Changes

Here, a geometric approach is used to represent the depositional dip cross-section shape of a clinoform with a dimensionless shape function, BLTN13190eq62 ([[:File:BLTN13190fig2.jpg|Figure 2E]]), such as a power law for concave-upward, sandy, shoreline clinoforms:  

Here, a geometric approach is used to represent the depositional dip cross-section shape of a clinoform with a dimensionless shape function, BLTN13190eq62 ([[:File:BLTN13190fig2.jpg|Figure 2E]]), such as a power law for concave-upward, sandy, shoreline clinoforms:  

:<math>EQUATIONS/BLTN13190eqd7</math>

:<math>s(r_c) = \left ( \frac{(r_{\text{max}}(x, y) - r_c(x, y))^P}{r_{\text{max}}(x, y) - r_{\text{min}}(x, y))^P} \right )</math>

However, as the algorithm is generic, the mathematical expression of the dimensionless shape function is interchangeable so that other clinoform geometries can be represented; for example, a sigmoid function can be used to represent clinoforms in a larger, shelf-slope margin settings (e.g., Steckler et al., 1999). By combining the height function (equation 1), with the shape function (equation 7), the clinoform shape function, BLTN13190eq63, is used to construct the shape of a clinoform surface:  

However, as the algorithm is generic, the mathematical expression of the dimensionless shape function is interchangeable so that other clinoform geometries can be represented; for example, a sigmoid function can be used to represent clinoforms in a larger, shelf-slope margin settings (e.g., Steckler et al., 1999). By combining the height function (equation 1), with the shape function (equation 7), the clinoform shape function, BLTN13190eq63, is used to construct the shape of a clinoform surface:  

:<math>EQUATIONS/BLTN13190eqd8</math>

:<math>c(r_c) = h_{\text{min}}(r_c) + \left ( \frac{(r_{\text{max}}(x, y) - r_c(x, y))^P}{r_{\text{max}}(x, y) - r_{\text{min}}(x, y))^P} h(r_c) \right )</math>

By varying the exponent in the clinoform shape function, BLTN13190eq64, the user can increase or decrease the dip angle and change the shape of the clinoform ([[:File:BLTN13190fig2.jpg|Figure 2E]], Table 1). If a similar geometry is interpreted for each clinoform within a parasequence, because they are inferred to have formed under the influence of similar hydrodynamic and sedimentologic processes, then the same value of BLTN13190eq65 (equation 7) can be applied to each clinoform modeled in the parasequence. Different values of BLTN13190eq66 can be applied to distinct geographic regions of a parasequence in which clinoforms are interpreted to have different geometries (e.g., on different flanks of an asymmetric wave-dominated delta; Bhattacharya and Giosan, 2003; Charvin et al., 2010), provided that the bounding surfaces of these geographic regions have been defined (in the initial step of the method).

By varying the exponent in the clinoform shape function, BLTN13190eq64, the user can increase or decrease the dip angle and change the shape of the clinoform ([[:File:BLTN13190fig2.jpg|Figure 2E]], Table 1). If a similar geometry is interpreted for each clinoform within a parasequence, because they are inferred to have formed under the influence of similar hydrodynamic and sedimentologic processes, then the same value of BLTN13190eq65 (equation 7) can be applied to each clinoform modeled in the parasequence. Different values of BLTN13190eq66 can be applied to distinct geographic regions of a parasequence in which clinoforms are interpreted to have different geometries (e.g., on different flanks of an asymmetric wave-dominated delta; Bhattacharya and Giosan, 2003; Charvin et al., 2010), provided that the bounding surfaces of these geographic regions have been defined (in the initial step of the method).