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[STT39-02] Inverse modeling for double-layer structures using gravity gradient tensor Δgzz component
Keywords:Gravity gradient, Double-layer structures, Inverse modeling, Kamegawa Fault
Two models, namely, the layer model and the non-layer model, are assumed as subsurface structures used to estimate subsurface structures using gravity anomalies using inverse modeling. The basic model for representing a layered subsurface structure is a double-layer structure. When estimating multilayer structures by inverse modeling, appropriate filtering and double-layer analysis are often combined to estimate subsurface structures. The Fourier series method (Tsuboi and Fuchida, 1937), Hagiwara's method (Hagiwara, 1987), and Bott's method (Bott, 1960) are well-known double-layer inverse models. In this study, Bott's method was extended using gravity anomaly Δgz to the method using gravity gradient Δgzz component. The Δgzz gravity gradient tensor component has often been used for subsurface structure estimation during airborne gravity gradient surveys.
The Bott's method estimates the basement structure from gravity anomaly Δgz through iterative calculations. In the iterative calculations, the difference between observed and calculated gravity anomalies from the assumed subsurface structures was treated as equivalent to the gravity anomaly of the Bouguer plate with thickness h, which was subsequently determined as a correction. Bott's method for Δgz was extended to Δgzz method by applying the equation for Δgzz on the Bouguer plate to the correction term in the iterative calculations. Hence, the equation for Δgzz on the Bouguer plate was derived and used as the correction term, transforming the difference between observed and calculated Δgzz from assumed subsurface structures to the correction amount of the assumed model.
Numerical tests using the test model discovered that the correction term alone did not reach solution convergence. Therefore, a parameter ω was introduced to prompt the convergence, and its characteristics were investigated using a numerical test. It was observed that the solution converted when ω was less than 0.16, with smaller ω increasing the number of iterative calculations.
In Bott's method, the density contrast and average depth of the boundary between the basement and sedimentary layers were set as initial conditions. In general, these methods are limited due to initial condition dependency. The proposed method is no exception and estimates the subsurface structures based on initial values. To mitigate this limitation, it is preferable to employ additional geophysical or geological data such as seismic survey results, drilling data, and power spectrum analysis results to improve the credibility of the initial condition.
To apply our method to field data, a gravity survey line was selected across the Kamegawa fault located in Beppu City in Oita Prefecture, Kyushu District, Japan. As we use Δgzz for the subsurface structures in this study, Δgz was transformed to Δgzz using the Fourier transformation method (Kusumoto, 2017). This transformation resulted in a conspicuous peak at the point where the Kamegawa Fault was estimated using a topographic survey. Our inversion method was applied to the obtained Δgzz, revealing the normal fault structure with 20-m steps at the predicted fault site. Additionally, few Δgzz peaks were observed due to unknown step structures around the Kamegawa fault. These peaks have steps of several meters to tens of meters in height near the surface. However, classifying these step structures as fault structures remained a challenge due to a lack of sufficient geophysical and geological data.
References
Bott, M. H. P. (1960): The use of rapid digital computing methods for direct gravity interpretation of sedimentary basins, Geophys. Jour. Royal Astron. Soc, 3, 63–67, doi: 10.1111/j.1365-246X.1960.tb00065.x
Hagiwara, Y. (1987): A new gravity method for analyzing double-layer structures, Journal of Geodetic Society of Japan, 33, 315-320.
Kusumoto, S. (2017): Eigenvector of gravity gradient tensor for estimating fault dips considering fault type, Prog. Earth Planet. Sci., 4: 15. doi: 10. 1186/ s40645-017- 0130-0
Tsuboi, C., and Fuchida, T. (1937): Relations between gravity and corresponding subterranean mass distribution, Bull. Eathq. Res. Inst., 15, 636-649.
The Bott's method estimates the basement structure from gravity anomaly Δgz through iterative calculations. In the iterative calculations, the difference between observed and calculated gravity anomalies from the assumed subsurface structures was treated as equivalent to the gravity anomaly of the Bouguer plate with thickness h, which was subsequently determined as a correction. Bott's method for Δgz was extended to Δgzz method by applying the equation for Δgzz on the Bouguer plate to the correction term in the iterative calculations. Hence, the equation for Δgzz on the Bouguer plate was derived and used as the correction term, transforming the difference between observed and calculated Δgzz from assumed subsurface structures to the correction amount of the assumed model.
Numerical tests using the test model discovered that the correction term alone did not reach solution convergence. Therefore, a parameter ω was introduced to prompt the convergence, and its characteristics were investigated using a numerical test. It was observed that the solution converted when ω was less than 0.16, with smaller ω increasing the number of iterative calculations.
In Bott's method, the density contrast and average depth of the boundary between the basement and sedimentary layers were set as initial conditions. In general, these methods are limited due to initial condition dependency. The proposed method is no exception and estimates the subsurface structures based on initial values. To mitigate this limitation, it is preferable to employ additional geophysical or geological data such as seismic survey results, drilling data, and power spectrum analysis results to improve the credibility of the initial condition.
To apply our method to field data, a gravity survey line was selected across the Kamegawa fault located in Beppu City in Oita Prefecture, Kyushu District, Japan. As we use Δgzz for the subsurface structures in this study, Δgz was transformed to Δgzz using the Fourier transformation method (Kusumoto, 2017). This transformation resulted in a conspicuous peak at the point where the Kamegawa Fault was estimated using a topographic survey. Our inversion method was applied to the obtained Δgzz, revealing the normal fault structure with 20-m steps at the predicted fault site. Additionally, few Δgzz peaks were observed due to unknown step structures around the Kamegawa fault. These peaks have steps of several meters to tens of meters in height near the surface. However, classifying these step structures as fault structures remained a challenge due to a lack of sufficient geophysical and geological data.
References
Bott, M. H. P. (1960): The use of rapid digital computing methods for direct gravity interpretation of sedimentary basins, Geophys. Jour. Royal Astron. Soc, 3, 63–67, doi: 10.1111/j.1365-246X.1960.tb00065.x
Hagiwara, Y. (1987): A new gravity method for analyzing double-layer structures, Journal of Geodetic Society of Japan, 33, 315-320.
Kusumoto, S. (2017): Eigenvector of gravity gradient tensor for estimating fault dips considering fault type, Prog. Earth Planet. Sci., 4: 15. doi: 10. 1186/ s40645-017- 0130-0
Tsuboi, C., and Fuchida, T. (1937): Relations between gravity and corresponding subterranean mass distribution, Bull. Eathq. Res. Inst., 15, 636-649.