*Article* **Applicability Analysis of Pre-Stack Inversion in Carbonate Karst Reservoir**

**Rui Wang <sup>1</sup> and Bo Liu 2,\***


**Abstract:** Although pre-stack inversion has been carried out on reservoir prediction, few studies have focused on the application of pre-stack for seismic inversion in fractured-cavity carbonate reservoirs. In carbonate rock, complicated combinations and fluid predictions in karst caves are remain unclear. Post-stack methods are commonly used to predict the position, size, and fillings of caves, but pre-stack inversion is seldom applied in carbonate karst reservoirs. This paper proposes a pre-stack inversion method for forward modeling data and oil survey seismic data, using both points to indicate the application of pre-stack inversion in karst caves. Considering influence of cave size, depth, and filler on prediction, three sets of models (different caves volume; different fillings velocity of caves; complicated combination of caves) are employed and inverted by pre-stack inversion. We analyze the pre-stack results to depict Ordovician oil bearing and characterize caves. Geological model parameters came from actual data of the Tahe oilfield, and seismic data were synthesized from geological models based on full-wave equation forward simulation. Moreover, a case study of pre-stack inversion from the Tahe area was employed. The study shows that, from both the forward modeling and the oil seismic data points of view, pre-stack inversion is applicable to carbonate karst reservoirs.

**Keywords:** carbonate cavern reservoir application; pre-stack inversion; model

#### **1. Introduction**

Unconventional energy sources and those of deep oil and gas are showing increasing significance in energy structures, and the demand for exploration is increasing in China [1,2]. The Tarim Basin is a famous oil-rich basin in China with significant deep carbonate reserves, and is an important energy source for China. However, The Ordovician carbonate rocks in the target layer are buried at a depth of about 5500–6500 m, and fractured vuggy reservoirs show "string of beads" characteristics in the seismic section. The seismic responses of caves usually consist of one–three seismic peaks and troughs, which look like strings of beads. Therefore, it is called the beaded response [3–6]. Karst caves are generally made up by soft, porous fillings and fluids, surrounded by tight carbonate rocks. This composition leads to considerable impedance differences. In addition, the caves are limited not only vertically but also horizontally; as a result, their bright spots are limited both vertically and horizontally [7,8]. Caves are a main type of reservoir in the Tarim Basin [9]. Geologically, it is because of tectonic action that large faults were initially formed, and after uplifting and exposing the surface, they were leached by atmospheric water and eroded along the faults, thus forming favorable storage spaces. At present, the structure and distribution of fractured cavity reservoirs are not clear. Petroleum engineers must characterize combination and fluid-bearing caves and design wells to improve enhanced oil recovery (EOR) [10]. In recent years, due to the complexity of fractured cavity carbonate reservoirs and the multiresolution nature of seismic data, it is necessary to understand the

**Citation:** Wang, R.; Liu, B. Applicability Analysis of Pre-Stack Inversion in Carbonate Karst Reservoir. *Energies* **2022**, *15*, 5598. https://doi.org/10.3390/en15155598

Academic Editors: Yong Li, Fan Cui and Chao Xu

Received: 5 July 2022 Accepted: 27 July 2022 Published: 2 August 2022

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prediction ability of seismic data, analyze the fillings or fluids in karst cavity reservoirs, and the improve quantitative analysis approaches for carbonate reservoirs.

Previous studies have shown that post-stack inversion has been commonly used for characterization of the top of caves, which has achieved certain results; however, research concerning the application of P-impedance elastic parameters to characterize caves is limited, and there are not many applications of other elastic parameters [11,12]. Previous researchers indicated that AVO (amplitude variation with offset) attribute analysis technology can be used to identify fluids in carbonate reservoirs, and the fluid prediction accuracy reached 83.3%, indicating that the elastic parameters information of pre-stack seismic data is more abundant, and it is a requirement for carrying out pre-stack seismic inversion research. Therefore, for the purposes of clarifying the quantitative prediction ability and reliability of pre-stack seismic inversion, this study addresses its use in a carbonate karst reservoir, in the interest of hydrocarbon exploration and development.

Pre-stack elastic impedance inversion contains more lithological and elastic impedance and physical information than post-stack impedance, and is obtained independently from pre-stack seismic data, rather than from acoustic impedance, as is the case in traditional poststack inversion [13]. Thus, this makes up for the shortcomings of the acoustic impedance inversion results overlapping in the reservoir and increases the capacity of seismic inversion to predict the characteristics of reservoirs. Pre-stack inversion has rarely been applied to the Tarim Basin. A previous researcher [14] physically modeled the seismic response of a karst cave, and drew some conclusions surrounding the effects of the cave scale, velocity, spatial distribution, shape, and fluids on the "beads" and the corresponding relationships between six types of "beads" and karst caves; However, there is no validity analysis for pre-stack inversion. The authors of [15–19] used pre-stack inversion based on seismic data for an Ordovician TZ45 area, and indicated that pre-stack inversion can be applied for cave carbonate reservoir prediction. We note that previous researchers have not made a complete argument for the validity of pre-stack inversion in carbonate reservoirs.

In this study, we use pre-stack inversion from two perspectives to a carbonate cavern reservoir: the accuracy of the pre-stack inversion based on forward seismic data; application of pre-stack inversion based on measured seismic data in Tarim. First, three sets of geological models that take into consideration different cave sizes, cave buried depths, and fills in cave are constructed using the Tarim karst cave reservoir parameters Subsequently, Seismic inversion study by Jason Workbench was performed using synthetic seismic data that was generated by forward modeling using the full-wave equation on the basis of the above geological model [20–23]. Pre-stack inversion's characteristics are analyzed, along with the application impacts of pre- and post-stack inversion in complicated combination geological models and various fluid geological models [24,25]. Finally, the cave carbonate reservoirs in the Tahe area are predicted using pre-stack inversion. According to the findings of our study, pre-stack inversion is a viable method for predicting complicated fracture-cavity carbonate reservoirs since it significantly improves reservoir prediction accuracy.

#### **2. Geological Modeling Design**

The geological model in the paper was designed to simulate carbonate karst reservoirs with various velocities, depths, and scales. In this section, we describe the construction of our geological model in detail.

#### *2.1. Model Design*

The model design was based on both easy and difficult concepts and considers three cases: the external shape of the cave, the internal filling of the cave, and the cave system. According to the computing conditions and computing power required by the threedimensional wave equation, the length of the smallest cave we designed is 10 m, and the lengths of other caves are different multiples of 10 m. The main frequency of the target layer is 30 Hz. The wavelength of a seismic wave in a cave would be 100 m based on a velocity of 3000 m/s, and the wavelength of a seismic wave in a cave would be 133 m based

on a velocity of 4000 m/s; if the average speed of the upper layer of an Ordovician system is 4000–4500 m/s, then the wavelength of the earthquake wave in the Ordovician upper layer is 133–150 m. Therefore, when studying the resolution of a cave, the size of the cave can be set with a multiplied wavelength. Considering that the analysis needs to minimize the influence of structural relief on a given reservoir prediction, the stratigraphy frame tends to be designed with horizontal layers. The vertical depth of the entire three-dimensional model was controlled within 4 km.

In the Tarim Basin, the velocity of 4000 m/s is the average value of oil-bearing layers in carbonate reservoirs. In addition to reservoir filling fluid differences, the size of the caves also affects the accuracy of reservoir predictions. Therefore, we divided karst caves into three different sets by considering the complicated combination of characteristics and the accuracy of reservoir prediction. Table 1 gives the P wave velocity, density, and S wave velocity for 3 sets of models and 18 caves.


**Table 1.** Parameters of modeled caves.

Geological model 1: Different fillings in the karst caves. Six caves were designed in model 1. Differences in seismic response caused by different fillings in karst caves. Figure 1a,d show depth domain geological model, Figure 1a shows a section of the model, Figure 1d shows a map of the model. The study area of model 1 is within the black dotted line. The six different colored caves in the model are the same size, and the volumes are all 40 m × 40 m × 40 m. Their filling velocities are 2800 m/s, 3150 m/s, 3550 m/s, 4200 m/s, 4550 m/s, and 5150 m/s; these are equivalent to gas, live oil, oil, oil–water, argillaceous, and calcareous mudstone fillings, respectively. More than 100 m separate the caves, ensuring that their seismic reflections are independent of one another.

Geological model 2: Different sizes and depths. Differing vertical and horizontal seismic resolutions were modeled for the caves. Figure 2a,d present a view of the depth domain and the models map: Figure 2a shows a section of the model; Figure 2d shows a map of the model. A series of models with varying volumes are designed to analyze the reflection characteristics. We based our study on the background of karst paleogeomorphology and previous research. The length, width, and height of the caves are 10 m, 20 m, 40 m, and 80 m, respectively, which correspond to lengths of 1/16, 1/8, 1/4, and 1/2 the wavelengths, in which the filling velocity is 4000 m/s. The depths from the top interface are between 0 m and 70 m. The distances of the caves from each other more than 100 m, which ensures that the seismic reflections between the caves do not interact with each other.

**Figure 1.** Models of different fillings in the caves. Geological model 1: (**a**,**d**) geological models; (**b**) seismic model; (**c**) RMS amplitude map.

**Figure 2.** Model of caves of different sizes and depths. Geological model 2: (**a**,**d**) geological models; (**b**) seismic models; (**c**) RMS amplitude map.

Geological model 3: Complicated combinations. This model addresses reservoir lateral connectivity and adjacent caves imaging problems. The analysis of the different reservoir predictions was influenced by the different sizes of the caves and the different distances between them. Figure 3a,d present the view of the depth domain and the map models: Figure 3a shows a section of the model; Figure 3d shows a map of the model. The lateral intervals between the caves are 10 m, 20 m, 80 m, and 120 m. The sizes of caves are 10 m × 10 m, 20 m × 20 m, 80 m × 80 m, 160 m × 160 m, 80 m × 160 m, 20 m × 160 m, and 10 m × 160 m, respectively. All caves have the same velocity of 4000 m/s.

**Figure 3.** Model of complicated combination caves. Geological model 3: (**a**,**d**) geological models; (**b**) seismic models; (**c**) Seismic RMS amplitude map.

#### *2.2. Method and Workflow*

Methods for forward modeling seismic using geological models. The basic steps are as follows: (1) The model is drawn in the display interface based on the principle of non-average quality, layer-shaped technical principles; (2) We accounted for the seismic geometry parameters, the sampling interval, the sampling point, and the initial conditions; (3) The vertical wave dynamic equation can be set as an acoustic wave, an elastic wave, or a viscoelastic wave. The details directly affect the output results, including the decision of whether to use a high-order algorithm, mesh parameters, and boundary bars; (4) Solve the equation. The acoustic wave equation model contains the conversion wave and the S wave effects. It accounts for the distribution of density, the P waves, and the S wave velocity [24,25]. When the wave transitions to the segmentation interface, it produces reflective waves, transparent waves, scattered waves, and wound waves, etc. We used three-dimensional acoustic wave equation modeling [26,27]. In the interest of simulating the actual conditions more precisely, seismic data were used, and the results of each model

are shown in Figures 1b, 2b and 3b. In this study, we did not focus on model simulation and seismic reflection instead of the application of pre-stack seismic inversion.

Pre-stack seismic inversion was used to study the applicability of different sets of karst caves in analyzing carbonate caves reservoirs. Synthetic seismic are obtained using 3D full wave equation forward modeling to simulate shot-gather records and then using the Kirchhoff pre-stack depth migration process. As such, our work refers to the main frequency of the actual area in Tahe oil field. A theoretical 30 Hz wavelet was used as the source wavelet, and the max-offset range was 5200 m for forward modeling simulation process [28,29]. We used RockTrace (a CGG pre-stack inversion module) to estimate the elastic parameter (a combination of the P wave velocity, the S wave velocity, and the density) using contained data in multiple-input seismic data (either partial angle stacks or partial offset stacks) to ensure that the entire research process was as close as possible to the actual pre-stack inversion work. As such, we aimed to objectively reflect the effect of applying pre-stack inversion. At each CRP gathering point, the seismic value was recognized as the convolution of a set of reflection coefficients with one or more wavelets. The reflection coefficients were educed from the elastic parameters using Knott–Zoeppritz equations. Converting the angle-dependent seismic amplitudes to elastic parameters provided a quantitative measure of the rock properties.

The RockTrace constrained sparse-peak inversion module created an elastic model based on the superposition of multiple seismic parts (angles or offsets). In each CMP, earthquakes were modeled as a set of reflection coefficients, which convolved with one or more wavelets. The reflection coefficient was derived from the elastic parameter using Knott– Zoeppritz equations (P+P−, P+S−, S+P−, and S+S− reflectivity) or the Aki–Richards approximation. Figure 4 displays the pre-stack constrained sparse-spike inversion which was used in this study. Pre-stack seismic inversion was used in the development of three sets of models. P wave velocity, P wave impedance, S wave impedance, *Vp*/*Vs*, and density were produced by inversion. High inversion data quality should be ensured before analysis of the application of pre-stack inversion.

**Figure 4.** Pre-stack constrained sparse-spike inversion workflow.

#### **3. Results**

The carbonate fracture-cave reservoir can be approximately assumed to be an HTI anisotropic medium [28–31], but since the scale of the cave reservoir formed by karst is much larger than fractures, it is approximated as is an isotropic medium. Therefore, the velocity of the geological model and the velocity of the pre-stack inversion can be compared as the best method to evaluate the quality of the inversion data (Figure 5). It is worth noting that the pre-stack seismic inversion can effectively invert the P-wave velocity in the oil and gas production process, and the inverted P-wave velocity is basically consistent with the P-wave velocity of the geological model (Table 2).

**Figure 5.** Comparison of P wave velocity of the geological model and that of the pre-stack inversion. The upper picture is the P wave velocity from the geological model; the lower picture is the P wave velocity from the pre-stack inversion.

**Table 2.** P wave velocity errors between the P wave velocity of the geological model and that of the pre-stack inversion.


Figure 6 shows three sections of the pre-stack result for geological model 1: P-impedance, *Vp*/*Vs*, and density. P-impedance only shows the position of the caves and the post-stack inversion. *Vp*/*Vs* a result only produced by pre-stack inversion, predicts different fillings in cave reservoirs which correspond to the elastic parameters of different fillings. *VP*/*VS* values can effectively characterize the differences between the different fillings in the caves. The *Vp*/*Vs* reflection is strong when the filling velocity is that of gas (2800 m/s), live oil (3150 m/s), oil–water (3550 m/s), or oil (4200 m/s), whereas *Vp*/*Vs* has no reflection when the filling is argillaceous (4550 m/s) and calcareous mudstone (5150 m/s). Pre-stack inversion showed significantly improved fluid prediction in comparison with post-stack inversion. The results indicate that pre-stack inversion can obtain basic elastic parameters

for fluid prediction. Pre-stack inversion is applicable for fluid prediction in carbonate karst reservoirs.

**Figure 6.** Seismic inverted results of geological model 1: P-impedance prediction the cave reservoir; *Vp*/*Vs* ratio effectively predicted in non-oil-bearing caves; density predicted a result between P-impedance and *Vp*/*Vs* ratio prediction.

Geological model 2 allowed a comparison between pre-stack inversion and post-stack inversion as there was no fluid filling in the caves.

#### **4. Discussion**

#### *4.1. Cave Top Prediction*

In Tahe oilfield, the main objective of the current exploration and development is well location design and drilling on top of the cavern reservoir. In Figure 7, the upper picture shows a post-stack inversion section, and the lower picture shows a pre-stack inversion section. Blue indicates the inversion result, and purple indicates the depth of the model's position. The P-impedance of post-stack inversion has been used to predict the position of the top of caves in recent years; however, our results show that pre-stack inversion can more accurately predict the top of the cave. The error is controlled within 1 m, an improvement on the 10 m error of post-stack inversion, which indicates that pre-stack inversion is more effective and applicable for predicting the tops of reservoirs. Pre-stack inversion prediction is a more accurate method for the prediction of the depth of a cave than post-stack inversion prediction. Pre-stack inversion is applicable for the prediction of the full-depth position in carbonate karst reservoirs.

**Figure 7.** Comparison of P-impedance between post-stack inversion and pre-stack inversion. Purple rectangles indicate models with different distances from the upper surface. Pre-stack inversion shows more effective prediction results.

#### *4.2. Cave Size Prediction*

Figure 8 shows four pictures: a geological model map, a seismic attribute map (from acoustic forward modeling), a pre-stack inversion map, and a post-stack inversion map. The four different results show that a 20 m × 20 m cave can be accurately predicted by pre-stack inversion: post-stack inversion predicts a size a little bigger than it is, and the seismic attribute prediction is the least accurate of the four. For caves sized at 40 m × 40 m, the same results were found. Seismic attribute prediction has long been considered as a popular and effective method for characterizing caves in a map. This case shows that pre-stack inversion prediction is the most accurate method for predicting the size of caves compared with seismic data prediction and post-stack inversion prediction. The caves map distribution obtained by post-stack inversion was too different from the geological model: more than 100%. The predictions by pre-stack inversion for the size of the caves are closer to the geological model, especially for smaller caves. Pre-stack inversion is applicable for cave size prediction in carbonate karst reservoirs.

**Figure 8.** Comparisons of prediction caves size (map): post-stack inversion prediction; pre-stack inversion prediction; seismic attribute prediction. The sizes of the caves predicted by pre-stack inversion are closest to those of the geological model.

Figure 9 shows three pictures for geological model 3: the upper one is the post-stack inversion prediction, the middle one is the pre-stack inversion prediction, and the lower one is the model prediction. The pre-stack inversion result shows layered characteristics for the complicated combination model. The prediction for the top of cave reservoir becomes more accurate with the increase in volume. Pre-stack inversion can more accurately describe the boundary of a single cave in the combination condition than the results of post-stack inversion (shown in Figure 9). Pre-stack inversion displays the shape of these two caves, but the outline is not sufficiently obviously due to the 10 m distance between the two models. The connectivity of the left two caves, measuring 20 m × 20 m and 10 m × 10 m, is poorly defined in post-stack inversion, with little reflection.

Different elastic parameters have different ability to predict reservoirs, the elastic parameters from pre-stack inversion are suitable for the prediction of different types of carbonate reservoirs (shown in Table 3). The density is also relevant in the fluid reservoir, which can help P-impedance and the *Vp*/*Vs* in reservoir prediction. P-impedance reflects the position and size of the caves well, and the *Vp*/*Vs* and *Vp* reflects the fluid prediction. Pre-stack inversion is applicable for cave connectivity prediction in carbonate karst reservoirs because it predicted the connectivity of the caves more accurately than post-stack inversion.

**Figure 9.** Comparison of P-impedance between post-stack inversion and pre-stack inversion: The black square shows the boundary of one of the caves clearly in the complicated combination; the post-stack inversion result has a lower resolution.


**Table 3.** Quantitative analysis results of pre-stack inversion.

#### **5. Case Study**

Pre-stack inversion was studied using seismic data from the Tahe oilfield in the Tarim Basin of Northwestern China. The reservoir is overlaid by a thick layer of clastic rock. The key aim of searching for carbonate reservoirs is to locate karst caves accurately and find water-eroded caves which are filled with oil. As is analyzed in this study, pre-stack inversion was applied for carbonate karst reservoirs.

The application results of pre-stack inversion are shown in Figure 10, where pre-stack inversion P-impedance and *Vp*/*Vs* ratio are plotted at the top, and the seismic section is shown at the bottom. The seismic section shows that W1 and W2 are both characterized as cave reservoirs, and the P-impedance result indicates the W1 position and size. W1 is a larger cave than W2, indicating that W1 is a better reservoir than W2; it was hard to judge whether W2 is an oil-bearing reservoir from the P-impedance results. In contrast, the *Vp*/*Vs* ratio indicated that W2 is not filled with oil, which is consistent with the known production data.

Figure 11 shows a complicated combination of caves. Seismic data show many strings of beads, and it is hard to distinguish where the caves are. Post-stack inversion indicates about five large caves, as analyzed above, but this indication is difficult for complicated combinations of caves. The pre-stack inversion results show small-scale caves and their boundaries.

**Figure 10.** Predicting cave-filling fluids based on pre-stack inversion.

**Figure 11.** Comparison of P wave impedance profile between post-stack inversion and prestack inversion.

#### **6. Conclusions**

Through the application of pre-stack inversion in carbonate reservoirs, it can be seen that Pre-stack inversion, as compared to post-stack inversion, provides for more accurate estimates of the depth of carbonate karst reservoirs.

The P wave velocity of the pre-stack inversion is well capable of predicting cave fillings and can perform a quantitative analysis of cave fillings.

Pre-stack inversion has improved cave size prediction in carbonate karst reservoirs to 20 m × 20 m, greatly outperforming seismic data in the prediction of caves.

Pre-stack inversion can be applied for complex reservoirs in carbonate karst reservoirs and is more effective than post-stack inversion at predicting cave connectivity.

Analysis of pre-stack inversion suggests that it is a useful technique for predicting carbonate karst reservoirs in cave reservoir. The comparison results demonstrate that pre-stack inversion improves the prediction of karst reservoir capacities.

**Author Contributions:** Conceptualization, R.W.; methodology, B.L.; validation, R.W. and B.L.; formal analysis, R.W.; investigation, R.W. and B.L.; resources, R.W.; data curation, B.L.; writing—original draft preparation, B.L.; writing—review and editing, R.W. and B.L.; visualization, B.L.; supervision, R.W.; project administration, R.W.; funding acquisition, R.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was jointly supported by the National Science and Technology Major Project of China (Beijing) (No. 2017ZX05005004).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

