Introduction

Shear wave velocity (VS) data is a key geophysical parameter in petroleum exploration engineering, for calculating elastic properties, evaluation of reservoir quality, and reservoir characterization. Unfortunately, this valuable information is not available in many wells, in particular the old wells, due to technical and/or cost-related problems (Greenberg and Castagna 1992; Nourafkan and Kadkhodaie-Ilkhchi 2015; Mehrgini et al. 2019; Kheirollahi et al. 2023). Therefore, in recent decades, many methods have been proposed to estimate the VS data from other related parameters, using methods such as empirical relations, rock physics templates, intelligent algorithms, and seismic attributes (Greenberg and Castagna 1992; Gholami et al. 2014, 2020; Du et al. 2019; Mehrgini et al. 2019; Babasafari et al. 2020; Leisi et al. 2022; Sadeqi et al. 2022; Kheirollahi et al. 2023; Leisi and Shad Manaman 2023). In recent decades, the use of petrophysical logs to estimate the VS has been suggested by many researchers (Nourafkan and Kadkhodaie-Ilkhchi 2015; Mehrgini et al. 2019; Rajabi et al. 2023; Kheirollahi et al. 2023). Mehrad et al. (2022) and Ebrahimi et al. (2022) estimated one-dimensional (1D) VS data from well-logging data in an Iranian carbonate oil reservoir using machine learning (ML) algorithms. However, these studies are limited to the well locations and don’t provide the VS distribution in the area between the wells. Thus, many researchers have used well-logging and seismic data integration for 3D reservoir evaluation and characterization (Imran et al. 2020; Leisi and Shad Manaman 2023; Mehdipour et al. 2024; Bashir et al. 2024). To obtain the VS information, various data can be used, including core, well-logging, and seismic data (Talha Qadri et al. 2019, 2021; Li et al. 2020). In some cases, it is possible to integrate several categories, for instance, the integration of wells and seismic data (Iturrarán-Viveros and Parra 2014; Kadkhodaie-Ilkhchi et al. 2014; Farfour et al. 2015; Guo et al. 2023; Bashir et al. 2024). The well-logging data have better accuracy and resolution. However, they are only limited to the location of the wells, while the seismic data cover the entire field area. Therefore, by combining these two groups of data, the cube of elastic parameters can be obtained in the reservoirs (Zahmatkesh et al. 2018; Saadu and Nwankwo 2018; Ali et al. 2020; Leisi and Saberi 2023; Bashir et al. 2022). Seismic attributes (SA) are extracted from seismic data and are widely used in predicting the lithological, geophysical, and petrophysical properties of reservoirs (Shalaby et al. 2020; Abdolahi et al. 2022; Bashir et al. 2022). The spatial variability of geophysical features can be analyzed using available wells and seismic data for reservoir characterization (Kadkhodaie-Ilkhchi et al. 2014; Farfour et al. 2015; Gogoi and Chatterjee 2019; Ashena et al. 2020; Guo et al. 2023).

In recent decades, Seismic attributes have been successfully applied for a variety of purposes in reservoir characterization (Kadkhodaie-Ilkhchi et al. 2014; Farfour et al. 2015; Gogoi and Chatterjee 2019; Leisi and Saberi 2023; Guo et al. 2023). In addition, the seismic data inversion to map the acoustic impedance (AI) has been proposed as the first step to estimate the petrophysical parameters of the reservoir, such as porosity, permeability, and lithology (Aftab et al. 2024; Leisi et al. 2024). AI is the product of the velocity and density of geological layers and has a substantial relationship with reservoir properties. Integration of well-logging data and SA is widely used to reduce the spatial uncertainty of the reservoir characterization (Leite and Vidal 2011; Zahmatkesh et al. 2018; Saadu and Nwankwo 2018; Ali et al. 2019; Aftab et al. 2023). Through valid prediction of geophysical and petrophysical parameters (reservoir characterization) by using well-logging and seismic data integration, the spatial distributions of geological properties are obtained, which can be applied to guide the drilling strategy for developing hydrocarbon reservoirs (Iturrarán-Viveros and Parra 2014; Kadkhodaie-Ilkhchi et al. 2014; Farfour et al. 2015; Leisi et al. 2022; Guo et al. 2023).

Hampson et al. (2001) and Leite and Vidal (2011) estimated reservoir porosity from 3D post-stack seismic amplitude data. In some case studies, machine learning algorithms have been successfully used to estimate reservoir parameters based on the integration of wells and seismic data (Khoshdel and Riahi 2011; Jalalhosseini et al. 2014; Na’imi et al. 2014; Iturrarán-Viveros and Parra 2014; Anifowose et al. 2016; Yasin et al. 2021). The results show that intelligent algorithms have better prediction accuracy than conventional and straightforward methods. Gogoi and Chatterjee (2019), Yasin et al. (2020), Yasin et al. (2021), Leisi and Saberi (2023) and Guo et al. (2023) estimated petrophysical features, such as porosity, permeability, fluid saturation, and lithology using integration of well-logging and seismic data inversion. As mentioned in literature studies, the 3D distribution of the petrophysical parameters of the reservoir can be estimated successfully using an integration of well-logging and seismic data. Recently, researchers have suggested well-logging and seismic data integration workflow to estimate the VS in the reservoir zone (Gholami et al. 2014, 2020). On the other hand, few studies have been assigned to the modelling of VS as a function of seismic attributes. The prediction of this geophysical parameter is of great importance in the studies of reservoir quality assessment, reservoir characterizations, and reservoir geomechanics.

In this research, we present an application of 3D post-stack seismic attributes for obtaining VS distribution in the Asmari formation in one of the Iranian oil fields. For this aim, first, seismic inversion was performed using a model-based algorithm to convert seismic section to the acoustic impedance (AI) section. In the next step, AI and seismic volumes were fed into the cross-validation (CV) algorithm to select the relevant attributes as input for VS volume prediction using the ANN. Moreover, we describe an innovative seismic and well-logging data integration workflow to predict the shear velocity volume in our case study. To evaluate the results, the computed VS logs and its section are compared with the actual logs, which have been neglected in previous studies. Since the conventional method for obtaining VS information by the inversion of pre-stack seismic data, is computationally costly and time-intensive, we used post-stack seismic data, which is available for many hydrocarbon reservoirs.

Geological setting

The studied formation in this research is the Asmari Formation in one of Iranian oil fields, which is located in Dezful embayment in southwest Iran. This youngest reservoir rock of the Zagros region is divided into sandstone and carbonate reservoir rocks. These reservoirs are geologically composed of calcite and quartz, and there is some dolomite in both zones (Amiri Bakhtiar et al. 2016; Zohrabzadeh et al. 2020). Asmari Formation reservoirs are divided into several zones by thin shaly interlayers. Structurally, the studied field is located in the folded Zagros zone. Most of the reservoir zones in Zagros oil fields consist of long anticlines that are the result of the Palaeocene, early Miocene, and Paleo-Pleistocene orogenes. The reservoir rocks of the study field are Asmari and Bangestan Formations (Ilam and Sarvak), as well as the source rocks include Pabdeh, Kazhdumi, and Gurpi (Amiri Bakhtiar et al. 2016; Zohrabzadeh et al. 2020). The Asmari Formation is the richest oil reservoir in Iran and the Middle East and one of the richest carbonate reservoirs in the world.

Database and methods

To predict the VS volume in the Asmari Formation, well-logging and 3D post-stack seismic data have been selected. This data includes six wells in which compressional wave velocity (VP), VS and density logs were measured, as well as check shot data to convert depth to time. Also, well tops and seismic horizons information have been used to distinguish the top and base of the reservoir. The actual VS logs are available in 3 wells (wells number 2, 4, and 6), and in other wells (wells number 1, 3, and 5), VS data is calculated using the regression method from VP and density (\(\rho\)) logs. To predict VS log in blind wells, the regression methods are presented for Asmari formation in well #2. Because the Asmari Formation consists of carbonate and sandstone sections, the following models are provided in each section.

$$V_{S} = 751.04 + 0.304 V_{P} + 153.1 \rho \quad ({\text{for carbonate reservoir}})$$
(1)
$$V_{S} = 1620.38 + 0.308 V_{P} - 227.83 \rho \quad ({\text{for sandstone reservoir}})$$
(2)

Figure 1 shows the scatter-plot between the actual and estimated VS data using Eqs. (1) and (2) in well #2. The scatter-plot of the estimated versus actual shear wave velocities, which are presented in Fig. 1, have a correlation of 91%. This level of correlation justifies using regression relations for the wells that lack shear wave velocity data.

Fig. 1
figure 1

The comparison of the actual and estimated VS data using proposed regression models in well #2. The color bar shows the depth

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The statistical description of well #2 data is given in Table 1. Also, the graphical demonstration of the used logs in well #2 is shown in Fig. 2.

Table 1 The statistical description well #2 data
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Fig. 2
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The graphical representation of petrophysical logs in well #2. From left to right: VP, VS and ρ logs. The vertical axis shows the true vertical depth from Kelly bushing

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To provide a practical workflow to predict shear wave velocity volume using the integration of well-logging and seismic attributes in our case study, the following steps have been taken:

  • Data import such as well logs, seismic, horizons and well tops.

  • Using check shot data, we corrected the relationship between the time and depth for each well.

  • Wavelet extraction to generate synthetic seismograms (at each well) using statistical method.

  • Well to seismic correlation (investigating the correlation between synthetic seismograms and actual seismograms at each well). The convolution model of forward modelling to generate synthetic seismograms is written as follows:

    $$S\left( t \right) = R\left( t \right)*W\left( t \right) + N\left( t \right)$$
    (3)

where \(S\left( t \right)\), \(R\left( t \right)\), \(W\left( t \right)\) and \(N\left( t \right)\) represent seismic trace, reflection coefficient, wavelet and noise, respectively, and * is convolution operator. The reflection coefficient is also defined as follows:

$$R_{i} = \frac{{AI_{i + 1} - AI_{i} }}{{AI_{i + 1} + AI_{i} }}$$
(4)

where \(AI_{i}\) is acoustic impedance of ith layer, and \(R_{i}\) is reflection coefficient between ith and \(\left( {i + 1} \right)\)th layers. AI is acoustic impedance and defined as follows:

$$AI_{i} = V_{{P_{i} }} \rho_{i}$$
(5)

where \(V_{{P_{i} }}\) is compressional wave velocity of ith layer, and \(\rho_{i}\) is density of ith layer (Azevedo et al. 2021; Soares 2021).

  • Generating an initial model for recovering lower frequencies and adding it to the final model.

  • In this step, we inverted the 3D post-stack seismic section to the acoustic impedance section using a model-based seismic inversion algorithm.

  • Selection of the relevant seismic attributes related to shear wave velocity (VS) using the CV method. Two crucial parameters in the CV method are the optimal selection of the operator length and attribute numbers. The first parameter eliminates the frequency difference between well-logging and seismic data, and the second is determined so that the validation error reaches the lowest value. In the CV method, when the validation error reaches the global minimum value, the optimal number of attributes is selected.

  • Finally, the VS volume is estimated from selected seismic attributes using the ANN method and, its distribution in the entire reservoir area is determined. The workflow comprises of some major steps as represented in Fig. 3.

Fig. 3
figure 3

The flowchart for the prediction of VS distribution using integration of well-logging and seismic data

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Results and discussion

We have demonstrated the use of well logs and seismic data integration approach to predict VS volume in Asmari formation. The major step is performing seismic data inversion to convert seismic volume to the acoustic impedance volume. The statistical wavelet and model-based algorithm are employed for synthetic seismogram generation and seismic data inversion, respectively. In Fig. 4, the extracted statistical wavelet is represented. The wavelet presents in Fig. 4 is a zero-phase wavelet which has been extracted from seismic data employing statistical methods. Accurate extraction of wavelet is the key step in seismic inversion and directly influences the results. The performance of the model-based algorithm for synthetic seismogram generation and acoustic impedance estimation at the location of well #3 is displayed in Fig. 5, and for other wells are given in Table 2. As depicted in Fig. 5 and Table 2, there is a high matching between synthetic and actual seismograms.

Fig. 4
figure 4

The extracted statistical wavelet to synthetic seismogram generation. a Time domain, b frequency domain

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Fig. 5
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a The comparison of the original AI log with estimated AI log, b the correlation and error between synthetic and actual seismogram in the location of well #3

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Table 2 The results (the correlation and error between actual and estimated values) of the model-based inversion method at the location of each well
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The cross-plot between the actual and estimated acoustic impedance using the model-based algorithm in the location of wells is displayed in Fig. 6, which indicates a strong correlation. As it is seen from Figs. 5 and 6, the performance of the model-based seismic inversion algorithm is acceptable. Firstly, there is high concordance between the calculated and the actual seismogram. Secondly, the correlation between the predicted and actual acoustic impedance is more than 96% for all of the wells (Table 2). Thus, we used the model-based seismic inversion algorithm for calculating acoustic impedance volume in reservoir zone (Fig. 7). As the acoustic impedance is the product of velocity and the density of the layers, the denser rocks have higher impedances. In contrast, the acoustic impedance is smaller in hydrocarbon reservoirs due to porosity and reserved fluids. Moreover, lithologic variations result in variation in impedance (Fig. 7). According to Fig. 7, porous zones have lower impedance and can be identified by the AI section. Also, the change in lithology has caused a change in impedance (hard rocks have a higher impedance than soft rocks).

Fig. 6
figure 6

The cross-plot between the actual and estimated acoustic impedance (AI) in the location of wells. The color bar shows the time

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Fig. 7
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The acoustic impedance section. As can be seen, there is a very high similarity between the cross-section and the actual log at the location of well #2

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After post-stack seismic data inversion and obtaining the AI section, AI and seismic data were fed into the CV method to select the relevant attributes for VS volume prediction using the ANN. Our inputs are selected attributes, and the target is VS. According to the CV algorithm, the set of attributes that have the lowest validation error with the target parameter (VS) has been selected as the optimal inputs for prediction. The results of the CV method to select the relevant attributes are given in Tables 3 and Fig. 8.

Table 3 The list of attributes is given to the CV method to select the optimal number of the relevant attributes for VS volume prediction, with corresponding training and validation errors
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Fig. 8
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The selection of an optimal number of attributes in the CV method

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According to the results of the CV method (Fig. 8 and Table 3), the validation error has reached the global minimum in attribute number 5. But in this article, we have chosen 14 attributes as the optimal number for VS cube prediction. When the number of attributes increases from 1 to 14, the validation error doesn’t significantly change, but from 14 to 27, the error is greatly increased. In our case study, the combination of 14 attributes has better prediction accuracy than 5 attributes. Therefore, 14 attributes with an operator length of 5 (the attribute of the Acoustic impedance, quadrature trace, amplitude weighted frequency, time, dominant frequency, average frequency, Amplitude Envelope, filter 35/40–45/50, Instantaneous Phase, Amplitude Weighted Phase, Second Derivative Instantaneous Amplitude, Filter 5/10–15/20, Filter 45/50–55/60, and Filter 55/60–65/70) have been used to estimate the shear wave velocity distribution in the entire reservoir area. The section of the raw seismic data and some extracted attributes from it to estimate the VS cube is displayed in Fig. 9. So, the VS volume is predicted from selected attributes as input features using ANN (Figs. 10 and 11). The distribution of shear-wave velocity in Asmari reservoir is presented in Figs. 10 and 11, respectively, around wells #2 and #4. Also included in both Figures are the actual VS logs to illustrate the excellent correlation between logs and the sections. As it may be remarked from the Figs. 10 and 11, the VS at the lower parts of Asmari formation is less than the VS at upper parts, because the sandstone constituent of the lower part is less dense than the carbonate constituents of the upper part and the VS scales with the density. According to Figs. 10 and 11, the interlayers with a thin thickness are also detected by the obtained section.

Fig. 9
figure 9

The section of selected attributes for VS prediction. a Raw seismic data, b amplitude envelope, c instantaneous phase, d dominant frequency, e amplitude-weighted frequency, and f quadrature trace

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Fig. 10
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The obtained VS section using seismic attributes in the reservoir zone. The actual VS log in well #2 is shown on the section, which shows that there is a good matching between the log and the section

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Fig. 11
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The obtained VS volume using seismic attributes in the reservoir zone. The actual VS log in well #4 is shown on the section, which shows that there is a good matching between the log and the section

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The performance of the proposed method for estimation of the VS in the location of wells, based on the seismic attributes as input data of the model is presented in Figs. 12 and 13. As it is seen, there is a high matching (correlation) between predicted and real data. Therefore, this method can be utilized to build a 3D model of VS (Fig. 14). Figure 14 shows the 3D prediction of the VS in the Asmari reservoir area. According to Fig. 14, as the Asmari formation in this case study is divided into two parts, carbonate (upper zone) and sandstone (lower zone), the VS values in the upper zone are higher than the lower zone (because carbonates are denser than sandstones).

Fig. 12
figure 12

The comparison of the actual and estimated VS logs using seismic attributes at the location of wells

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Fig. 13
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The comparison of the estimated VS logs using regression method and seismic attributes at the location of the blind wells

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Fig. 14
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The 3D representation of the VS in the Asmari formation

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The results show that if the VS information can be obtained using seismic attributes, these results can be applied across the entire reservoir area to predict elastic properties such as Young's modulus, bulk modulus, Poisson's ratio, and shear modulus. Though it is convenient to use pre-stack seismic inversion for estimating shear wave velocity volume, but those data are massive and requiring costly and time-consuming processing for inversion. Therefore, in the present study, we have used post-stack seismic data for estimating 3D shear wave velocity. Moreover, the easy-to-use post-stack seismic data are available for most hydrocarbon reservoirs.

Conclusions

In this study, attempts were made to show an application of well-logging and seismic data integration in the estimation of shear wave velocity (VS) distribution in the Asmari formation (AF). For this aim, first, a model-based seismic inversion (MBSI) algorithm was employed to convert the seismic volume to the acoustic impedance (AI) volume. In the next step, AI and seismic data were fed into the cross-validation (CV) method to select the relevant attributes for VS cube prediction. The followings are concluded:

  • We found out that the combination of the CV method with the artificial neural network (ANN) is an optimal integrated workflow to predict the VS distribution using seismic and well-logging data.

  • The use of the proposed method in this research to estimate VS data eliminates the requirement of conducting a dipole shear imager (DSI) log for measuring this feature in all wells, and spatial variability of this parameter in the entire area of the reservoir can be determined.

  • Our results indicated that a reliable correlation between the actual and estimated values for VS is provided with the coefficient of determination of 94% and root mean square error (RMSE) of 109 m/s.

  • In addition to the one-dimensional (1D) estimation of the VS, the three-dimensional (3D) distribution of the VS can be estimated using seismic and well-logging data integration.

  • The spatial variability of the VS can be analyzed using available wells and seismic data for various purposes in petroleum engineering, such as reservoir characterization, elastic properties calculation, reservoir quality assessment and reservoir geomechanics.

  • The integration of well-logging data and seismic attributes for the VS cube estimation can be used to reduce the spatial uncertainty of the reservoir characterization.