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.

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.

scholarly journals STUDI PENERAPAN METODE ANALISIS DERIVATIF PADA DATA POTENSIAL GRAVITASI

2020 ◽  
Author(s):  
ahmad zarkasyi
Keyword(s):  
Field Research ◽  
Vertical Gradient ◽  
Geothermal System ◽  
Horizontal Gradient ◽  
Subsurface Structure ◽  
Gravity Method ◽  
Derivative Analysis ◽  
Research Goal ◽  
Vertical Contact ◽  
Gravity Acceleration

In geothermal exploration, geophysics method is one of main method which is used to detect the existence geothermal system. The existence of geothermal system can be known with searching earth subsurface structure. Our research goal is to identify subsurface structure that can be used to know geothermal system belong. The method that we used is gravity method. Gravity method is method based on gravity acceleration variation on earh surface. This method can detect subsurface geology structure such as fault, basin, graben, and caldera. To imaging subsurface structure geology more clearly, the result of gavity processing will be processed more advance with derivative analysis method. One of derivative metode that is often used, is horizontal gradient method and second order vertical method. Both of them can know vertical contact between subsurface body and know what kind of fault structure. The final result is anomaly horizontal gradient contour map and anomaly secong ordel vertical gradient map. And than both of map will be analyzed and integrated with gelogical data in field research.

An alternate derivation of the three‐dimensional Hilbert transform relations from first principles

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 1014-1015 ◽  
Author(s):  
J. Bradley Nelson
Keyword(s):  
Hilbert Transform ◽  
Magnetic Field Intensity ◽  
Three Dimensional ◽  
Gradient Methods ◽  
Vertical Gradient ◽  
Horizontal Gradient ◽  
Implicit Assumption ◽  
Limited Applicability ◽  
Magnetic Gradients ◽  
The Magnetic Field

Several techniques for determining the location, geometry, and strength of a source are based on a knowledge of the magnetic gradients generated by that source. Hood (1965), Bhattacharyya (1966), and Rao et al. (1981) detailed three of these gradient methods. For many years, geophysicists have used the two‐dimensional (2-D) Hilbert transform to approximate the vertical gradient from measurements of the horizontal gradient in the magnetic‐field intensity (Nabighian, 1972; Stanley and Green, 1976; Stanley, 1977; Mohan et al., 1982). This technique is of limited applicability because of the implicit assumption that the source is a linear, 2-D body oriented at right angles to the profile direction.

EXPLORING FOR STRATIGRAPHIC TRAPS WITH GRAVITY GRADIENTS

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 256-268 ◽  
Author(s):  
Sigmund Hammer ◽  
Rodolfo Anzoleaga
Keyword(s):  
Gradient Method ◽  
Torsion Balance ◽  
Important Application ◽  
Theory And Practice ◽  
Horizontal Gradient ◽  
Gravity Gradients ◽  
Limited Extent ◽  
Field Surveys ◽  
New Instrumentation ◽  
Vertical Gradients

The vast and growing literature on the search for stratigraphic traps for petroleum ignores gravity gradients, for which the theory has been available since the heyday of the Eötvös torsion balance decades ago. These are discussed in this paper. The horizontal and vertical gradients can be measured with available gravimeters and (to a limited extent) with the Eötvös torsion balance. A major advantage of the gradient method is that surveying to determine position and elevation of the station is not required. Both theory and practice have been reported in the geophysical literature, but the important application to stratigraphic traps has not been mentioned. We evaluate here the method for locating “pinchouts”, a term which embraces “stratigraphic” and “unconformity” traps in Halbouty’s (1972) classification. Both position and depth of the assumed pinchout are determined by the gradient anomaly. The magnitudes of anomalies of horizontal and vertical gradients are about equal. However, pending new instrumentation, only the horizontal gradient is practically useful for field surveys. The gradient method is quantitatively promising and, used in conjunction with other methods, should significantly advance the search for stratigraphic traps for petroleum.

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.

scholarly journals Bryophyte communities along horizontal and vertical gradients in a human-modified Atlantic Forest remnant

Botany ◽  
2013 ◽  
Vol 91 (3) ◽  
pp. 155-166 ◽  
Author(s):  
Mércia P.P. Silva ◽  
Kátia C. Pôrto
Keyword(s):  
Atlantic Forest ◽  
Environmental Heterogeneity ◽  
Vertical Gradient ◽  
Horizontal Gradient ◽  
Landscape Characteristics ◽  
Host Trees ◽  
Forest Remnant ◽  
Significant Difference ◽  
Edge Distance ◽  
Vertical Gradients

We compared the richness, diversity, and composition of epiphytic bryophytes in a Brazilian Atlantic Forest remnant along zones of height within host trees (vertical gradient) and edge to interior (horizontal gradient). We established five classes of edge distance, and within each one, three host trees were selected (15 in total). Samples were collected in five height zones within host trees from the base to the top. The highest average values of richness and diversity were found in the trunk zone. There was no significant difference of bryophyte total richness and diversity along edge distance and vertical zones. However, the guilds of light tolerance displayed particularities regarding vertical zonation. Shade epiphytes decreased significantly along vertical gradients, whereas sun epiphytes increased, demonstrating a compositional vertical stratification within host trees. Thus, bryophyte distribution in both understories and canopies is more related to microenvironmental conditions than landscape characteristics such as edge distance. Moreover, the features of the Atlantic Forest associated with the environmental heterogeneity of the remnant may play an important role in the lack of gradient in species' composition from the edge to the interior of the forest.

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.

Theory of 2-D complex seismic trace analysis

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 264-272 ◽  
Author(s):  
Arthur E. Barnes
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Hilbert Transform ◽  
Instantaneous Frequency ◽  
Trace Analysis ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Instantaneous Amplitude ◽  
Dip Angle

The ideas of 1-D complex seismic trace analysis extend readily to two dimensions. Two‐dimensional instantaneous amplitude and phase are scalars, and 2-D instantaneous frequency and bandwidth are vectors perpendicular to local wavefronts, each defined by a magnitude and a dip angle. The two independent measures of instantaneous dip correspond to instantaneous apparent phase velocity and group velocity. Instantaneous phase dips are aliased for steep reflection dips following the same rule that governs the aliasing of 2-D sinusoids in f-k space. Two‐dimensional frequency and bandwidth are appropriate for migrated data, whereas 1-D frequency and bandwidth are appropriate for unmigrated data. The 2-D Hilbert transform and 2-D complex trace attributes can be efficiently computed with little more effort than their 1-D counterparts. In three dimensions, amplitude and phase remain scalars, but frequency and bandwidth are 3-D vectors with magnitude, dip angle, and azimuth.

Microgravimetric and gravity gradient techniques for detection of subsurface cavities

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1084-1096 ◽  
Author(s):  
Dwain K. Butler
Keyword(s):  
Case History ◽  
Vertical Gradient ◽  
Gravity Gradient ◽  
Horizontal Gradient ◽  
Shallow Subsurface ◽  
Gradient Profile ◽  
First Case ◽  
Profile Line ◽  
Cavity System ◽  
Subsurface Cavities

Microgravimetric and gravity gradient surveying techniques are applicable to the detection and delineation of shallow subsurface cavities and tunnels. Two case histories of the use of these techniques to site investigations in karst regions are presented. In the first case history, the delineation of a shallow (∼10 m deep), air‐filled cavity system by a microgravimetric survey is demonstrated. Also, application of familiar ring and center point techniques produces derivative maps which demonstrate (1) the use of second derivative techniques to produce a “residual” gravity map, and (2) the ability of first derivative techniques to resolve closely spaced or complex subsurface features. In the second case history, a deeper (∼ 30 m deep), water‐filled cavity system is adequately detected by a microgravity survey. Results of an interval (tower) vertical gradient survey along a profile line are presented in the second case history; this vertical gradient survey successfully detected shallow (<6 m) anomalous features such as limestone pinnacles and clay pockets, but the data are too “noisy” to permit detection of the vertical gradient anomaly caused by the cavity system. Interval horizontal gradients were determined along the same profile line at the second site, and a vertical gradient profile is determined from the horizontal gradient profile by a Hilbert transform technique. The measured horizontal gradient profile and the computed vertical gradient profile compare quite well with corresponding profiles calculated for a two‐dimensional model of the cavity system.

Magnitude of anomalies in the vertical gradient of gravity

Geophysics ◽  
1981 ◽  
Vol 46 (11) ◽  
pp. 1609-1610 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Vertical Gradient ◽  
Spherical Body ◽  
Density Contrast ◽  
Maximum Gradient ◽  
Maximum Value ◽  
Simple Mass ◽  
Spherical Mass ◽  
Vertical Gradient Of Gravity

The maximum gradient which can be caused by a simple mass is that of a spherical body. The equation for the vertical gradient at the point P above the center of a spherical mass of density contrast σ (see insert on Figure 1) can be written in the form [Formula: see text] where G is the universal gravity constant [Formula: see text] Expressing the gradient in the Eötvös units, we have [Formula: see text] In terms of percentage of the earth’s normal vertical gradient, the anomaly is [Formula: see text] of 3086 E°. At the surface of the sphere (h = 0), we have the maximum value [Formula: see text] of 3086 E° which is independent of the radius R.

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