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Application of the wavelet transform and Hilbert–Huang transform in stratigraphic sequence division of Jurassic Shaximiao Formation in Southwest Sichuan Basin

  • Zheng Li , Jingchun Tian , Laixing Cai and Tian Yang EMAIL logo
Published/Copyright: September 3, 2024
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Open Geosciences
From the journal Open Geosciences Volume 16 Issue 1

Abstract

In the southwestern Sichuan Basin, the Jurassic Shaximiao Formation encompasses a multitude of working areas, displaying intricate sedimentary traits. Traditional methods of stratigraphic division based on sequence suffer from inherent subjectivity and limitations. This study employs a combined mathematical approach to use the wavelet transform (WT) and the Hilbert–Huang transform (HHT). It decomposes the natural gamma ray (GR) logging curve into energy spectrum plots and wavelet coefficients at different scales, high and low frequency signals at different frequencies, and a set of intrinsic mode function components and residual functions. The study conducted a detailed stratigraphic division of the Jurassic Shaximiao Formation in the southwestern Sichuan Basin using these methods. The WT offers greater resolution for the periodic changes in the base level, whereas the HHT demonstrates a superior correlation with the positions of stratigraphic interfaces. The combined utilization of the continuous wavelet transform, the discrete wavelet transform, and HHT methods has demonstrated encouraging outcomes in the stratigraphic division of the Jurassic Shaximiao Formation. These methods have been shown to enhance the accuracy of stratigraphic division and to reduce the influence of subjective factors. This study presents new insights and approaches for geological data processing, offering significant theoretical and practical implications and novel technical means for oil and gas exploration and development.

Keywords: southwestern Sichuan Basin; Shaximiao Formation; wavelet transform; Hilbert–Huang

1 Introduction

In recent years, China has made significant progress in exploring and developing of tight sandstone oil and gas resources. The proportion of tight sandstone oil and gas reserves has been increasing, with major deposits found in basins such as the Sichuan Basin, Ordos Basin, and Tarim Basin [1,2,3,4]. The Shaximiao Formation in the Middle Jurassic of the Sichuan Basin has become an important exploration target in recent years [5]. The daily gas production is 136 × 104 m3, which has great exploration potential and is the main replacement force of tight sandstone gas reservoirs in the Xujiahe Formation [6]. And the southwestern region of the Sichuan Basin has significant terrestrial tight gas resources that have not been fully explored, indicating high exploration potential [7,8]. Accurate stratigraphic partitioning is critical for successful oil and gas exploration, and can even determine the success or failure of gas field development [9]. Stratigraphic division in conventional methods is typically performed using data such as outcrops, core samples, and well logs. However, this process can be influenced by subjective human factors [10,11,12,13]. In the southwestern Sichuan Basin, the Shaximiao Formation covers a large area spanning multiple working zones. However, no unified sequence stratigraphy work has been conducted, leading to numerous stratigraphic division schemes. Some scholars propose that the Shaximiao Formation can be subdivided into three third-order sequences and five fourth-order sequences, while others propose that the formation can be divided into Upper Shaximiao Formation (J2s) and Lower Shaximiao Formation (J2x), or alternatively be divided into two sections: Shaximiao Formation Section 1 (J2s1) and Shaximiao Formation Section 2 (J2s2) based on lithological characteristics and thickness [14,15,16]. This has hindered a comprehensive understanding of the internal complex sand bodies, which has been severely impeding the progress of exploration and development [17]. Therefore, it is necessary to conduct more refined, high-resolution sequence stratigraphy work to establish a precise foundation for subsequent oil and gas exploration and development.

Logging curves can effectively reflect information about cycles of different periods in sedimentary strata and serve as compelling evidence for performing sequence stratigraphic division [18]. Related high-resolution sequence stratigraphic classification methods, such as the Fourier transform [19,20], the wavelet transform (WT) [21,22,23], and the Hilbert–Huang transform (HHT) [24,25], can be used in intelligent identification tasks within sequence stratigraphy. These methods can help reduce the impact of the aforementioned limitations on sequence stratigraphic work. The WT can identify both time and frequency information within signals, extracting the necessary information from well logging data. It provides high resolution for the periodic variations in sequence stratigraphic cycles on the base level [26]. The earliest application of the WT in stratigraphic partitioning dates back to 2003 [27]. Since then, an increasing number of scholars have applied the WT to sequence stratigraphic division work, including both the continuous wavelet transform (CWT) and the discrete wavelet transform (DWT) [28,29,30,31]. The HHT is a tool used to deal with complex, nonlinear, and nonstationary signals [32,33,34]. It has good identification capabilities for small-scale sedimentary bodies and concealed geological features, especially providing higher resolution for delineating the boundaries of different geological bodies [35,36]. Using of computational techniques to identify and compare reference surface cycles in well logging data can significantly reduce workload and human error [37].

The sedimentary characteristics of the Shaximiao Formation in the southwestern Sichuan Basin are complex, characterized by the development of shallow-water delta-river sedimentary systems. Sediments of shallow-water deltas and fluvial facies exhibit striking similarities in their characteristics and distribution. The complexity of the sedimentary environment, in conjunction with the extensive distribution area, presents a significant challenge to the conduct of stratigraphic work on target layers within the study area. It is evident that the stratigraphic division criteria established through conventional methods are unable to fully address this issue. Therefore, this study combines the advantages of the WT and HHT, conducts comparative analyses, and addresses the limitations of individual methods to accurately identify hidden sedimentary cyclical information within well logging curves. The approach enables more precise high-resolution sequence stratigraphic work.

2 Geological setting

The Sichuan Basin is situated in southwestern China (Figure 1a). It is a cratonic basin with multiple-cycle superimposed sedimentation, covering an area of approximately 18,000 km2. Ending the Late Triassic period, the Sichuan Basin transitioned into the Jurassic Red Basin stage. The Micangshan-Dabashan uplift occurred in the northeastern part of the basin during the deposition of the Shaximiao Formation, and served as the primary source of sediment during this period [38] (Figure 1b). The Sichuan Basin underwent marine sedimentation from the Ediacaran to the Middle Triassic of the Mesozoic Era, and it was mainly composed of carbonate rocks. During the Late Middle Triassic period, the Upper Yangtze region experienced uplift due to the Indosinian movement. This caused the cessation of marine transgression and led to erosion of the basin interior. By the Late Triassic, the sedimentary environment had shifted from shallow marine platforms to inland lake basins, marking a transition from marine to continental facies deposition. During the Jurassic, Cretaceous, and Paleogene periods, sedimentation was mainly continental, consisting of clastic rocks [39]. In the study area, the Middle Jurassic Lianggaoshan Formation is underlain by the Shaximiao Formation. The sedimentary environment of the first member of the Shaximiao Formation is similar to that of the Lianggaoshan Formation, characterized by the development of a deltaic-fluvial depositional system. Towards the end of the first member of the Shaximiao Formation, there is a brief period of littoral-lake sedimentation. Fluvial depositional environments dominate the second member of the Shaximiao Formation. The formations are mainly composed of sandstone, siltstone, and mudstone, with a thickness of approximately 1,200–2,000 m [40,41] (Figure 1c).

Figure 1 (a) Map of the Sichuan Basin’s location. (b) Location map of the study area in southwest Sichuan Basin. Location of the studied wells H, YQ, and ZT is shown on the map by filled red circles. (c) Schematic diagram of the regional stratigraphy of the study area in Jurassic Shaximiao Formation in southwest Sichuan Basin.
Figure 1

(a) Map of the Sichuan Basin’s location. (b) Location map of the study area in southwest Sichuan Basin. Location of the studied wells H, YQ, and ZT is shown on the map by filled red circles. (c) Schematic diagram of the regional stratigraphy of the study area in Jurassic Shaximiao Formation in southwest Sichuan Basin.

3 Methodology

3.1 Wavelet Transform

The WT is a sophisticated technique that builds on the Fourier Transform. Its fundamental concept involves breaking down signals into wavelet function series, allowing for the projection of signals in various time-frequency spaces. This approach addresses the limitation of poor time domain resolution in the Fourier Transform and demonstrates excellent localization characteristics in both time and frequency domains simultaneously. This makes it particularly suitable for processing well logging curves [42,43]. Through the WT, well logging curves can be transformed into one-dimensional wavelet coefficient and two-dimensional spectrograms, which reveal hidden information in the curves. This makes it useful for geological interpretation. The WT includes the CWT and the DWT.

The CWT possesses means the properties of time-frequency localization and adjustable time windows, enabling more precise determination of the time-frequency characteristics of well logging data. This capability facilitates the identification of different scales of sedimentary cycles based on these variations, allowing for more efficient sequence stratigraphic works [44,45]. The specific definition of the CWT is defined as follows:

(1) W f ( a , b ) = ∣ a ∣ − 1 / 2 ∫ R f ( t ) ψ t − b a d t ,

where “a” represents the scale parameter, “b” represents the time shift parameter, f(t) represents the well logging signal sequence, and “ψ” is the wavelet function. The WT adjusts the sampling step size in the time domain for different frequencies by varying “a” and “b.” The initial step involves comparing the selected wavelet ψ with the initial portion of the input signal f(t). This is followed by computing the correlation between the chosen wavelet ψ and the input signal f(t), shifting it to the right, and repeating this process until the entire input signal f(t) has been covered. Finally, by scaling (stretching) the wavelet, the process is repeated to accomplish continuous WT analysis. The CWT has high frequency resolution but poor time resolution at low frequencies. Conversely, the CWT has high time resolution at high frequencies and low frequency resolution. This characteristic allows for the analysis of slow changes in low-frequency signals and rapid changes in high-frequency signals, which is the basis for signal analysis using the CWT.

Because the scaling and translation coefficients of the CWT are independent of each other, there is some similarity between the different wavelet functions obtained by scaling and translation. However, due to the independence between these two coefficients, redundant signals can be generated. The DWT was introduced to reduce redundancy.

The DWT decomposes a signal into a set of mutually orthogonal discrete and shifted signals, obtaining corresponding high frequency and low frequency wavelet reconstruction coefficients. The low-frequency component tends to match the inherent characteristics of the signal itself, while the high-frequency component is often contaminated by noise. By decomposing the low-frequency component further, we can obtain different levels of wavelet reconstruction coefficients, which allows for a more precise signal analysis [42,46]. The specific definition of the DWT is defined as follows:

(2) Ψ j , k ( t ) = a 0 j 2 Ψ ( a 0 − j t − k b 0 ) ,

where Ψ j , k ( t ) represents the discrete wavelet function， a 0 and b 0 are discretized scale and shift parameters, respectively, with a = a 0 j and b = ka 0 j b 0, j ∈ Z, a 0 is always greater than 1, and k is an integer. First, the selected wavelet function ψ is matched with the characteristics of the input signal f(t). Second, the chosen wavelet function ψ is used as the core of the filter to perform convolution on the input signal f(t), decomposing the signal into low-frequency components (approximation coefficients) and high-frequency components (detail coefficients). Subsequently, the convolution result is down sampled in order to reduce the data volume while preserving the essential information, thereby generating a set of approximation coefficients and a set of detail coefficients representing signal components at different frequency ranges. Finally, the aforementioned steps are repeated, with the low-frequency part (approximation coefficients) being further decomposed until the desired decomposition level is achieved or the maximum depth of decomposition is reached. The inverse WT is employed to reconstruct the decomposed approximation coefficients and detail coefficients into an approximate value of the original signal, thereby enabling the analysis of signal characteristics at different scales.

3.2 Hilbert-Huang transform

The HHT differs significantly from traditional signal processing methods and is a time-frequency analysis technique that possesses unique advantages in high-resolution analysis of nonlinear signals. This method decomposes the original signal into intrinsic mode functions (IMF) of different frequencies using empirical mode decomposition (EMD). The HT is then applied to these IMFs to generate instantaneous frequencies that reflect the abrupt changes in the original signal. This approach effectively addresses issues such as signal distortion [47,48,49]. The specific definition of the HHT is defined as follows:

(3) H ( t ) = ∑ j = 1 n e j ( t ) + C n ( t ) ,

where e j ( t ) is defined as the IMF components at different scales, representing different frequency components that change according to the variations in the original signal. C n ( t ) is defined as the residual component function, indicating the trend of signal changes, where n denotes the level of signal decomposition. First, compute the local maxima and minima of the input signal f(t) and use these to construct the upper and lower envelopes of the original signal. The upper envelope is formed by connecting line segments between adjacent local maxima, while the lower envelope is formed by connecting line segments between adjacent local minima. This process yields an approximation of the upper and lower bounds of the original signal. Second, the upper and lower envelopes are added together and divided by two to obtain the mean function, which describes the overall trend of the original signal. The mean function is then subtracted from the original signal to obtain the residual signal, which reflects the local oscillatory component between the original signal and the mean function. Subsequently, it is necessary to ascertain whether the residual signal satisfies the convergence criteria of the IMF. This entails determining whether the residual signal is a monotonic or quasi-static function and whether the number of extremum points and zero crossings of the residual signal is equal or differs by no more than one. In the event that the aforementioned criteria are not met, it is necessary to repeat the aforementioned steps. Conversely, if the criteria are met, the residual signal must be defined as one of the IMFs and saved. Finally, the aforementioned steps should be repeated until the maximum decomposition limit is reached, with the aim of gradually capturing different frequency components within the signal.

3.3 Specific steps

The above signal processing methods can be implemented using MATLAB software’s Wavelet Toolbox, Main Menu toolbox, and HHT custom function code program. To perform time–frequency analysis on well logging curves, it is necessary to organize the well logging data of the target formation into text format. These data can then be processed using MATLAB software for analysis. Well logging curves can accurately reflect the superimposed oscillations of sedimentary cycles of different periods. By applying the WT and the HHT to well logging curves, it is possible to identify the periodic oscillatory characteristics of sedimentary cycles. These oscillations can then be matched with sequence interfaces of different orders, aiding in conducting more refined sequence stratigraphic work.

4 Application to the Shaximiao Formation

In the field of the HT analysis research, matching pursuit algorithm is used for selection of the most appropriate wavelet for signal processing [42]. Examining different wavelets revealed that Daubechies (db) wavelet is associated with the lowest mean squared error in signal approximation. The db wavelet was selected for analysis of well logging data based on the unique geological features of the research area. In principle, signals can be decomposed to an infinite degree after being input into the HHT [50]. However, following an analysis of the data from various well locations within the research area, it was determined that the most effective approach would be to employ seven IMFs and one residual signal (R) in order to conduct high-resolution stratigraphic work.

The Shaximiao Formation in the southwestern region of the Sichuan Basin can be divided into two third-order base level descents/rises and five fourth-order base level descents/rises. This corresponds to two third-order sequences and five fourth-order sequences, respectively. The GR logging curve of well YQ was analyzed using MATLAB software. A comprehensive interpretation of the upper boundary of the Shaximiao Formation (SB1), the lowest boundary of the Shaximiao Formation (SB2), secondary stratigraphic boundary (sb1, sb2, sb3), the maximum flooding surface (MFS1), and the secondary flooding surface (mfs1, mfs2, mfs3, and mfs4) was conducted for high-resolution sequence stratigraphy.

The GR curve of well YQ was subjected to the CWT using the db6 wavelet as the mother wavelet. This resulted in the corresponding time–frequency spectrogram and wavelet coefficient reconstruction curve (Figure 2). The time–frequency spectrogram shows regions of increasing color intensity from light to dark, indicating the increasing energy of sedimentary water bodies and representing the cyclicity of sedimentary formations. The accommodation space to sedimentation rate (A/S) ratio can effectively reflect the variations in the cycles of the reference surfaces [51]. When the A/S ratio is smaller, the sand bodies exhibit obvious overlapping and cutting characteristics, and the vertical accretion is stronger. Conversely, when the A/S ratio is large, isolated sandstone surrounded by mudstone often develops, resulting in poor lateral connectivity. Typically, a complete sequence boundary (SB) comprises a rising surface (A/S > 1) and a falling surface (A/S < 1). Regarding the time–frequency spectrogram, there is a clear transition of the strong energy cluster from the SB to the weak energy cluster at the MFS, followed by a transition back from the weak energy cluster at the MFS to the strong energy cluster at the SB, forming a complete stratigraphic cycle. Based on Figure 2, it is evident that SB1, SB2, sb2, and sb3 correspond well on the time–frequency spectrogram. Using sb2 as an example, there is a distinct mutation between strong and weak energy clusters, whereas the correspondence for sb1 is not evident. MFS1, mfs1, mfs3, and mfs4 also show good correspondence in the time-frequency spectrogram, while mfs2 does not correspond to a stronger energy cluster. The GR logging curve underwent denoising processing at three different frequencies: a = 32 (high frequency), a = 64 (medium frequency), and a = 128 (low frequency). The resulting wavelet reconstruction coefficient curves were obtained. Most interfaces correspond well with the abnormal regions of the wavelet reconstruction coefficient curves, providing valuable reference information. When using the CWT for sequence stratigraphy identification, it is important to note that higher frequencies reveal more details. In the CWT, not all areas of abrupt change in the time–frequency spectrogram and wavelet reconstruction coefficients can be explained as SBs and MFCs. Most of these correspond to specific areas of SBs. Therefore, combining geological knowledge and other evidence is necessary to identify and delineate stratigraphic SBs.

Figure 2 The results of applying CWT on the GR log of well YQ to interpret the stratigraphic cycles of the Jurassic Shaximiao Formation. MFS is the maximum flooding surface and SB is the sequence boundary.
Figure 2

The results of applying CWT on the GR log of well YQ to interpret the stratigraphic cycles of the Jurassic Shaximiao Formation. MFS is the maximum flooding surface and SB is the sequence boundary.

Based on Figure 3, continuing with the selection of db wavelet, the GR logging curve is decomposed into 11 high-frequency to low-frequency detail signals (d1–d11) and one approximation signal (a11). From d1–d11, it can be observed that there is a good correspondence between the anomaly regions and the MFSs. Using mfs2 as an example, a corresponding response at d5 and d7 is observed when the base level rises (A/S＞1), while its response in the CWT is less prominent (Figure 2). In contrast, sb1 shows a clear correspondence at d5, d7, and d11, indicating a complete process of the base level transitioning from rising to falling.

Figure 3 The results of applying DWT on the GR log of well YQ to interpret the stratigraphic cycles of the Jurassic Shaximiao Formation. MFS is the maximum flooding surface and SB is the sequence boundary.
Figure 3

The results of applying DWT on the GR log of well YQ to interpret the stratigraphic cycles of the Jurassic Shaximiao Formation. MFS is the maximum flooding surface and SB is the sequence boundary.

As decomposition levels increase, the signal’s noise is gradually filtered out, allowing for better identification of MFSs. The a11 curve shows a similar fluctuation trend compared to the original GR well logging data. After removing significant noise, it displays clearer and more intuitive peaks and troughs.

Generally, the a11 signal’s troughs correspond to the opposing sides of the base level descent (A/S < 1) and base level ascent (A/S > 1). In contrast, the peaks correspond to the transition surfaces from base level ascent (A/S > 1) to base level descent (A/S < 1). Overall, the use of DWT provides a more intuitive recognition of the transition surfaces (MFSs) between base level ascent (A/S > 1) and base level descent (A/S < 1) compared to the response of the CWT. However, it also exhibits some degree of offset. For instance, taking MFS1 as an example, there is a noticeable downward shift. Similar to the CWT, the DWT also limits the identification of sequence boundaries and flooding surfaces to a relatively small range, rather than providing precise responses for accurate interface positioning.

The results of processing the GR logging curve using HHT are shown in Figure 4. The GR logging curve of well YQ was decomposed into seven IMFs (IMF1–IMF7) and one residual function (R7) through EMD. A good correspondence between various sequence boundaries and maximum flooding surfaces was observed in IMF3 and IMF7. Using MFS1, mfs1, mfs2, and mfs4 as examples, there is a significant peak response from baseline rise (A/S > 1) to baseline fall (A/S < 1) in IMF3 and IMF7. Additionally, in the IMF3 curve, mfs3 also exhibits a significant peak response. Similarly, on the opposite side of the baseline fall (A/S < 1) and baseline rise (A/S > 1), SB1, SB2, sb1, sb2, and sb3 have reasonable interpretations in the IMF3 curve. The IMF7 and R7 curves closely match the variations in the original GR log curve. The peak-valley positions of the MFS1 correspond precisely to the peaks and valleys in IMF7 and R7, completely coupled with the position of the MFS1. In summary, the use of the HHT for identifying sequence boundaries and maximum flooding surfaces results in more precise point locations compared to the range reflected by the DWT and CWT. For instance, in the case of MFS1, the peak value in IMF7 is significantly higher than the anomaly response shown at a = 128 in the CWT and at d11 in the DWT.

Figure 4 The results of applying HHT on the GR log of well YQ to interpret the stratigraphic cycles of the Jurassic Shaximiao Formation. MFS is the maximum flooding surface and SB is the sequence boundary.
Figure 4

The results of applying HHT on the GR log of well YQ to interpret the stratigraphic cycles of the Jurassic Shaximiao Formation. MFS is the maximum flooding surface and SB is the sequence boundary.

5 Discussion

The structure of the fluvial facies sequence is usually influenced by changes in base level and accommodation space, resulting in a dynamic process. High-resolution sequence stratigraphy, which utilizes the HT and HHT, can provide more detailed and comprehensive stratigraphic information. This serves as an essential method for finely dividing strata. The text uses GR logging curves as a starting point and applies the CWT, DWT, and HHT to process them. This process aims to remove extraneous interference signals from the GR logging curves, resulting in more precise identification of sequence boundaries and flooding surfaces.

As shown in Figure 5, the application of the CWT, DWT, and the HHT to the GR logging curves of well YQ reveals significant anomaly responses for most of the sequence boundaries and flooding surfaces. This approach minimizes the impact of subjective factors in sequence stratigraphy analysis. In the study area, the Suining Formation comprises “flood-overlake” strata dominated by meander river deposits and is located at the upper part of the top boundary (SB1) of the Shaximiao Formation [52]. The section below the lower boundary (SB2) corresponds to the Lianggaoshan Formation, which is primarily characterized by the development of delta-lake sedimentary systems [53,54]. A stable thick layer of sandstone deposited at SB1 and SB2 serves as a marker bed for stratigraphic division. The interval between 1,220 and 1,320 m can be identified as the SB1 interface if stratigraphic divisions are based solely on well logging curves. At depths of 2,340 and 2,370 m, potential indications of the SB2 interface exist. However, for a more precise delineation of SB1 and SB2, it is necessary to consider the anomalous response characteristics of low-frequency signals such as a = 32, d7, d11, IMF7, and R7. The time–frequency spectrogram does not provide significant indications due to the divergence of boundary energy.

Figure 5 The results of applying CWT, DWT, HHT on the GR log of well YQ to interpret the stratigraphic cycles of the Jurassic Shaximiao Formation. MFS is the maximum flooding surface and SB is the sequence boundary.
Figure 5

The results of applying CWT, DWT, HHT on the GR log of well YQ to interpret the stratigraphic cycles of the Jurassic Shaximiao Formation. MFS is the maximum flooding surface and SB is the sequence boundary.

The lower part of the Shaximiao Formation continues the sedimentary systems of the Lianggaoshan Formation period, which are predominantly characterized by shallow-water delta-fluvial facies. It experienced a brief period of shallow lake sedimentation in the later stages, resulting in a stable set of conchostracans shales [38]. These shales represent the MFS1 of this formation. Based on the well logging curves, MFS1 can be identified at 2,138–2,197 m depths. However, based on the analysis of the low-frequency signal IMF7, it is suggested that MFS1 should be positioned at 2,170 m.

The upper part of the study area, the Shaximiao Formation is characterized by typical deposits of fluvial deposition [55]. The thickness of the sand bodies increases significantly, allowing for the identification of four fourth-order sequences. Each of these sequences represents a trend where the curvature of meandering river channels initially increases and then decreases. On the one hand, sb1, sb2, and sb3 indicate positions where the curvature of river channels is relatively low, with a significant development of sandstone. On the other hand, mfs1, mfs2, mfs3, and mfs4 represent locations where the curvature of river channels is relatively high, with a fairly significant development of mudstone. These fourth-order sequence boundaries and their sub-level flooding surfaces are characterized by multiple similar points in well logging curves, which greatly increases uncertainty. However, analyzing the changing trends in the color of energy clusters in the time–frequency spectrogram, as well as high-frequency signals such as d5, d6, and IMF3, can provide a more precise identification of these boundaries.

The CWT maps the GR logging curve into the WT domain, allowing the creation of time–frequency spectrograms and wavelet reconstruction coefficient curves. This visual approach, supplemented by denoising curves, aids in identifying the features of the GR logging curve, facilitating the recognition of the cyclical periods of different sequences. The DWT and HHT are used to decompose the GR logging curve into fluctuation signals of different scales and frequencies, which reduces irrelevant noise. This process enhances the clarity of the amplitude in the original logging curve, enabling a more efficient revelation of the cyclical characteristics of sequence stratigraphy. After undergoing processing with the CWT and DWT, the GR logging curve can capture the cyclical signals of different stratigraphic sequences more clearly. Typically, interfaces can be constrained within specific depth ranges. However, the HHT provides more accurate identification of anomalous points by enhancing the curve characteristics of anomalous regions to determine the specific locations of interfaces.

However, when applying the WT and the HHT for high-resolution stratigraphy work, it is necessary to ensure that the input signal is sampled at a high rate. Therefore, before processing the GR curve, it is necessary to combine other methods to address this issue. Second, there may be instances where stratigraphic boundaries are eroded or older layers are overlaid by newer ones. In some well locations (Figure 6), the response characteristics of SB1 and SB2 in the CWT, DWT, and HHT are not distinct. In such cases, confirmation can only be obtained through other sources of data.

Figure 6 Comparative analysis of stratigraphic well Logs for Wells H, YQ, and ZT in the study area based on CWT, DWT and HHT of GR well log curves.
Figure 6

Comparative analysis of stratigraphic well Logs for Wells H, YQ, and ZT in the study area based on CWT, DWT and HHT of GR well log curves.

The CWT, DWT, and HHT can be used to identify sequence boundaries. However, well logging curves have inherent uncertainties, and anomalously low or high-value areas could be misinterpreted as sequence stratigraphic interfaces, adding to the overall uncertainty. Therefore, it is essential to first select logging curves that exhibit high sensitivity to sequence stratigraphic cycles. A combination of multiple logging curve processing methods should be employed to determine the stratigraphic division. The different advantages of each method should be leveraged by integrating and optimizing the results obtained from various methods. Various well logging curve processing methods can distinguish high-frequency signals corresponding to fourth-order cycles, while medium to low-frequency signals correspond to third-order cycles. This allows for the acquisition of high-resolution signals at different frequencies. High-resolution sequence stratigraphy can be achieved by combining and corroborating multiple methods.

It is evident that the stratigraphic division method described in this study is derived from the distinctive sedimentary characteristics of the Shaximiao Formation in southwestern Sichuan Basin. When dividing shallow-water delta-river facies, the primary considerations are the periodicity of sedimentary units and variations in accommodation space (A/S ratio) [14]. The utilization of the CWT, DWT, and HHT for the processing of the GR curve allows for the accurate identification of its periodic variations and anomalous responses, thus resulting in more precise stratigraphic division results. However, when it comes to stratigraphic division for different sedimentary systems, such as for gravity flow deposition, considerations shift towards the sedimentary body type, structural features, and the dynamic nature of the depositional environment [56]. The particle size and bedding characteristics of gravity flow deposition differ significantly from those of shallow-water delta-river facies sedimentation. The methods employed in this study may not be readily apparent in identifying these features, and the responses of different sequence boundaries may vary. Consequently, the aforementioned methods may not be suitable for the analysis of more complex sedimentary systems. A case-by-case approach is therefore required. The research methodology of this study primarily focuses on stratigraphic division work for shallow-water delta-river facies sedimentary systems. The method combining the CWT, DWT, and HHT has been applied to the study area of two additional wells, Well H and Well ZT. It was observed that similar sequence boundaries and flooding surfaces exhibit comparable response characteristics in these wells (Figure 5). In the southwestern Sichuan region, the Jurassic Shaximiao Formation is mainly supplied by sediment sources that are directed toward the northeast. In contrast, secondary sediment sources are present in the southwest direction. The stratigraphic thickness exhibits a distribution pattern of being thinner in the south and west and thicker in the north and east. The northeastern part of the region typically features thicker strata ranging between 1,000 and 1,600 m, while the southwestern part tends to have thinner strata ranging between 500 and 800 m. Sequence stratigraphy division is conducted by combining the three methods. The study utilized the CWT, DWT, and HHT to analyze sequence stratigraphy by comparing it with continuous well stratigraphic profiles (Figure 6). The results show that the overall trend of stratigraphic thickness variation is consistent with the distribution of stratigraphic thickness in the study area, further confirming the reliability of this comprehensive analysis approach.

Following the application of the CWT and DWT, it can be employed for the extraction of features from geological data, thereby enabling the identification of the frequency domain characteristics of underground structures. The HHT can be employed to extract both vibration modes and resonance characteristics from geological data. By leveraging these analytical techniques in combination, they can guide both imaging and signal recovery processes. The application of the method is not limited to stratigraphic division. There has been significant progress in the characterization of sand bodies [57], the interpretation of seismic profiles [58], the identification of fractures in well logging data [59], and the evaluation of reservoirs [29,60], among other areas. The application of these methods in geology is bound to increase with the advancement of technology, further enhancing the efficiency and accuracy of geological data processing and promoting rapid development in the fields of geology and geophysics.

6 Conclusion

This study presents a comprehensive study of the stratigraphic division of the Shaximiao Formation in southwestern Sichuan, which is subject to complex stratigraphic conditions. The research employs a range of high-resolution stratigraphy methods, including the CWT, DWT, and HHT, in order to gain a detailed understanding of the formation’s stratigraphic characteristics. The principal findings are as follows:

  1. The CWT, DWT, and HHT are more accurate in revealing the periodicity of stratigraphic changes and the anomalous response characteristics of well logging curves than traditional methods, overcoming the subjectivity and limitations of these traditional methods.

  2. Any individual method can be employed to guide stratigraphic work. However, by combining the CWT, DWT, and HHT, the precision of stratigraphic division can be further enhanced, providing favorable support for the stratigraphic division of the Shaximiao Formation in southwestern Sichuan where geological conditions are complex.

These findings are of significant importance not only for geological exploration and resource evaluation, but also for the methodology of geology. Nevertheless, despite the significant outcomes achieved, there are still some issues that require further investigation. These include the question of the universal applicability of the methods and the potential for further optimization to enhance efficiency. Future research could investigate the potential for combining other high-resolution geological methods with those proposed in this study, with a view to enhance the accuracy and reliability of stratigraphic division.

Acknowledgements

We would like to thank the constructive comments by the editors and the anonymous reviewers.

  1. Funding information: This work is funded by the Scientific Research and Technological Development Project of PetroChina: A comprehensive evaluation and optimization of the conditions for tight gas accumulation in the southwest Sichuan Province (JS2021-038).

  2. Author contributions: Zheng Li: conceptualization, data analysis, methodology, plotting, and writing – original draft. Tian Yang: supervision, validation, writing – review and editing. Jingchun Tian: supervision, validation, and writing – review and editing. Laixing Cai: supervision, validation, and writing – review and editing.

  3. Conflict of interest: All authors state no conflict of interest.

  4. Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Received: 2024-03-03
Revised: 2024-04-23
Accepted: 2024-05-01
Published Online: 2024-09-03

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/geo-2022-0657
Keywords for this article
southwestern Sichuan Basin; Shaximiao Formation; wavelet transform; Hilbert–Huang
Creative Commons
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