## 3 Dataset and Methods
### Methods
#### 3.2.1 Rock Physics Study  
The cross-plotting approach was used in rock physics study. The main aim of this approach is to visibly recognise or observe anomalies, which could be inferred as the existence of hydrocarbons or other fluids, and the type of lithology. Three types of cross-plots are generated in this study, i.e., \(\mathrm{Vp}/\mathrm{Vs}\) ratio versus P-Impedance, \(\mathrm{SQp}\) versus \(\mathrm{SQs}\), and lambda-rho versus mu-rho. The cross-plot zonation is then carried out to identify the cluster patterns of lithology and fluid type from the resulting elastic parameter cross-plots. A direct understanding of the reservoir characterisation can be obtained from Lame parameters, which normally consist of lambda (\(\lambda\)) and mu (\(\mu\)) parameters. A cross-plot of lambda-rho (\(\lambda\rho\)) versus mu-rho (\(\mu\rho\)) can be used to classify the lithology and types of pore-filled fluids. \(\lambda\rho\) and \(\mu\rho\) are derived from P- and S-Impedances, as in Equations (1) and (2). The basic principle in characterising lithology from the perspective of the Lame parameter is the relationship amidst incompressibility (\(\lambda\)) and rigidity (\(\mu\)) [16]. An implication of grains organisation can be gained through the dispersion of stress between Lame parameters when a rock experiences effective stress. For instance, when a substance is more incompressible than rigid (\(\lambda>\mu\)), an anisotropic division of stresses distorts the grain shape, causing considerable aspect ratios. These types of grain shapes are frequently discovered in laminated shales. Suppose there is equal dissemination of stress (\(\lambda=\mu\)). In that case, the grains are identified as having an aspect ratio of 1, or the grains are randomly ordered. This grain characteristic is regularly observed in the sand. Therefore, the ratio of lambda to mu is beneficial in recognising shale versus sand lithologies [17]. For fluid identification, considering the rock characteristics do not alter, the Lame parameter affected is only \(\lambda\). As an example, sand can be filled with various types of fluids. The fluid will reduce the incompressibility of the sand. The incompressibility is least affected by brine, while gas is affected the most. The following are the Equations (1) and (2). \[\lambda\rho=Z_{\mathrm{P}}^{2}-Z_{\mathrm{s}}^{2} \tag{1}\]  
\[\mu\rho=Z_{\mathrm{s}}^{2} \tag{2}\]  
where \(2.0\leq c\leq 2.5\), \(\rho\) represents density, \(\mathrm{Zp}\) is acoustic impedance, \(\mathrm{Zs}\) is shear impedance [16]. Furthermore, the novel attributes, \(\mathrm{SQp}\), and \(\mathrm{SQs}\) attributes were implemented in rock physics study in this work. These attributes allow minimising the ambiguity in reservoir characterisation from seismic data. The \(\mathrm{SQp}\) and \(\mathrm{SQs}\) attributes were also implemented to enhance petrophysical properties prediction accuracy. These attributes were derived from elastic properties and successfully proved their effectiveness in formation evaluation, reservoir characterisation, facies classification [18; 19; 20]. \(\mathrm{SQp}\) attributes have a similar response as gamma-ray that indicate the lithology. In contrast, the \(\mathrm{SQs}\) attribute gives a similar response to resistivity. \(\mathrm{SQp}\) and \(\mathrm{SQs}\) attribute in well log scale has been successfully patented [21]. \(\mathrm{SQp}\) and \(\mathrm{SQs}\) attributes were derived from the following equations:  
\[\mathrm{SQp}=\frac{5}{6}\frac{1}{\rho}\Bigg{[}\frac{\left(\left(\frac{\mathrm{ M}}{\mathrm{G}}\right)^{2}-2\right)^{2}}{\left(\left(\frac{\mathrm{M}}{\mathrm{G}} \right)^{2}-1\right)}\Bigg{]} \tag{3}\]  
\[\mathrm{SQs}=\frac{10}{3}\frac{1}{\rho}\Bigg{[}\frac{\left(\left(\frac{\mathrm{ M}}{\mathrm{G}}\right)^{2}\right)}{\left(3\left(\frac{\mathrm{M}}{\mathrm{G}} \right)^{2}-2\right)}\Bigg{]} \tag{4}\]  
where \(\mathrm{M}/\mathrm{G}\) is the bulk and shear modulus ratio that can be approximated from the P-wave and S-wave velocity ratios [22].