair of simple finite-difference equations for each layer, which can be solved recursively starting from the bedrock. The upgoing and downgoing energy flux in the layers allows calculation of the energy demand and energy dissipation in each layer. The methodology is applicable to linear, as well as nonlinear structures. ?? 2000 Published by Elsevier Science Ltd.

Soil Dynamics and Earthquake Engineering↗