Gravity modeling of 21/2-D sedimentary basins — a case of variable density contrast (original) (raw)

Abstract

An algorithm and associated codes are developed to determine the depths to bottom of a 2 1/2-D sedimentary basin in which the density contrast varies parabolically with depth. This algorithm estimates initial depths of a sedimentary basin automatically and modifies thereafter appropriately within the permissible limits in an iterative approach as described in the text. Efficacy of the method as well as the code is illustrated by interpreting a gravity anomaly of a synthetic model. Further, the applicability of the method is exemplified with the derived density-depth model of the Godavari sub-basin, India to interpret the gravity anomalies due to the basin. Interpretations based on parabolic density profile are more consistent with existing geological information rather than with those obtained with constant density profile.

Key takeaways

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  1. The algorithm effectively estimates depths to sedimentary basins using a parabolic density contrast with depth.
  2. GRA2P5MOD code demonstrates superior accuracy over constant density profiles in gravity anomaly interpretation.
  3. Gravity anomalies reveal a maximum sedimentary basin thickness of 4.0 km in the Godavari sub-basin case study.
  4. Iterative modification of initial depth estimates enhances model accuracy, reducing misfit function significantly over iterations.
  5. The text presents a novel interpretation method for 2 1/2-D sedimentary basins, improving geological consistency.

Figures (5)

The integral in Eq. (4) can be solved either using an analytical or numerical approach. Here, we adopt Simpson’s rule to numerically evaluate Eq. (4). It is obvious that Eq. (4) is strictly valid for the profile, which passes through the origin, R(0,0), of the prism. In the case that the profile runs at an offset distance, s, from the origin, R(0,0), along the y-axis of the prism (shown as R’x’ in Fig. 1A), the gravity anomaly at any point on the profile, R’x’, can be calculated by evaluating Eq. (4) twice by substituting S—s and S+s for S and taking the average.

The integral in Eq. (4) can be solved either using an analytical or numerical approach. Here, we adopt Simpson’s rule to numerically evaluate Eq. (4). It is obvious that Eq. (4) is strictly valid for the profile, which passes through the origin, R(0,0), of the prism. In the case that the profile runs at an offset distance, s, from the origin, R(0,0), along the y-axis of the prism (shown as R’x’ in Fig. 1A), the gravity anomaly at any point on the profile, R’x’, can be calculated by evaluating Eq. (4) twice by substituting S—s and S+s for S and taking the average.

“ig. 1. (A) Geometry of a 2'?-D vertical prism. Note that S' is half strike length of prism and s is offset distance of profile R’x' fro rigin R(0, 0); (B) Gravity effect due to a 2'/?-D vertical prism for different offset distances.

“ig. 1. (A) Geometry of a 2'?-D vertical prism. Note that S' is half strike length of prism and s is offset distance of profile R’x' fro rigin R(0, 0); (B) Gravity effect due to a 2'/?-D vertical prism for different offset distances.

The method of interpretation begins by calculating the initial depth estimates of a sedimentary basin, assuming that the residual gravity anomaly at each Fig. 2. (A) Plain view of a synthetic model and its approximation by juxtaposed prisms; (B) Theoretical gravity anomaly computed for parabolic and constant density profiles (PDP and CDP) along with observed anomaly; (C) Interpreted depth structure of sedimentary basin with PDP and CDP; (D) Density contrast—-depth profile.

The method of interpretation begins by calculating the initial depth estimates of a sedimentary basin, assuming that the residual gravity anomaly at each Fig. 2. (A) Plain view of a synthetic model and its approximation by juxtaposed prisms; (B) Theoretical gravity anomaly computed for parabolic and constant density profiles (PDP and CDP) along with observed anomaly; (C) Interpreted depth structure of sedimentary basin with PDP and CDP; (D) Density contrast—-depth profile.

Fig. 3. Geology and Bouguer gravity map of Godavari sub-basin (modified after Rao, 1982) 2'?_D vertical prisms each with different strike lengths are used to approximate the cross-section of the basin (Fig. 2A). It can be seen from Fig. 2A that the profile, DD’, along which the interpretation is intended to be performed fails to bisect all the prisms, except the first one. Dotted lines on the prisms (Fig. 2A) correspond to the respective central points. Based on the depth of the structure shown in Fig. 2C and with parameters Apy = —0.45gm/cm? and « = 0.02 gm/cm?/km, a theoretical gravity anomaly at a 2km station interval was generated (Fig. 2B). The required parameters Apy and « of the density function to invert the gravity anomaly is obtained from the density contrast—depth data (Fig. 2D) and the half strike lengths of the prisms and the offset distances of the profile from Fig. 2A. For such a problem, 75 iterations were required before the program The same anomaly as shown in Fig. 2B is also interpreted using a constant density profile (CDP) by letting « = 0, for which the misfit function, J, reduced from its initial value of 229 to 0.19 at the end of the 75th iteration. No significant improvement in depth structure was noticed beyond the 75th iteration. The inverted anomaly and the corresponding depth structure of the basin are also shown in Fig. 2B and C for comparison. It can be observed from Fig. 2C that the depth structures obtained using PDP and CDP coincide each other at the ends of the profile, whereas the depth

Fig. 3. Geology and Bouguer gravity map of Godavari sub-basin (modified after Rao, 1982) 2'?_D vertical prisms each with different strike lengths are used to approximate the cross-section of the basin (Fig. 2A). It can be seen from Fig. 2A that the profile, DD’, along which the interpretation is intended to be performed fails to bisect all the prisms, except the first one. Dotted lines on the prisms (Fig. 2A) correspond to the respective central points. Based on the depth of the structure shown in Fig. 2C and with parameters Apy = —0.45gm/cm? and « = 0.02 gm/cm?/km, a theoretical gravity anomaly at a 2km station interval was generated (Fig. 2B). The required parameters Apy and « of the density function to invert the gravity anomaly is obtained from the density contrast—depth data (Fig. 2D) and the half strike lengths of the prisms and the offset distances of the profile from Fig. 2A. For such a problem, 75 iterations were required before the program The same anomaly as shown in Fig. 2B is also interpreted using a constant density profile (CDP) by letting « = 0, for which the misfit function, J, reduced from its initial value of 229 to 0.19 at the end of the 75th iteration. No significant improvement in depth structure was noticed beyond the 75th iteration. The inverted anomaly and the corresponding depth structure of the basin are also shown in Fig. 2B and C for comparison. It can be observed from Fig. 2C that the depth structures obtained using PDP and CDP coincide each other at the ends of the profile, whereas the depth

Fig. 4. (A) Theoretical gravity anomaly computed for parabolic (PDP) and constant density (CDP) profiles along with observed anomaly, Godavari sub-basin, India; (B) Interpreted depth models with PDP and CDP. As an example, a gravity profile EE’ (Fig. 3), which passes through the Chinnur high and cuts across the strike of the basin is interpreted. It can be noted that the profile, EE’, fails to bisect the strike of the basin, and hence a need to specify the offset distances of the profile from the centre of the prisms. The regional gravity field is determined by extending the profile to stations resting on the Proterozoic basement (Pakhal Formation). The values of residual anomaly at these stations are zero as the regional gravity field is defined by the Bouguer gravity anomaly itself. The resulting residual gravity anomaly along the profile, EE’, is shown in Fig. 4. The Bouguer gravity field is shown superimposed on the geology of the basin in Fig. 3. A gravity minima flanked by maxima on either side of the basin is

Fig. 4. (A) Theoretical gravity anomaly computed for parabolic (PDP) and constant density (CDP) profiles along with observed anomaly, Godavari sub-basin, India; (B) Interpreted depth models with PDP and CDP. As an example, a gravity profile EE’ (Fig. 3), which passes through the Chinnur high and cuts across the strike of the basin is interpreted. It can be noted that the profile, EE’, fails to bisect the strike of the basin, and hence a need to specify the offset distances of the profile from the centre of the prisms. The regional gravity field is determined by extending the profile to stations resting on the Proterozoic basement (Pakhal Formation). The values of residual anomaly at these stations are zero as the regional gravity field is defined by the Bouguer gravity anomaly itself. The resulting residual gravity anomaly along the profile, EE’, is shown in Fig. 4. The Bouguer gravity field is shown superimposed on the geology of the basin in Fig. 3. A gravity minima flanked by maxima on either side of the basin is

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