Forward modeling serves as the basis of seismic exploration methods and in seismic data interpretation, it primarily used to validate interpretation schemes and to identify anomalous geological bodies. When real seismic data are ambiguities, forward modeling technology provides an intuitive and effective tool to support interpretation and to help resolve difficult problems in seismic exploration ([10]).

Seismic forward modeling technology involves constructing geological models that reflect actual underground geological features and simulating these models to generate synthetic seismic records, and then inferring geological conditions by analyzing the response characteristics of these synthetic records ([11]). In geophysics, forward modeling primarily encompasses two methods: the physical modeling method and the numerical modeling method ([1]). This method relies on the assumption that the medium structure and rock physical parameters of underground geological bodies are known. The numerical modeling calculations utilize mathematical techniques. Within a computer environment, researchers design a suitable observation system based on the characteristics of the target body and derive the propagation characteristics of seismic waves in underground media through numerical modeling. Subsequently, the numerical seismic records are computed at predetermined observation points, and these records undergo routine processing and interpretation to yield a specific numerical modeling result of the seismic response profile ([1]). The essence of this approach lies in the numerical simulation of the established geological model. Numerical modeling offers advantages such as flexibility, simplicity, speed, and cost-effectiveness, making it highly significant for interpreting actual seismic data and characterizing underground structures and lithology. Based on the given conditions and comprehensive considerations, the numerical modeling method is adopted in this study for investigation.

The quality monitoring procedure in seismic data processing has reached a relatively advanced stage. Commonly used one-dimensional forward modeling primarily simulates the single seismic record channel of underground horizontal strata at zero offset, with artificial synthetic seismic records serving as the representative ([5]). The artificial synthetic seismic record method is currently the predominant approach for layer calibration, and the creation of high-precision synthetic seismic records is a prerequisite for the calibration of these artificial synthetic records ([9]). This method constructs the seismic response at the wellbore through theoretical simulation, subsequently comparing it with the actual ground seismic profile to achieve alignment of geological layers and the seismic events. Essentially, it employs well logging data to deduce theoretical seismic signals, and then adjust parameters to ensure that the theoretical signals correspond with the actual ones, thereby elucidating the relationship between layers. In this study, one-dimensional forward modeling was conducted to analyze the seismic reflection characteristics of various lithological interfaces.

In contrast to one-dimensional seismic forward modeling, two-dimensional seismic forward modeling employs two-dimensional geological models to simulate the propagation of seismic waves through subsurface media and to generate corresponding seismic responses. This method emphasizes geological features at the “planar section” scale, wherein underground strata exhibit not only vertical lithological and thickness variations but also lateral distribution differences, such as variations in strata thickness, lateral lithological phase transitions, and structural forms like faults, folds, and spicles. By simulating seismic wave propagation within these two-dimensional models, the resulting seismic responses can reflect lateral variations more accurately, thereby aligning more closely with actual subsurface geological conditions. SMI (Seismic Meme Inversion, Beijing Zhongheng Lihua Petroleum Technology Research Institute, version 4.5) offers an integrated workflow that effectively combines structural and property modeling with seismic simulation, achieving high efficiency. So this paper employed the SMI software to develop a two-dimensional geological model that incorporates lateral variations and generated two-dimensional seismic profiles, thereby providing a theoretical foundation for interpreting real seismic data.

The Ricker wavelet is selected for the subsequent forward modeling in this study, considering its close approximation to actual seismic sources, distinct advantages in mathematics and signal processing, good stability, and its established role as a standard test wavelet in the field of seismic exploration.

The research scope of this study encompasses the Paleo-Uplift in the northwestern and central regions of Sichuan Province, as well as the Deyang-Mianyang Depression (Figure 1). Well Pengshen 6, Well Pengshen 2, and Well Longtan 1 were selected for detailed analysis. The target formation for this research is the Ordovician System (Figure 2). It can be observed that the Ordovician System in the study area is characterized by mixed sedimentation of both clastic and carbonate rocks. The data utilized primarily consist of well logging, mud logging, and seismic data from the Ordovician system in the study area, allowing for the acquisition of lithology, lithology thickness, velocity, and other relevant data for each well (Tables 1-3).

Table 1. Statistical summary of petrophysical parameters in Well Pengshen 6.

Table 2. Statistical summary of petrophysical parameters in Well Pengshen 2.

Table 3. Statistical summary of petrophysical parameters in Well Longtan 1.

Figure 1. Location map of the study area.

Figure 2. Stratigraphic column of the Sinian Ordovician in the Sichuan Basin.

Based on the data from the Ordovician system in northwest Sichuan Province, Wells Pengshen 2, Pengshen 6, and Longtan 1 were selected for detailed analysis. Accordingly, a one-dimensional geological model was constructed to represent the various lithological interfaces within the mixed sedimentary rock layers of the Ordovician system in the study area. The analysis reveals that in Well Pengshen 6, the Wufeng Formation consists of shale, the Linxiang Formation through to the Shizipu Formation comprises limestone, the Meitan Formation is calcareous mudstone and mudstone, the Honghuayuan Formation is limestone, and the Tongzi Formation includes dolomite, mudstone, and argillaceous dolomite. In Well Pengshen 2, the Wufeng Formation to Linxiang Formation is composed of shale, the Linxiang Formation to Shizipu Formation consists of limestone, the Meitan Formation is mudstone, the Honghuayuan Formation is dolomite, and the Tongzi Formation consists of argillaceous dolomite and dolomite. In Well Longtan 1, the Wufeng Formation is shale, the Linxiang Formation to the Shizipu Formation comprises limestone, the Shizipu Formation to the Meitan Formation consists of mudstone, the Honghuayuan Formation is dolomite, and the Tongzi Formation is argillaceous dolomite.

Using logging data, the seismic responses in underground strata were simulated with software. The synthetic seismic records were then aligned with the actual seismic profile adjacent to the well. By adjusting parameters such as the wavelet phase and local velocity, the reflection events (e.g., strong peaks and troughs) of the synthetic records were matched with those of the actual seismic data in terms of phase and amplitude as closely as possible. When the synthetic record aligns with the actual seismic profile, the geological layer positions identified in the logging can be directly correlated with specific reflection events on the actual seismic profile.

Through one-dimensional seismic forward simulation (Figures 3-5), the following seismic responses were determined: The top of the Ordovician at Well Pengshen 6 exhibits a peak reflection, while the Lower Ordovician, with a thickness of 54 meters, displays a double-peak reflection. Both the Tongzi Formation and the Meitan Formation are characterized by peak reflections. In Well Pengshen 2, the top of the Ordovician also shows a peak reflection. However, the lower Ordovician, with a thickness of 42 meters, presents a composite wave reflection. The Meitan Formation exhibits peak reflections, whereas the Tongzi Formation is in a near-zero phase. In Well Longtan 1, the top of the Ordovician system reveals a slightly upward reflection of the wave peak, while the lower Ordovician system, with a thickness of 19 meters, demonstrates a semi-peak reflection. The Meitan Formation shows a zero phase, and the Tongzi Formation reflects slightly below a wave peak.

Figure 3. Well to seismic calibration for Well Pengshen 6.

Figure 4. Well to seismic calibration for Well Pengshen 2.

Figure 5. Well to seismic calibration for Well Longtan 1.

Based on the summary of the three selected wells (Table 4) and analysis of the one-dimensional forward modeling results, it can be concluded that strata thicker than 45 meters exhibit a double-peak reflection with both the top and base interfaces as peaks. For thicknesses between 25 and 45 meters, the response is a composite wave, with the top as a peak and the base near zero-phase. When the thickness is less than 25 meters, the response becomes a single to semi-peak reflection, where the top is at zero-phase and the base is reflected slightly below a peak.

Table 4. Summary of 1D forward modeling results.

3.2.1. Two-Dimensional Geological Model

Utilizing the one-dimensional geological models of the Ordovician formations from Well Pengshen 6, Well Pengshen 2, and Well Longtan 1, along with the lithological velocities derived from logging data (Tables 1-3), two two-dimensional geological models were ultimately developed using SMI software. The model’s horizontal extent measures 1000 meters, while the vertical dimension corresponds to the actual depth. In Figure 6, Well Pengshen 2 is characterized by a lateral width ranging from 0 to 300 meters. The lithological sequence, from top to bottom, consists of the following layers: the first layer is shale; the second layer is limestone, with a thickness of 42 meters ; the third layer is mudstone, with a thickness of 40 meters; the fourth layer is dolomite, with a thickness of 16 meters ; the fifth layer is argillaceous dolomite, with a thickness of 15 meters ; the sixth layer is dolomite, with a thickness of 11 meters; and the seventh layer is limestone from the Cambrian Xixiangchi Formation. In the horizontal width range of 700 to 1000 meters, Well Pengshen 6 exhibits a different lithological composition, which, from top to bottom, includes: the first layer is shale; the second layer is limestone, with a thickness of 36 meters; the third layer is gray mudstone, with a thickness of 14 meters; the fourth layer is mudstone, with a thickness of 47 meters; the fifth layer is limestone, with a thickness of 22 meters; the sixth layer is dolomite, with a thickness of 12 meters; the seventh layer is mudstone, with a thickness of 6 meters; the eighth layer is argillaceous dolomite, with a thickness of 14 meters; and the ninth layer is limestone from the Cambrian Xixiangchi Formation. The lithology between 300 and 700 meters in lateral width represents a transitional zone from Well Pengshen 2 to Well Pengshen 6. In Figure 7, Well Longtan 1 is located within the model’s lateral width ranging from 0 to 300 meters. The lithological sequence, from top to bottom, consists of the following layers: the first layer is shale; the second layer is limestone, with a thickness of 47 meters; the third layer is mudstone, with a thickness of 11 meters; the fourth layer is dolomite, with a thickness of 7 meters; the fifth layer is argillaceous dolomite, with a thickness of 12 meters; and the sixth layer is limestone from the Xixiangchi Formation of the Cambrian period. Within the horizontal width range of 700 to 1000 meters lies Well Pengshen 6. The lithology within the lateral width range of 300 to 700 meters represents a transitional zone from Well Longtan 1 to Well Pengshen 6.

Figure 6. Two dimensional geological model between Wells Pengshen 2 and Pengshen 6.

Figure 7. Two dimensional geological model between Wells Longtan 1 and Pengshen 6.

Figure 8. Well correlation profile between Wells Pengshen 2 and Pengshen 6.

Figure 9. Well correlation profile between Wells Longtan 1 and Pengshen 6.

Subsequently, the actual well connection profiles of Wells Pengshen 2-Pengshen 6 and Longtan 1-Pengshen 6, illustrated in Figure 8 and Figure 9, were compared with the established two-dimensional geological model to assess the validity of the model.

3.2.2. Two-Dimensional Seismic Forward Modeling

Forward modeling of the two distinct two-dimensional geological models was conducted using the SMI software, resulting in synthetic seismic profiles for the geological models of Well Pengshen 2-Well Pengshen 6 and Well Longtan 1-Well Pengshen 6 (Figure 10,Figure 11).

Figure 10. Synthetic seismic section between Wells Pengshen 2 and Pengshen 6.

Figure 11. Synthetic seismic section between Wells Longtan 1 and Pengshen 6.

The synthetic seismic profiles reveal pronounced wave peaks at the stratum interfaces where significant differences in wave impedance exist. The seismic responses of Well Pengshen 2, Well Pengshen 6, and Well Longtan 1 align with the results from one-dimensional seismic forward modeling. As the transition occurs from Well Pengshen 6 to Well Longtan 1, where some lithological units gradually pinch out and bed thickness decreases, the seismic response evolves from a double-peak to a composite wave and then to a single peak. This finding is similarly reflected in the composite seismic profile of Wells Pengshen 2 to Pengshen 6. Comparison with the actual seismic profiles (Figure 12,Figure 13) reveals that the phenomenon of double peaks transitioning to single peaks is also evident in the real seismic data.

Figure 12. Actual seismic section between Wells Pengshen 2 and Pengshen 6.

Figure 13. Actual seismic section between Wells Longtan 1 and Pengshen 6.

Two-dimensional seismic forward modeling using a Ricker wavelet observed that the magnitude of the sesmic dominant frequency significantly influences the identification capability of thin layers. In the Pengshen 2-Pengshen 6 well model, the results indicate that when the selected seismic dominant frequency is 15 Hz, a 6-meter-thick mudstone layer is not discernible in the synthesized seismic profile (Figure 14(a)). In contrast, it became clearly identifiable at 35 Hz and above (Figure 14(b)). Even at 80 Hz, thin-layer interfaces with subtle impedance contrasts were detected (Figure 14(c)). Similarly, two-dimensional forward modeling was executed on the Longtan 1-Pengshen 6 well model, low dominant frequencies failed to clearly delineate several thin layers and interfaces near Well Pengshen-6 (Figure 14(d)). However, as the dominant frequency increased, the responses of all interfaces became distinctly observable (Figure 14(e), Figure 14(f)). Consequently, it can be concluded that an increase in the dominant frequency of seismic waves correlates with enhanced identification accuracy of thin layers.

Figure 14. Synthetic seismic sections at different dominant frequencies. (a) Synthetic seismic section between Wells Pengshen 2 and Pengshen 6 at 15 Hz; (b) Synthetic seismic section between Wells Pengshen 2 and Pengshen 6 at 35 Hz; (c) Synthetic seismic section between Wells Pengshen 2 and Pengshen 6 at 80 Hz; (d) Synthetic seismic section between Wells Longtan 1 and Pengshen 6 at 15 Hz; (e) Synthetic seismic section between Wells Longtan 1 and Pengshen 6 at 40 Hz; (f) Synthetic seismic section between Wells Longtan 1 and Pengshen 6 at 60 Hz.