THE ANOMALOUS FREE‐AIR VERTICAL GRADIENT IN BOREHOLE EXPLORATION

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 441-443 ◽  
Author(s):  
Stephen Thyssen‐Bornemisza
Keyword(s):  
Observation Interval ◽  
Vertical Gradient ◽  
Gravitational Effects ◽  
Free Air ◽  
Gravity Measurements ◽  
Source Of Error ◽  
Vertical Gradients ◽  
Interpretation Of Results

Hammer (1950) and Smith (1950), in discussions about gravity measurements in vertical shafts and boreholes, have pointed out that gravitational effects originating in zones or layers above or below the gravity‐meter observation interval may easily produce anomalous free‐air vertical gradients. These anomalous gradients cannot well be corrected without the proper density information and, therefore, would represent a possible source of error in the interpretation of results.

Interval gravity‐gradient determination concepts

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 828-832 ◽  
Author(s):  
Dwain K. Butler
Keyword(s):  
Finite Difference ◽  
Gravity Data ◽  
Vertical Gradient ◽  
Gravity Gradient ◽  
Gravity Gradients ◽  
Tower Structure ◽  
Gravity Measurements ◽  
Vertical Gradients

Considerable attention has been directed recently to applications of gravity gradients, e.g., Hammer and Anzoleaga (1975), Stanley and Green (1976), Fajklewicz (1976), Butler (1979), Hammer (1979), Ager and Liard (1982), and Butler et al. (1982). Gravity‐gradient interpretive procedures are developed from properties of true or differential gradients, while gradients are determined in an interval or finite‐difference sense from field gravity data. The relations of the interval gravity gradients to the true or differential gravity gradients are examined in this paper. Figure 1 illustrates the concepts of finite‐difference procedures for gravity‐gradient determinations. In Figure 1a, a tower structure is illustrated schematically for determining vertical gradients. Gravity measurements are made at two or more elevations on the tower, and various finite‐difference or interval values of vertical gradient can be determined. For measurements at three elevations on the tower, for example, three interval gradient determinations are possible: [Formula: see text]; [Formula: see text]; [Formula: see text]; where [Formula: see text] and [Formula: see text] etc. For a positive downward z-;axis, these definitions for [Formula: see text] and [Formula: see text] will result in positive values for the vertical gradient. Relations of the interval gradients to each other and to the true or differential gradient are examined in this paper.

A Large Annual Cycle in Ozone above the Tropical Tropopause Linked to the Brewer–Dobson Circulation

2007 ◽  
Vol 64 (12) ◽  
pp. 4479-4488 ◽  
Author(s):  
William J. Randel ◽  
Mijeong Park ◽  
Fei Wu ◽  
Nathaniel Livesey
Keyword(s):  
Annual Cycle ◽  
Seasonal Cycle ◽  
Annual Variation ◽  
Lower Stratosphere ◽  
Vertical Gradient ◽  
Relative Amplitude ◽  
Vertical Layer ◽  
Satellite Measurements ◽  
Tropical Tropopause ◽  
Vertical Gradients

Abstract Near-equatorial ozone observations from balloon and satellite measurements reveal a large annual cycle in ozone above the tropical tropopause. The relative amplitude of the annual cycle is large in a narrow vertical layer between ∼16 and 19 km, with approximately a factor of 2 change in ozone between the minimum (during NH winter) and maximum (during NH summer). The annual cycle in ozone occurs over the same altitude region, and is approximately in phase with the well-known annual variation in tropical temperature. This study shows that the large annual variation in ozone occurs primarily because of variations in vertical transport associated with mean upwelling in the lower stratosphere (the Brewer–Dobson circulation); the maximum relative amplitude peak in the lower stratosphere is collocated with the strongest background vertical gradients in ozone. A similar large seasonal cycle is observed in carbon monoxide (CO) above the tropical tropopause, which is approximately out of phase with ozone (associated with an oppositely signed vertical gradient). The observed ozone and CO variations can be used to constrain estimates of the seasonal cycle in tropical upwelling.

Airborne gravity measurements over mountainous areas by using a LaCoste & Romberg air‐sea gravity meter

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 807-816 ◽  
Author(s):  
Jérôme Verdun ◽  
Roger Bayer ◽  
Emile E. Klingelé ◽  
Marc Cocard ◽  
Alain Geiger ◽  
...  
Keyword(s):  
Data Reduction ◽  
Classical Method ◽  
Gravity Data ◽  
Airborne Gravity ◽  
Mountainous Area ◽  
Vertical Acceleration ◽  
Mountainous Areas ◽  
Free Air ◽  
Gravity Measurements ◽  
Free Air Anomaly

This paper introduces a new approach to airborne gravity data reduction well‐suited for surveys flown at high altitude with respect to gravity sources (mountainous areas). Classical technique is reviewed and illustrated in taking advantage of airborne gravity measurements performed over the western French Alps by using a LaCoste & Romberg air‐sea gravity meter. The part of nongravitational vertical accelerations correlated with gravity meter measurements are investigated with the help of coherence spectra. Beam velocity has proved to be strikingly correlated with vertical acceleration of the aircraft. This finding is theoretically argued by solving the equation of the gravimetric system (gravity meter and stabilized platform). The transfer function of the system is derived, and a new formulation of airborne gravity data reduction, which takes care of the sensitive response of spring tension to observable gravity field wavelengths, is given. The resulting gravity signal exhibits a residual noise caused by electronic devices and short‐wavelength Eötvös effects. The use of dedicated exponential filters gives us a way to eliminate these high‐frequency effects. Examples of the resulting free‐air anomaly at 5100‐m altitude along one particular profile are given and compared with free‐air anomaly deduced from the classical method for processing airborne gravity data, and with upward‐continued ground gravity data. The well‐known trade‐off between accuracy and resolution is discussed in the context of a mountainous area.

The calculation of deflexions of the vertical from gravity anomalies

1950 ◽  
Vol 204 (1078) ◽  
pp. 374-395 ◽  
Keyword(s):  
Gravity Data ◽  
Gravity Anomalies ◽  
Sources Of Error ◽  
Free Air ◽  
Gravity Measurements ◽  
Standard Deviations ◽  
The Difference ◽  
Different Sources

The theory of the application of gravity measurements to geodetic calculations is discussed, and the errors involved in calculating deflexions of the vertical are estimated. If the gravity data are given as free air anomalies from Jeffreys’s (1948) formula, so thdt the second and third harmonics of gravity are assumed known, the orders of magnitude of the standard deviations of the different sources of error are the following: Single deflexion: neglect of gravity outside 20° 1" Difference of deflexions: neglect of gravity outside 5° 0"·5 Calculation of effects of gravity from 0º·05 to 5° 0"·1 Calculation of effects of gravity within 0º·05 between 0"·1 and 0"·5 Estimates of the deflexions are made for Greenwich, Herstmonceux, Southampton and Bayeux, and the difference between Greenwich and Southampton is compared with the astronomical and geodetic amplitudes.

Relative precision of vertical and horizontal gravity gradients measured by gravimeter

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 99-101 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Survey Data ◽  
Hilbert Transform ◽  
Gravity Data ◽  
Gradient Methods ◽  
Vertical Gradient ◽  
Gravity Gradients ◽  
Relative Precision ◽  
The Hilbert Transform ◽  
Vertical Gradients ◽  
Vertical Gradient Of Gravity

Several recent publications advocate the use of the vertical gradient of gravity from gravimeter measurements at two elevations in a portable tower (Thyssen‐Bornemisza, 1976; Fajklewicz, 1976; Mortimer, 1977). Contrary opinions have also been expressed (Hammer and Anzoleaga, 1975; Stanley and Green, 1976; Thysen‐Bornemisza, 1977; Arzi, 1977). The disagreement revolves around the question of practically attainable precision of the vertical gradient tower method. Although it is possible to calculate both horizontal and vertical gradients from conventional gravity survey data by use of the Hilbert transform (Stanley and Green, 1976), it should be noted that highly precise gravity data are required. Also the need for connected elevation and location surveys, the major cost in gravity surveying, is not avoided. This is a significant advantage of the gradient methods. The purpose here is to present a brief consideration of the relative precision of the horizontal and vertical gradients, as measured in the field by special gravimeter observations.

POSSIBLE APPLICATION OF THE ANOMALOUS FREE‐AIR VERTICAL GRADIENT TO MARINE EXPLORATION

Geophysics ◽  
1966 ◽  
Vol 31 (1) ◽  
pp. 260-263
Author(s):  
Stephen Thyssen‐Bornemisza
Keyword(s):  
Vertical Cylinder ◽  
Vertical Gradient ◽  
Gravity Gradient ◽  
Average Gradient ◽  
Vertical Gravity Gradient ◽  
Free Air ◽  
Vertical Gravity ◽  
Lithologic Unit ◽  
Marine Exploration ◽  
Anomalous Average

Recently it could be shown (Thyssen‐Bornemisza, 1965) that a vertical lithologic unit cylinder generates a relatively strong anomalous free‐air vertical gravity gradient F′ along the cylinder axis. The following simple example may serve as a demonstration. A small vertical cylinder made of gold or tungsten, where radius r and length L are identical, would generate the anomalous average gradient F′∼3,223 Eötvös units over the interval h=r=L going from the cylinders top surface upward. Suppose r=l=1 cm, then an average gradient exceeding the earth’s normal free‐air vertical gradient F is present over the interval h=1 cm.

Effects of terrain on borehole gravity data

Geophysics ◽  
1980 ◽  
Vol 45 (2) ◽  
pp. 234-243 ◽  
Author(s):  
J. R Hearst ◽  
J. W. Schmoker ◽  
R. C. Carlson
Keyword(s):  
Gravity Data ◽  
Radial Distance ◽  
Ground Surface ◽  
Absolute Maximum ◽  
Near Surface ◽  
Free Air ◽  
Gravity Measurements ◽  
Terrain Elevation ◽  
Lower Magnitude ◽  
Terrain Features

The effect of terrain on gravity measurements in a borehole and on formation density derived from borehole gravity data is studied as a function of depth in the well, terrain elevation, terrain inclination, and radial distance to the terrain feature. The vertical attraction of gravity [Formula: see text] in a borehole resulting from a terrain element is small at the surface and reaches an absolute maximum at a depth of about one and one‐half times the radial distance to the terrain element, then decreases at greater depths. The effect of terrain on calculated formation density is proportional to the vertical derivative of [Formula: see text] and is maximum at the surface, passes through zero where |[Formula: see text]| is greatest, and reaches a second extremum of opposite sign to the first and of much lower magnitude. Accuracy criteria for borehole‐gravity terrain corrections show that elevation accuracy requirements are most stringent for a combination of nearby terrain features and near‐surface gravity stations. Sensitivity to terrain inclination is also greatest for this combination. The measurement of the free‐air gradient of gravity, commonly made’slightly above the ground surface, is extremely sensitive to topographic irregularities within about 300m of the measurement point. The effect of terrain features 21.9 to 166.7 km from the well [Hammer’s (1939) zone M through Hayford‐Bowie’s (1912) zone O] on calculated formation density is nearly constant with depth. At these distances, the terrain correction will be equivalent to a dc shift of about [Formula: see text] of average elevation above or below the correction datum. The effect of topography beyond 166.7 km is not likely to exceed [Formula: see text].

CORRELATING SEA‐SURFACE AND AERIAL GRAVITY MEASUREMENTS

Geophysics ◽  
1966 ◽  
Vol 31 (1) ◽  
pp. 264-266 ◽  
Author(s):  
Stephen Thyssen‐Bornemisza
Keyword(s):  
Ground Surface ◽  
Sea Surface ◽  
Surface Gravity ◽  
Sea Floor ◽  
Gravity Measurements ◽  
Vertical Gradients

When sea‐surface gravity observations were supplemented by corresponding values from the airborne meter, average vertical gradients of gravity could be computed. In a borehole these gradients are observable by moving the borehole gravity meter up and down to another level (Thyssen‐Bornemisza, 1963, 1964, 1965a), but measurements taken on two horizontal profiles separated by the constant vertical interval h could furnish only relative gradient values or variations in the profile direction. Of course, gravity profiles on the ground surface or the sea floor can be likewise supplemented by aerial observations.

Ensemble simulation of sea water temperature and salinity and their seasonal variations in vertical gradient – An application to aquaculture operations in Southern Aegean Sea, Greece

2020 ◽  
Author(s):  
Nithin Shettigar ◽  
Anna Spinosa ◽  
Lorinc Meszaros ◽  
Sandra Gaytan Aguilar ◽  
Ghada El Serafy
Keyword(s):  
Water Quality ◽  
Sea Level ◽  
Seasonal Variations ◽  
Aegean Sea ◽  
Vertical Gradient ◽  
Atmospheric Forcing ◽  
Mean Sea Level ◽  
Ensemble Simulation ◽  
Water Quality Variables ◽  
Vertical Gradients

<p>During the past decades, aquaculture industry has developed rapidly and, due to a continuously growing market, a high demand for new installations, both near and off-shore, is already observed. Various studies show direct correlations between fish growth parameters and water quality variables, among which the most important are temperature, salinity and dissolved oxygen concentration. Those variables can directly impact planning and farming operations such as location, height and depth of cages, stocking density, or fish feeding rate. Moreover, for a sustainable seafood production, necessary management practices should be in place aiming to reduce food waste and spread of diseases.</p><p>At present, large section of the farming sector depends on ad-hoc measurements of water quality without a forecast mechanism. With availability of ocean hydrodynamic and water quality data from various sources such as Copernicus Marine Environmental Monitoring Service (CMEMS), atmospheric data from European Centre for Medium-Range Weather Forecasts (ECMWF), water quality variables can be simulated and forecasted well in advance with the use of numerical modelling tools.</p><p>Within the framework of the EU H2020 funded HiSea Project, a new high-resolution coastal 3D hydrodynamic model aiming at describing the vertical gradients of temperature and salinity and their seasonal variations is developed for southern Aegean Sea of Greece. The Delft3D Flexible Mesh modelling tool is used which allows for computationally economic grid development. Data from CMEMS are utilized to setup the model boundary conditions. A complex heat flux model of temperature computations is employed, which means that the model needs to be provided with several atmospheric forcing data such as wind speed, air temperature, dew point temperature, and mean sea level pressure. These data are derived from ERA5 single level reanalysis data of ECMWF. The output variables show a seasonal trend due to changes in atmospheric forces. Therefore, the developed model simulates seasonal water quality conditions and gives important insights into the vertical gradient of temperature and salinity. Validation of the model outputs is carried out at multiple levels. The water level simulation is verified against Intergovernmental Oceanographic Commission (IOC) mean sea level measurements while the simulated temperature at the two aquaculture sites is verified against the daily in-situ measurements.  </p><p>The uncertainties in the model outputs (temperature and salinity) are estimated through ensemble simulation using different atmospheric forcing from ERA5 and perturbed model process parameters as source of uncertainty. The application of ensemble simulations to understand the vertical gradients of the water quality parameters is a unique approach. Moreover, the application of the numerical model simulations to optimize the aquaculture planning and operation is innovative. The research could be replicated for other marine sectors where water quality variables are of paramount importance.</p><p><em>This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 821934.</em></p>

GRAVITY GRADIENTS AND THE INTERPRETATION OF THE TRUNCATED PLATE

Geophysics ◽  
1976 ◽  
Vol 41 (6) ◽  
pp. 1370-1376 ◽  
Author(s):  
John M. Stanley ◽  
Ronald Green
Keyword(s):  
Hilbert Transform ◽  
Theoretical Data ◽  
Vertical Gradient ◽  
Density Contrast ◽  
Horizontal Gradient ◽  
Gravity Gradients ◽  
Gravity Method ◽  
Commercially Important ◽  
Dip Angle ◽  
Vertical Gradients

The truncated plate and geologic contact are commercially important structures which can be located by the gravity method. The interpretation can be improved if both the horizontal and vertical gradients are known. Vertical gradients are difficult to measure precisely, but with modern gravimeters the horizontal gradient can be measured conveniently and accurately. This paper shows how the vertical gradient can be obtained from the horizontal gradient by the use of a Hilbert transform. A procedure is then presented which easily enables the position, dip angle, depth, thickness, and density contrast of a postulated plate to be precisely and unambiguously derived from a plot of the horizontal gradient against the vertical gradient at each point measured. The procedure is demonstrated using theoretical data.

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