According to Hafez (2017) [6] , the earth subsurface comprises stratified rock layers that have different elastic properties. The boundaries separating the individual layers are referred as interfaces (Figure 1).

The wave transmission and reflection coefficients are obtained from the partition of amplitudes that occurs when an incident plane wave strikes a plane interface separating two elastic, homogeneous, isotropic, and semi-infinite layers [7] .

According to Yenwongfai (2011) [4] , an incident P-wave striking orthogonally the interface generates only other P-waves (reflected and transmitted). However, when the impact is not orthogonal, a pair of S waves (reflected and transmitted) is also generated as shown in Figure 2.

The waves at the interface are reflected and refracted according to Snell’s Law (Equation (1)).

sin θ 1 sin θ 2 = v 1 v 2 (1)

The reflection coefficient can be defined as Shuey approximation to Zoeppritz equations providing the angular dependence of the reflection coefficient R ( θ ) of the P wave with two parameters: the intercept AVO (A) and the AVO gradient (B) (Equation (2)) [9] .

R ( θ ) = A + B sin 2 ( θ ) (2)

In practice, the “A” is a measure of the amplitude of normal incidence, indicating the normal reflection coefficient when θ = 90˚ and “B” is a measure of amplitude variation with offset [9] .

From the view of seismic acquisition, seismic trace is a measure of time associated with a source-receptor pair. The distance between the source and the receptor is referred as offset. The main parameters used to generate a synthetic seismogram are density and speed that provide acoustic impedance, besides the waveform used, which is called wavelet [4] .

The reflectivity relates layers with contrasting acoustic impedances. Thus, the reflection coefficients are calculated to determine the density and velocity profiles. However, the reflection coefficients are a function of depth, then a conversion to time is necessary. This conversion can be accomplished by choosing a sampling time, transforming speed profiles, which are a function of depth to profiles in transit time function [10] .

Thus, the seismic traces are formed by a process called “convolution” of a series of reflection coefficients with a predefined wavelet (Equation (3)).

S ( t ) = w ( t ) r ( t ) (3)

In which S ( t ) is the synthetic seismic trace, w ( t ) is the wavelet and r ( t ) is the reflectivity. Figure 3 illustrates this process.

The AVO (Amplitude Versus Offset) analysis has been widely used in the oil and gas industry. This methodology is based on seismic amplitude response in a remote receptor. In addition to direct amplitude analysis, the graphs of the reflection coefficients from the top and the base of the reservoir allow the AVO classification

associated to anomalies, which may be a support tool of hydrocarbon indication [10] .

According to Ahmed et al. (2017) [11] , the AVO analysis has been used in hydrocarbon exploration due to be able to discriminate the hydrocarbon fluids from background geology. Conventionally, AVO analysis involves calculation of intercept and gradient from a linear fit of compressional wave reflection coefficient to the sine square of the incidence angle as Equation (2).

The AVO study allows to predict the variation of the reflector amplitude as a function of the source-receiver distance. Often, with this study, it is possible to infer the type of fluid and its distribution in a certain rock, mostly considered to be isotropic [7] .

The AVO modeling is an applied technique that allows the determination of the manner in which changes in density, velocity, lithology, porosity, fluid content, and thickness affect a seismic response [9] .

According to Yenwongfai (2011) [4] , the AVO anomalies are generally divided into four classes (Figure 4) depending on the coefficients of Equation (2).

Class I

The class I anomaly occurs when the normal incidence reflection coefficient (A) is strongly positive, showing a reduced amplitude with offset and the possible change in polarity for larger offsets, e.g. mature sands highly compressed in onshore environments.

Class II

The class II occurs when the normal incidence reflection coefficient (A) is small. Polarity changes may occur for near or moderate offsets. Some authors subdivide the anomaly into type II and IIp. In type II anomaly, the coefficient

(A) from Equation (2) is slightly positive, but with reverse polarity obtained because of displacement, it becomes slightly negative. In type IIp anomaly, coefficient (A) from Equation (2) is slightly negative, becoming more negative with the displacement e.g. sands showing median compression levels, common in offshore and onshore environments.

Class III

The class III anomaly occurs when the normal incidence reflection coefficient (A) is negative, becoming even more negative with the distance from source-receptor. In this case, there is a large reflectivity at all offsets, commonly being called bright spot anomaly occurring in typical marine sands.

Class IV

The Class IV anomaly is a subdivision of Class III. In this case, the coefficient at normal incidence (A) is negative, but the AVO gradient (B) has an anomalous behavior, being positive. This class is related to the presence of gas with inferior velocity compared to overlapping rock, thereby the amplitude decreases with the distance. Some sands of this class occur in the marine environment.

The classes of anomaly can be quickly interpreted through the crossploting graph (Figure 5) of the coefficients A and B from Equation (2).

The analysis of crossplot (A × B) is widely used to interpret AVO anomalies and infer the type of fluid in the pores of a rock. Since some rocks trend deviations can be hydrocarbon indicators [10] .

The analysis of the anomalies and crossplot A × B was synthesized by Castagna and Swan (1997) [9] shown in Table 1.

The study region has as interfaces the base of the salt and the base of the sag regions, being indicated by an arrow, according to Figure 8.

The simulated model is composed by three rock layers, chosen according to the geological model of the proposed region, configuring a possible “trap” with the source, reservoir and seal rocks of an oil system. Figure 9 highlights the region shown in Figure 8.

The region anomaly was verified by using values of sandstone filled with water and gas (Table 2).

Through SeisMod 1.04 software from Protolink, it was possible to obtain the seismogram of the region (Figure 10 and Figure 11), its reflection coefficient (Figure 12 and Figure 13), and the crossplot (Figure 14 and Figure 15), allowing us to classify the anomalies.

Seismogram analysis of sandstone filled with water (Figure 10) revealed that the input reflector presented a positive amplitude anomaly, meaning that the acoustic impedance of the sandstone layer filled with water is greater than the impedance anomaly of the overlying salt layer (gypsum). On the other hand, the anomaly of the output reflector is negative, denoting that the acoustic impedance of the shale layer is less than the acoustic impedance of the sandstone layer.

Seismogram analysis of sandstone filled with gas (Figure 11) revealed that the input reflector presented negative amplitude anomaly, meaning that the acoustic impedance of the sandstone filled with gas is smaller than the acoustic impedance of the overlying salt layer (gypsum). The output reflector anomaly remained negative, denoting that the acoustic impedance of the shale layer is lower than the acoustic impedance of the sandstone layer. Furthermore, it was noticed a slight delay in the response using the gas saturated system due to a lower wave velocity in sandstone saturated with gas.

The AVO analysis (Figure 12) denotes that layer 1 (red) has an anomaly classified as a Class II because the reflection coefficient of the first layer starts small and positive, but it becomes negative with increasing offset. According to the crossplot graph (Figure 14), the same anomaly can be observed. It is observed that layer 1 (red) is in the region of class II anomalies.

When the sandstone parameter is changed, now saturated with gas (Figure 13), we obtain a new type of anomaly in layer 1 (red), where analyzing the graph of the reflection coefficient and comparing with the characteristics of the anomalies, we conclude that layer 1 can now be classified as a Class III because the reflection coefficient of the first layer starts negative and becomes more negative with increasing offset. According to the new crossplot graph of the region (Figure 15), the same anomaly can be observed. It is observed that layer 1 (red) is in the region of class III anomalies. That is, lowering the acoustic impedance of the sandstone results in negative reflection coefficients, changing the anomaly from II to III with the change in saturation from water to gas.