## 1 Introduction  
The seismic attribute is a useful tool for hydrocarbon prediction, which is important in the petroleum industry. Many methods are proposed for hydrocarbon prediction from both reflectivity and impedance domains. The fluid factor in the reflectivity domain is one of the most popular and useful tools although it was introduced for more than 20 years ago. The fluid factor is defined as the difference between measured and estimated P wave velocity [1]. Its expressions are as follows:  
\[\text{FF}_{\text{Smith}}=\frac{\Delta V_{p}}{V_{p}}-a\frac{\Delta V_{s}}{V_{s}} /\gamma, \tag{1}\]  
where \(a\) and \(\gamma\) are the coefficients related to the Mudrock line [2] and fluid substitution, respectively. A recent work has been called \"new fluid factor (\(\text{FF}_{\text{new}}\))\" [3]. It is based on the J attribute [4] which is proposed to reduce the ambiguity using the amplitude versus offset (AVO) method in hydrocarbon prediction. To relate seismic amplitudes to geology, it is necessary to understand all the physical factors that influence seismic amplitudes [5]. Seismic amplitude is affected by pore fluid, rock matrix and porosity. J attribute is proven to be able to eliminate the porosity effect and enhance the accuracy in hydrocarbon prediction. The new fluid factor modified the equation of J attribute with consideration of the effect of the rock matrix. Mathematically, the new fluid factor is expressed as follows:  
\[\mathrm{FF_{new}}=J-J_{CT}, \tag{2}\]  
where,  
\[J=\mathrm{J_{p}sin\alpha-J_{s}cos\alpha}, \tag{3}\]  
\[J_{CT}=\mathrm{J_{p\_matrix}sin\alpha-J_{s\_matrix}cos\alpha}, \tag{4}\]  
where \(\mathrm{FF_{new}}\) is the new fluid factor, \(J\) is the \(J\) attribute, and \(J_{CT}\) is the correct term related to the rock matrix. The new fluid factor \(\mathrm{FF_{new}}\) is improved for hydrocarbon prediction with lower uncertainty. The brine responses are close to zero. Hydrocarbons are obviously separated from brine. The uncertainty of the new fluid factor value in the various \(V_{clay}\) cases are reduced to an acceptable degree without mixing between brine and hydrocarbons. The new fluid factor is stable in this scenario with various porosity and \(V_{clay}\)[3]. In the impedance domain, there are two popular methods to utilize the well log data or the inversion result. One is the cross plot of acoustic impedance (\(AI\)) and \(V_{p}/V_{s}\), which is introduced by [PERSON] and [PERSON] [6]. The brine sands and the shales in the sedimentary basin have a trend with the depth: low \(AI\) and high \(V_{p}/V_{s}\) in the shallow, and high \(AI\) and high \(V_{p}/V_{s}\) in the shallow. The response of brines and shales in the cross plot of \(AI\) vs. \(V_{p}/V_{s}\) is called the \"background trend\". Both \(AI\) and \(V_{p}/V_{s}\) shift towards lower values from the background trend when the rock contains hydrocarbons. Thus, this cross plot can be used to identify the hydrocarbon by the anomaly selection. Another technique is the Lambda-Mu-Rho (\(\lambda\)-\(\mu\)-\(\rho\)) to improve fluid dictation and lithology discrimination, where \(\lambda\) is 1 st Lame parameters, \(\mu\) is 2 nd Lame parameters or shear modulus, and \(\rho\) is density [7]. Mathematically, \(\lambda\) can be represented by bulk modulus \(K\) and shear modulus \(\mu\). The common attributes in the \(\lambda\)-\(\mu\)-\(\rho\) technique (\(\lambda\rho\) and \(\mu\rho\)) can be linked with acoustic impedance and shear wave impedance (\(SI\)). Generally, the hydrocarbon reservoir can be identified because it has lower \(\lambda\rho\) than brine sands. \(\lambda\rho\) and \(\mu\rho\) are defined as follows:  
\[\lambda\rho=AI^{2}-2 SI^{2}, \tag{5}\]  
\[\mu\rho=SI^{2}, \tag{6}\]  
The above methods work successfully in many hydrocarbon reservoirs, in particular, gas layers. Although these two methods have been proposed for more than 10 years, they are still applied in recent works [8; 9; 10]. A new method is named \"delta K (\(\Delta K\))\" [11].