Hello, Shanker KC!

The second derivatives Wzx and Wzy characterize the rate of change of gz (that is, its gradient) horizontally (in the XOY plane, tangent to the surface) and have a dimension of 1/ sec^2. They are called horizontal gravity gradients.

The vertical gradient of gravity is of great practical importance, its use can significantly expand the possibilities for the localization and interpretation of gravitational anomalies. The use of the measured vertical gradient of gravity on the earth's surface will improve the accuracy of the measured values of the acceleration of gravity to the reference surface, as well as find the average curvature of the level surface.

Horizontal gradient on gravity anomaly precisely define the contact of two lithology with significantly density contrast and fault zone.

The vertical gradient/ derivative gravity maps indicate the continuation of causative source to deeper level, may infer the depth.

Gravity gradient measurements, as explained above, generally provide higher resolution than the absolute value until they reach the noise threshold, typically between 3 - 5 km from the point of measurement. At longer distances, it is generally better to use the absolute value. A second benefit is that horizontal gradients provide information about density distributions in a lateral direction, yielding a 3D picture of densities, not just a vertical distribution.

Gravity anomalies are described by Professor E. Khalilov and Prof. Oleg Martynov.

I described this in the first stage of development of the earthquake process.

Deleted research item The research item mentioned here has been deleted

Yes, the gravity gradient is different from the absolute gravity value. Gravity gradient mathematically is simply the rate of change of gravity values if you go horizontally (X-axis, let’s say, is the horizontal gravity gradient), vertically (Y-axis, let’s say, is the vertical gravity gradient), or in the direction perpendicular to the X-Y axis that fulfills the right-hand thumb rule.

Furthermore, gravity gradient is the second derivative of the gravitational potential, it is a tensor field, it is a matrix. Usually measured in Eötvös unit ( 1 Eötvös unit = 10-9Sec-2).

Moreover, outside Earth, you can relate the Laplace Equation (which is nth but the sum of the gravity gradients along X-, Y- and Z- axes) to zero; which serves as the basis for the construction of Surface Harmonic Series (SHS) expressed in terms of Cnm and Snm Coefficients. These coefficients are used to calculate the gravity anomaly -> which is used to calculate the disturbing potential; which when combined with a normal gravity field gives you geoid undulation. This is one interpretation.

For another interpretation, let me give you a quick real-life employment of the gravity gradient:

This gravity gradient is used to compute the gravity anomaly by gradiometer onboard the GOCE gravity field mission, which can then be put in the stroke’s formula to derive the geoid undulation. After getting the geoid undulation, you can approximate the geoid very well, which is the first-order approximation of the Earth’s topography or the Earth as a whole.

Nonetheless, in free air reduction, the actual vertical gravity gradients are replaced by normal gravity gradients, due to the fact that we do not know the actual vertical gravity gradient.

Thank you very much Sudur Bhattarai .

It is the variation in gravitational field strength across an object or a region of space. By measuring the gravity gradient, scientists can infer several pieces of information: Shape and Mass distribution, density variations, internal structure, tidal effects, and geophysical processes.