Here this result is applied to a velocity field that is Lip(α 0 ) except on a set of co-dimension κ 1 on which it is Lip(α 1 ), with uniformity that will be made precise below. We show that the Frisch-Parisi multifractal formalism is valid (at least in one direction) for such a function, and that there is energy conservation if min α (3α + κ(α)) > 1. Analogous conservation results are derived for the equations of incompressible ideal MHD (i.e., zero viscosity and resistivity) for both energy and helicity . In addition, a necessary condition is derived for singularity development in ideal MHD generalizing the Beale-Kato-Majda condition for ideal hydrodynamics.

Occurrence and fate of 45 pesticides and 40 pesticide degradates were investigated in four contrasting agricultural settings—in Maryland, Nebraska, California, and Washington. Primary crops included corn at all sites, soybeans in Maryland, orchards in California and Washington, and vineyards in Washington. Pesticides and pesticide degradates detected in water samples from all four areas were predominantly from two classes of herbicides—triazines and chloroacetanilides; insecticides and fungicides were not present in the shallow ground water. In most samples, pesticide degradates greatly exceeded the concentrations of parent pesticide. In samples from Nebraska, the parent pesticide atrazine [6‐chloro‐N‐ethyl‐N′‐(1‐methylethyl)‐1,3,5‐triazine‐2,4‐diamine] was about the same concentration as the degradate, but in samples from Maryland and California atrazine concentrations were substantially smaller than its degradate. Simazine [6‐chloro‐N,N′‐diethyl‐1,3,5‐triazine‐2,4‐diamine], the second most detected triazine, was detected in ground water from Maryland, California, and Washington. Metolachlor [2‐chloro‐N‐(2‐ethyl‐6‐methylphenyl)‐N‐(2‐methoxy‐1‐methylethyl)acetamide] rarely was detected without its degradates, and when they were detected in the same sample metolachlor always had smaller concentrations. The Root‐Zone Water‐Quality Model was used to examine the occurrence and fate of metolachlor at the Maryland site. Simulations accurately predicted which metolachlor degradate would be predominant in the unsaturated zone. In analyses of relations among redox indicators and pesticide variance, apparent age, concentrations of dissolved oxygen, and excess nitrogen gas (from denitrification) were important indicators of the presence and concentration of pesticides in these ground water systems.

During spring runoff events, herbicides in the Platte River are transported through an alluvial aquifer into collector wells located on an island in the river in 6 to 7 d. During two spring runoff events in 1995 and 1996, atrazine [2‐chloro‐4‐ethylamino‐6‐isopropylamino‐s‐triazine] concentrations in water from these wells reached approximately 7 µg/L, 70 times more than the background concentration in ground water. Concentrations of herbicides and metabolites in the collector wells generally were one‐half to one‐fifth the concentrations of herbicides in the river for atrazine, alachlor [2‐chloro‐2′‐6′‐diethyl‐N‐(methoxymethyl)‐acetanilide], alachlor ethane‐sulfonic acid (ESA) [2‐((2,6‐diethylphenyl) (methoxymethyl)amino)‐2‐oxoethane‐sulfonic acid], metolachlor [2‐chloro‐N‐(2‐ethyl‐6‐methylphenyl)‐N‐(2‐methoxy‐1‐methylethyl)acetamide], cyanazine [2‐((4‐chloro‐6‐(ethylamino)‐1,3,5 triazin‐2‐yl)‐amino)‐2‐methylpropionitrile], and acetochlor [2‐chloro‐N‐(ethoxymethyl)‐N‐(2‐ethyl‐6methyl‐phenyl) acetamide], suggesting that 20 to 50% river water could be present in the water from the collector wells, assuming no degradation. The effect of the river on the quality of water from the collector wells can be reduced through selective management of horizontal laterals of the collector wells. The quality of the water from the collector wells is dependent on the (i) selection of the collector well used, (ii) number and selection of laterals used, (iii) chemical characteristics of the contaminant, and (iv) relative mixing of the Platte River and a major upstream tributary.

Estimating sediment thickness and the geometry of the bedrock surface is a key component of many hydrogeologic studies. The horizontal-to-vertical (H/V) ambient-noise seismic method is a novel, non-invasive technique that can be used to rapidly estimate the depth to bedrock. The H/V method uses a single, broad-band three-component seismometer to record ambient seismic noise. The ratio of the averaged horizontal-to-vertical frequency spectrum is used to determine the fundamental site resonance frequency, which can be interpreted using regression equations to estimate sediment thickness and depth to bedrock.The U.S. Geological Survey used the H/V seismic method during fall 2007 at 11 sites in Cape Cod, Massachusetts, and 13 sites in eastern Nebraska. In Cape Cod, H/V measurements were acquired along a 60-kilometer (km) transect between Chatham and Provincetown, where glacial sediments overlie metamorphic rock. In Nebraska, H/V measurements were acquired along approximately 11-and 14-km transects near Firth and Oakland, respectively, where glacial sediments overlie weathered sedimentary rock.The ambient-noise seismic data from Cape Cod produced clear, easily identified resonance frequency peaks. The interpreted depth and geometry of the bedrock surface correlate well with boring data and previously published seismic refraction surveys. Conversely, the ambient-noise seismic data from eastern Nebraska produced subtle resonance frequency peaks, and correlation of the interpreted bedrock surface with bedrock depths from borings is poor, which may indicate a low acoustic impedance contrast between the weathered sedimentary rock and overlying sediments and/or the effect of wind noise on the seismic records.Our results indicate the H/V ambient-noise seismic method can be used effectively to estimate the depth to rock where there is a significant acoustic impedance contrast between the sediments and underlying rock. However, effective use of the method is challenging in the presence of gradational contacts such as gradational weathering or cementation. Further work is needed to optimize interpretation of resonance frequencies in the presence of extreme wind noise. In addition, local estimates of bedrock depth likely could be improved through development of regional or study-areaspecific regression equations relating resonance frequency to bedrock depth.

COVER:Collage showing multiple photographic images of surface nuclear magnetic resonance and aquifer-test data collection.Center top, a broad view showing trailer-mounted hydraulic pump, used in constant-discharge aquifer test. Project staff shown for general scale.Lower left, hydraulic head recording instrumentation in the observation wells, with wire reels (also shown in large photograph) approximately 25 centimeters in diameter.Lower right, surface nuclear magnetic resonance instrument. Boxes contain electronic equipment and are about 60 centimeters by 60 centimeters in plan view. For an overview of USGS information products, including maps, imagery, and publications, visit http://www.usgs.gov/pubprodTo order this and other USGS information products, visit