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

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Abstract

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.

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Funding

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Authors and Affiliations

  1. Department of Geosciences, Mountain Top University, Ogun State, Prayer City, Nigeria

    Oluwatimilehin B. Balogun & Akachukwu D. Nwobodo

  2. Department of Physics, Obafemi Awolowo University, Ile-Ife, Nigeria

    Oluwatosin F. Akereke

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  1. Oluwatimilehin B. Balogun
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  2. Oluwatosin F. Akereke
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  3. Akachukwu D. Nwobodo
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Contributions

BOB conceptualised, supervised, validated the results and wrote the write-up; OFA simulated the prisms numerically, did part of the modeling and spectral analysis; NAD did part of the modeling and spectral analysis.

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Correspondence to Oluwatimilehin B. Balogun.

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Appendix

Appendix

Tables of Values Generated for Gravity Response Simulated for a Buried Square Prism at Varying Depths of Burial (Tables 7, 8, 9)

Table 7 Table of Value Generated for Depth of Burial of 500 m, CSA of 25,000,000 m2, Density Contrast of 330 kgm−3 and Thickness of 250 m
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Table 8 Table of Value Generated for Depth of Burial of 2000 m, CSA of 225,000,000 m2, Density Contrast of 330 kgm−3 and Thickness of 1000 m
Full size table
Table 9 Table of Value Generated for Depth of Burial of 6000 m, CSA of 225,000,000 m2, Density Contrast of 330 kgm−3 and Thickness of 3000 m
Full size table

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Balogun, O.B., Akereke, O.F. & Nwobodo, A.D. Understanding the Constraints to the Correct Application of the Upward Continuation Operation in Gravity Data Processing. Pure Appl. Geophys. 180, 3787–3811 (2023). https://doi.org/10.1007/s00024-023-03348-1

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