Understanding the Constraints to the Correct Application of the Upward Continuation Operation in Gravity Data Processing

• Published in: Pure and applied geophysics 2023-11, Vol.180 (11), p.3787-3811
• Main Authors: Balogun, Oluwatimilehin B., Akereke, Oluwatosin F., Nwobodo, Akachukwu D.
• Format: Article
• Language: English
• Subjects: Analysis; Data analysis; Data processing; Depth; Earth and Environmental Science; Earth Sciences; Fourier transforms; Geophysics; Geophysics/Geodesy; Gravitational fields; Gravity; Gravity data; Gravity field; Height; Simulation; Spectral analysis; Spectrum analysis; Sums
• ISSN: 0033-4553; 1420-9136
• DOI: 10.1007/s00024-023-03348-1

Analytical simulation of the gravity response due to a square prism buried at known depths has been done and the resulting data have been upward continued to various heights. This was done with the aim of studying the constraints impeding the correct application of the upward continuation filter and the conditions necessary for consistency in the determination of height of upward continuation of gravity field by means of spectral analysis. 3D gravity response of a square prism with known thickness, dimensions and depth of burial was simulated using the expression for the gravity attraction due to a prism. Spectral analysis was then performed on the gravity response data to determine the depth to the top of the prism which was subsequently compared with the value of depth used in the simulation for agreement. Following this, upward continuation operation was performed on the simulated data to a known height such that the total depth to the buried body becomes the sum of depth of burial and the height of upward continuation. Spectral analysis was again performed on the upward continued data in order to compare if the expected total depth to the top of the buried body, which is the sum of the depth to the top of the prism from the ground level and the height of upward continuation, agrees with the depth estimate obtained from spectral analysis. The height of upward continuation at which the depth determined from spectral analysis start to differ significantly was noted. The depth to the top of the square prism was increased in a stepwise manner and the process was repeated. The height of upward continuation at which the depth determined from spectral analysis start to differ significantly was noted for all the various depths of burial as well. Results obtained showed that the computed depth from spectral analysis starts to differ significantly from expected depths at the total depth that is about half of the data grid size. Result also showed that the relationship between the height to which gravity data is upward continued and the true output effect verifiable by spectral analysis method of depth evaluation is ratio 1:1. The study concluded that the upward continuation filter is highly reliable when the aliasing threshold, which is half the data grid size, has not been exceeded.