Integrated SOM Multi-Attribute Optimization and Seismic Waveform Inversion for Thin Sand Body Characterization: A Case Study of the Paleogene Lower E₃d₂ Sub-Member in the HHK Depression, Bohai Bay Basin

Abstract

Thin-bedded beach-bar reservoirs in the continental faulted basins of eastern China hold significant potential, yet pose challenges for unconventional hydrocarbon development due to their thin-layer characteristics and heterogeneity. This study focuses on the Paleogene Lower E₃d₂ Sub-member in the HHK Depression, Bohai Bay Basin as a case study. We propose an innovative technical framework integrating Self-Organizing Map (SOM) multi-attribute optimization with seismic waveform inversion. Petrophysical analysis demonstrates that waveform-indicated inversion can detect 1.8–3.0 m thin sandstones, achieving a 90.2% mean match rate (95% CI: 87.5–92.7%, n = 12; bootstrap resampling) for training wells and 81.5% (95% CI: 76.8–85.3%, n = 11) for validation wells. By integrating SOM seismic attribute clustering with seismic waveform inversion, we were able to delineate microfacies boundaries with precision, enhancing the visibility of beach-bar sand body distributions. This methodology establishes a new paradigm for thin-bed sandstone prediction in low-well-control areas, providing critical support for geological interpretation and resource evaluation in complex depositional systems.

1. Introduction

As the exploration of structural hydrocarbon reservoirs in continental basins becomes increasingly challenging and the issue of reserve succession grows more severe, the focus of oil and gas exploration in these basins has gradually shifted and expanded from structural traps to lithostratigraphic traps, from shallow targets to deep exploration objectives, and from conventional to unconventional domains [1,2]. Among these, thin-bedded beach-bar sand bodies have emerged as a key focus for research and exploration in lithologic and unconventional hydrocarbon reservoirs. To date, numerous clastic beach-bar deposits have been identified in China’s continental basins, with significant breakthroughs in hydrocarbon exploration [3,4]. Thin-bedded sand bodies are significant types of sedimentary deposits found in the gentle slope zones of continental rift lake basins. They are characterized by their thin thickness, extensive lateral distribution, diverse sedimentary origins, complex diagenetic features, and unpredictable development patterns. The exploration of unconventional oil and gas resources in China has now entered a meticulous phase, with massive petroleum reserves residing within these thin-bedded sand bodies (defined as having a thickness of less than 10 m) located in subsurface strata [5,6]. The Bohai Bay Basin, a typical continental sedimentary basin in China, serves as a crucial area for unconventional hydrocarbon exploration [7,8]. Focusing on the Paleogene system in the HHK Depression of this basin, this study discusses the fine characterization of the boundaries of thin-bedded beach-bar sand bodies, which hold important implications for expanding exploration frontiers in unconventional hydrocarbon reservoirs within continental basins [9,10].

Currently, identifying thin-bedded sand bodies using conventional geological theories and methods poses considerable challenges. However, through comprehensive seismic sedimentology analysis [11], it is possible to study the lithological characteristics of the sedimentary rocks, identify thin-bedded sand bodies, and determine their sedimentary types and evolutionary processes [12,13], thereby providing new pathways for the exploration and development of deep unconventional oil and gas resources.

The fine characterization of thin-bedded sand body boundaries has become a focal point and a challenge in both oil and gas geological research and applied geophysics. With advancements and the widespread adoption of horizontal well technology and drilling fracturing techniques [14], the previously overlooked thin beds and interbedded reservoirs are garnering increasing attention from the oil and gas exploration and development community.

From the perspective of seismic exploration principles, thin sand layers are considered to be strata that strictly fall within the defined tuning thickness. Conventional seismic interpretation methods are insufficient for exploring these thin strata. To effectively predict such layers, it is essential to acquire wideband impedance signals during the inversion process. Furthermore, seismic attribute analysis has emerged as a reliable and efficient technique for interpreting seismic data, particularly in the context of thin-bedded sand body predictions, consistently yielding favorable results [15,16,17].

Traditional inversion methods acquire high-frequency components through two primary approaches. The first method utilizes deterministic interpolation models, typically employing techniques such as inverse distance weighting, natural neighbor interpolation, and Kriging [18,19,20]. While these models produce deterministic interwell interpolation results, they are inherently constrained by their model assumptions, resulting in low confidence levels [21,22]. Consequently, their application is primarily limited to reservoirs demonstrating stable lateral continuity and significant stratigraphic thickness. The alternative approach employs stochastic simulation, wherein variogram analysis quantifies spatial variability to guide optimal correlated sample selection for interwell reservoir parameter estimation, generating probabilistic outputs [23]. While this technique enhances vertical resolution, it inherently compromises lateral resolution and introduces significant stochasticity [24,25,26]. Additionally, the methodology requires evenly distributed sampling points to ensure statistical validity.

A critical limitation inherent in both seismic inversion methodologies lies in their over-reliance on well-derived data for high-frequency component estimation, while inadequately exploiting seismic information through integrated interpretation. Although seismic data’s narrow effective bandwidth inherently prevents direct high-frequency signal acquisition, its lateral amplitude variations systematically encode depositional environment evolution. Congenetic depositional systems manifest analogous stratigraphic architectures whose spatial transitions exhibit intrinsic correlations with waveform morphologies [27,28]. This causal relationship enables high-frequency component estimation through the systematic analysis of seismic waveform lateral variability.

Attribute fusion technology enables enhanced extraction of latent information within datasets, significantly improving the reliability of complex reservoir characterization. This methodology bifurcates into two fundamental paradigms: (1) algorithmic synthesis through mathematical transformations including composite attribute generation, principal component analysis (PCA), multivariate linear regression [29,30], and cluster analysis; (2) visual transformation techniques employing chroma-luminance binarization or RGB trichromacy to decode reservoir heterogeneity through enhanced data visualization [31,32]. The mathematical fusion approach, alternatively conceptualized as attribute optimization, frequently incorporates a priori well-derived constraints. In contrast, image-based visualization techniques operate independently of well data, proving particularly effective in highlighting reservoir anomalies through spatial pattern recognition—a capability exceeding conventional mathematical frameworks [33,34,35]. Intelligent seismic fusion fundamentally extends linear fusion principles through machine learning-driven nonlinear operators, implementing PCA and cluster analysis as essential preprocessing steps for dimensionality reduction [36,37,38].

Optimal algorithm selection requires a systematic evaluation of reservoir characterization objectives against available sample density. Current methodologies are stratigraphically categorized into supervised (well-constrained) and unsupervised (data-driven) fusion architectures [39]. Supervised techniques demonstrate superior performance through seismic-well log co-learning mechanisms, though their efficacy remains spatially constrained to well-penetrated zones and exhibits a positive correlation with well density. While seismic attributes effectively amplify specific geophysical signatures to enhance lithofacies discrimination, this spectral emphasis paradoxically induces information attenuation in complementary domains. Such inherent selectivity fundamentally limits their capacity for holistic stratigraphic representation, as substantiated in seismic interpretative practice [40].

Moreover, seismic attributes face a pervasive challenge in seismic interpretation, namely the inherent ambiguity associated with these attributes [41]. This ambiguity predominantly manifests in two aspects. First, distinct geological phenomena can present highly similar seismic attribute responses. For instance, strong amplitude responses may indicate the presence of unconformities, carbonate rocks, igneous intrusions, coal seams, and other geological features, leading to uncertainties in interpreting seismic attributes [42,43]. Second, factors such as resolution limitations, interference from adjacent formations, and tuning effects on amplitude and frequency further contribute to the ambiguity in the geological interpretation of seismic attributes [44,45]. For example, tuning effects can result in sand bodies of varying thicknesses displaying similar amplitude and frequency values across seismic attributes. Additionally, a pronounced amplitude response may originate from the target sand body or may be influenced by interference from neighboring geological formations [46].

Given the limitations and ambiguities associated with seismic attributes, numerous scholars have consistently focused their research efforts on two key areas aimed at improving the interpretive accuracy of these attributes. The first area emphasizes the development of novel seismic attributes [47], while the second explores methodologies for integrating multiple seismic attributes [48,49].

In regions lacking drilling data, the combination of seismic waveform inversion techniques with intelligent analysis of multiple seismic attributes—constrained by sedimentary models—proves advantageous. Artificial intelligence approaches are particularly effective for addressing nonlinear challenges, such as the quantitative relationships between petrophysical parameters and seismic attributes.

In the field of seismic waveform inversion and multimodal intelligent analysis, researchers have proposed a data-model co-driven seismic impedance inversion method [50]. Leveraging deep learning techniques, this approach identifies concealed fluvial channels in seismic images, overcoming the limitations of traditional model-driven methods. The inversion resolution is improved by 30% and the identification accuracy of hidden geological features (e.g., channels) exceeds 85% [51]. By integrating AI-generated initial impedance models with nonlinear modeling capabilities and physical constraints, the method optimizes low-frequency information in conventional inversion, achieving high-resolution seismic imaging [52]. Another study developed a multimodal deep learning framework for predicting reservoir parameters by fusing multimodal logging data (e.g., conventional logs and dynamic resistivity imaging) [53]. Applied to carbonate reservoirs in the Gaoshiti-Moxi block (Sichuan Basin), this method enhances porosity and permeability prediction accuracy by 25% compared to traditional approaches, addressing challenges in heterogeneous reservoir characterization [54]. AI-driven advancements including data-driven modeling, multimodal fusion, and automation significantly improve the precision and efficiency of geophysical exploration [55]. Applications span seismic inversion, reservoir prediction, and complex hydrocarbon reservoir development, offering innovative solutions for subsurface resource exploration [56].

In the field of computer science, artificial intelligence technologies, particularly those advancing through deep learning, are evolving rapidly. By actively employing machine learning methods to probe into the inherent complex features and patterns of seismic attributes, researchers can attain a more comprehensive and nuanced understanding of seismic data. The application of deep learning in geophysical research demonstrates significant potential for future advancements [57]. As a result, the integration of these attributes provides an objective and holistic depiction of the variations in geophysical responses and patterns across diverse lithological strata [58,59].

Self-Organizing Maps (SOM), an unsupervised learning technique for clustering and high-dimensional visualization, is an artificial neural network inspired by the human brain’s signal processing characteristics. This method, introduced by Professor Teuvo Kohonen of the University of Helsinki, Finland [60,61], has become the most widely utilized self-organizing neural network approach. Known for its robust self-organization and visualization capabilities, the SOM algorithm has gained widespread application and extensive research interest.

In the realm of petroleum geology, the SOM algorithm demonstrates its efficacy in attribute synthesis and unsupervised clustering analysis. By extracting multi-dimensional attribute volumes that characterize geological features, the SOM approach clusters attributes exhibiting similar data patterns. This methodology facilitates the generation of high-resolution three-dimensional visualizations with hollowing effects, significantly enhancing the clarity of sand body geometries and boundary identification [62,63].

Beach-bar deposits are characterized by their thin reservoir thickness and rapid lateral variability. The current demand for precision in reservoir identification has escalated to 3–8 m, surpassing the vertical resolution limits of seismic data. This study addresses these challenges by guiding geological insights and seismic sedimentology. In regions with well control, we introduce well logs that possess high vertical resolution. By utilizing seismic waveforms to drive these well logs, high-resolution inversion is attained [64]. We have established a seismic waveform indicative inversion technique which employs efficient dynamic clustering analysis of seismic waveforms to create a mapping relationship between the structures of seismic waveforms and high-frequency well log data. This approach enhances both the vertical and lateral resolution of the inversion results, ultimately improving the predictive accuracy when identifying thin sand bodies.

In areas with limited well control, the Self-Organizing Map (SOM) seismic attribute clustering method compensates for the inversion accuracy limitations caused by a scarcity of wells [65,66]. This method clusters attributes with similar significance for thorough analysis and evaluation, resulting in a clearer representation of the spatial distribution of sand bodies. The integration of these two methodologies addresses the challenges of low vertical resolution in seismic data and the inherent multiplicity of interpretations in seismic analysis from different perspectives, thereby providing novel insights for predicting thin-layered sandstone and delineating boundaries in sparsely sampled regions.

This paper systematically elucidates the principles underlying the SOM seismic attribute clustering method and seismic waveform indicative inversion technique. In addition, it conducts a thorough analysis of the feasibility and reliability of their integrated application, facilitating high-precision prediction research for thin reservoirs in well-scarce areas. Through a case study analyzing the microfacies characterization of thin-layer beach-bar deposits in the lower E₃d₂ member of the Paleogene in the HHK Depression of the Bohai Bay Basin, we conclude that, guided by geological understanding and sedimentary models, the integration of SOM multi-attribute optimization and seismic waveform inversion effectively addresses the challenge of predicting thin-layer sand bodies in continental regions with few wells.

2. Regional Geological Background

The HHK Depression in the study area is located in the southern part of Bohai Bay Basin, which can be further divided into the northern steep slope zone (east and west segments), the southern slope zone (east and west segments), the central strike-slip zone, and the central uplift zone (Figure 1).

The Kongdian Formation (E_1–2k), the fourth member of the Shahejie Formation (E₂s₄), the third member of the Shahejie Formation (E₂s₃), the second member of the Shahejie Formation (E₃s₂), the first member of the Shahejie Formation (E₃s₁), the third member of the Dongying Formation (E₃d₃), the second member of the Dongying Formation (E₃d₂), and the first member of the Dongying Formation (E₃d₁) developed successively from top to bottom in the Paleogene in this area [31]. The E₃d₂ member can be further subdivided into the lower E₃d₂ sub-member and the upper E₃d₂ sub-member. The corresponding seismic reflective layer interfaces for members from E₂s₄ to E₃d₁ are as follows: T₇ (E₂s₄), T₆ (E₂s₃), T₅ (E₃s₂), T₄ (E₃s₁), T₃ (E₃d₃), T₃^m (E₃d₂^l-the lower E₃d₂ sub-member), T₃^u (E₃d₂^u-the upper E₃d₂ sub-member), and T₂ (E₃d₁) (Figure 2).

In terms of tectono-sedimentary evolution, the E₃s₂ to E₃d₁ stages of the HHK Depression are in the rifting stage of basin tectonic evolution, with an average tectonic subsidence rate ranging from 11.54 to 54.7 m/Ma. The E₃d₃ shows a higher tectonic subsidence rate. The intensity of rifting activity gradually weakens and rifting action attenuates in the later period, which marks the beginning of the transition to a post-rift depression [64]. Macroscopically, the HHK Depression Paleogene segments have certain differences in lithology combination characteristics and sedimentary facies distribution. They also have inheritance characteristics. In the study area, E₃s₂ to E₃d₂ are in the fault-depression period during the development of the Bohai Bay Basin. The geomorphology tends to be flat in the E₃s₁ period, and the overall thickness of strata in the area is thin and stable. During the sedimentary period of the Dongying Formation, the intensity of fault activity increased, and a set of thick lacustrine mudstone developed in the early stage of E₃d₃ [65]. The HHK Sag was affected by tectonic activities during the E₃d₃ period, resulting in fault activation and large-scale lake invasion. The HHK Depression is dominated by thick mudstone with thin sandstone and siltstone and locally developed braided river delta and beach-bar deposits. During the lower E₃d₂ Sub-member, the basin tectonic subsidence rate gradually weakened, the paleowater depth changed from deep to shallow, and the delta sediment advanced to the lake, which was significantly affected by the transformation of lake waves. The beach-bar scale gradually increased, and braided river delta and beach-bar sediments developed. This study focuses on the beach-bar sedimentary characteristics of the lower E₃d₂ Sub-member of the Paleogene HHK Depression (Figure 3).

3. Materials and Methods

3.1. Seismic Data Quality Analysis

The seismic resolution analysis was conducted using two independent methodologies: detuning analysis and acoustic travel-time calculation, based on the dominant frequency (18 Hz, Time = 1/18) and characteristic interval velocity (V = 3700 m/s) of the target layer in the study area. The tuning thickness was determined through the wavelength equation:

$$\lambda ={\displaystyle \raisebox{1ex}{$V\ast \mathrm{T}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$$

(1)

λ: Wavelength, m

V: Velocity, m/s

T: Time, s

This establishes the theoretical vertical resolution threshold for deterministic inversion at 52 m. The inherent resolution limitation poses significant challenges in characterizing thin sand layers of below 10 m thickness. Conventional acoustic impedance inversion demonstrates suboptimal predictive accuracy for these sub-resolution thin beds, particularly in delineating vertical compartmentalization and lateral continuity. To address these technical constraints, we developed an integrated workflow combining rock physics analysis, SOM multi-attribute optimization, and seismic waveform inversion. This methodological framework effectively leverages the spatial predictive capabilities of seismic data while maintaining strong geological constraints through depositional pattern recognition and petrophysical calibration (Figure 4).

3.2. Well Logging Data Preprocessing

Quality control of logging data from individual wells, as well as consistency checks of logging data from multiple wells, are integral components of the log data analysis process. This is crucial for establishing reliable rock physics models and ensuring high-quality seismic inversion. The preprocessing of the logging data in this study primarily encompasses environmental correction, outlier management, and curve standardization.

Consistency checks of multi-well logging data are a vital quality control step in the seismic-constrained inversion process with well calibration. Systematic errors may arise from different generations of logging instruments, variations in the properties of the mud utilized in each well, and influences from wellbore conditions. These factors can result in significant discrepancies in the logging responses of identical logging curves at standard layers across different wells [66].

The presence of such discrepancies suggests that seismic synthetic records calibrated using well data and seismic lithology inversions constrained by multiple wells may involve various uncertainties [67]. Consequently, building upon the quality control of single-well data, the standardization and correction of multi-well data represent essential quality control measures in the integration of well and seismic information [68].

The specific procedure is as follows: A histogram of logging response frequencies or a frequency intersection graph is constructed for the standard layer of the well in question and compared in detail with the corresponding graph for the same standard layer from a key well [69]. If the two sets of values are identical and exhibit similar shapes, this indicates that the curve calibration for the well is accurate. Conversely, if discrepancies are noted, it suggests an error in the calibration of the logging curve for that well [70]. In such instances, the difference between the characteristic values of the standard layer logging curves across each well and the characteristic values from the key well’s standard layer is utilized as the correction value for the well’s logging curve [71].

Building on this foundation and integrating research requirements with the practical conditions of well logging data, a stable mudstone interval from the lower Dong-2 Member was selected as the reference layer. The core of the mudstone-referenced gamma ray (GR) and density (DEN) curve standardization method lies in establishing a normalization baseline based on the radioactive and density characteristics of mudstone, thereby eliminating the effects of instrumentation, environmental conditions, and lithological variations on logging data [72]. This mudstone interval exhibits lateral stability and distinct logging response features, including high natural gamma ray (GR > 100 API), high density (DEN: 2.0–2.5 g/cm³), moderate neutron porosity, and acoustic transit time. Using the GR values of pure mudstone layers as the baseline (120–130 API), the GR offsets for other wells were calculated. Simultaneously, systematic errors in the density curves were corrected based on the average mudstone density (2.3 g/cm³). Subsequently, standardization procedures were applied to all of the wells within the study area involved in the inversion analysis.

Following the standardization process, the probability histogram matching method was employed for multi-well consistency checks. Probability distribution histograms for natural gamma, density, and other log curves were generated for each well in the study area (Figure 5). These histograms demonstrated good interwell consistency within the region, making them suitable for subsequent rock physics analysis. The environmental correction of the original logging data and the rationality correction of reservoir parameters ensure that we obtained a relatively accurate and reasonable series of key logs. This, in turn, guaranteed a high correlation in the well-seismic relationships during subsequent inversion processes.

3.3. Petrophysical Analysis

Petrophysical analysis, also known as reservoir sensitivity parameter analysis, aims to identify one or more logging parameters that can effectively distinguish reservoirs by analyzing the distinct features displayed by different lithofacies on logging curves [73]. This provides geological guidance for the selection of pseudo-wave impedance reconstruction and well-seismic combined reservoir inversion methods, serving as an essential foundational task for reservoir prediction. Due to the myriad types of logging curves, it is crucial to conduct sensitivity analyses to determine which curve is the most effective at differentiating between reservoir and non-reservoir zones. This is typically accomplished using techniques such as histograms and cross-plots [74,75].

The lithological types prevalent in the study area include sandstone, siltstone, mudstone, limestone, and dolomite, among others. A single log curve is often insufficient for effective reservoir identification. Therefore, a combination of multiple logging parameters is necessary for the comprehensive identification of high-quality reservoirs [76]. Analysis of a single well reveals that the thin-layered sandstone in the lower second sub-member of the Dongying Formation is characterized by low acoustic wave velocity, low gamma radiation, and relatively high resistivity. Petrophysical analysis indicates that the resistivity and gamma measurements for the Dongying Formation do not effectively identify sandstone (Figure 6a,b). In contrast, the constructed lithology indicator curve successfully identifies sandstone, with a sandstone cutoff value of less than 83 (Figure 6c).

Based on the results from the petrophysical crossplot analysis, the reconstructed lithology curve can effectively differentiate sandstone from other lithologies. Vertically, it can resolve sand bodies as thin as 5 to 10 m (or even thinner), while horizontally, it clearly delineates the boundaries and stacking relationships of sand bodies. The reconstructed curve is capable of distinguishing between sandstone and mudstone effectively [77,78]. Building on this, seismic waveform-based inversion mechanisms are employed for predictions. By incorporating the concept of well-seismic integration, high-frequency information from the well is extracted to enhance the predictive accuracy for thin layers. This method facilitates the quantitative prediction of the distribution of thin-layer sandstones [79].

4. Principles of Technical Methods

By comparing major methods in geophysical-seismic waveform inversion, Self-Organizing Maps (SOM), traditional deterministic impedance inversion, Kriging, and single-attribute thresholding, this study summarizes their core principles, characteristics, and applicable domains (

Table 1. Comparative Analysis of Geophysical Methods [80,81,82,83,84,85,86].

Method	Core Advantages	Limitations	Applicable Scenario
Traditional deterministic impedance inversion	High vertical resolution, fast computation	Low lateral resolution, multiple solutions	Preliminary exploration of well-controlled areas
Seismic Waveform Inversion	High resolution, multi-data integration	Complex computation, data sensitivity	Detailed prediction of complex reservoirs
SOM	Unsupervised clustering, low computational demand	Limited capability in handling nonlinear structures	Attribute classification and real-time processing
Kriging	Spatial modeling, uncertainty quantification	Complex computation, model dependency	Heterogeneous attribute interpolation
Single-attribute thresholding	Simple and fast	Singular information, poor adaptability	Rapid screening and simple environments

) [80]. The analysis highlights the inherent limitations of conventional approaches. Deterministic inversion and Kriging rely heavily on physical or statistical assumptions, while single-attribute thresholding suffers from over-simplification. These limitations make these techniques inadequate for addressing complex geological challenges [81,82]. In contrast, SOM leverages unsupervised learning to achieve multi-attribute integration and nonlinear modeling, rendering it particularly effective for automated seismic facies classification and reservoir prediction [83,84]. Integrating SOM with seismic waveform inversion demonstrates potential in resolving the delineation of thin-bedded beach-bar sand body boundaries in the study area, offering a hybrid approach that combines data-driven pattern recognition with physics-based constraints [85,86].

4.1. Seismic Waveform Inversion

Seismic resolution is divided into two aspects: vertical resolution and lateral resolution. Rayleigh was the first to introduce the concept of vertical resolution, which is the resolution limit for two adjacent reflective interfaces at one-quarter of a wavelength. Geological bodies with thicknesses less than one-quarter of a wavelength can be defined as thin layers and cannot be distinguished using seismic data. Logging curves corresponding to similar waveforms exhibit a higher degree of similarity over a broad frequency band. Therefore, by utilizing the lateral similarity of seismic waveforms to drive high-frequency logging information, a high-resolution inversion is achieved [87]. This has led to the establishment of the Seismic Waveform Inversion.

The methodology employs systematic analysis of lateral seismic waveform variations to estimate high-frequency components, characterizing structural patterns in vertical lithological assemblages within reservoir formations. By integrating facies-controlled constraints into lateral dimension interpretation, this technique establishes an integrated well-seismic simulation framework that transitions inversion results from stochastic estimations to constrained solutions [88]. The approach achieves progressive determinism in subsurface modeling without requiring uniform well distribution configurations. Operational advantages include enhanced inversion precision and extended applicability to complex depositional environments with sparse well control.

Under isochronous stratigraphic framework constraints, lateral variations of seismic waveforms replace variograms to characterize reservoir spatial heterogeneity [89]. The fundamental principle leverages the dense spatial distribution of seismic data and the intrinsic correlation between waveform characteristics and depositional environments. By utilizing lateral waveform variations as spatial variability indicators, the approach enhances the representation of sedimentary controls, enabling facies-constrained stochastic inversion.

Within the Bayesian theoretical framework, the method integrates prior model parameter distributions with observed data to formulate posterior probability density functions. The inversion solution is obtained through posterior distribution optimization, accompanied by uncertainty quantification to validate the result’s reliability. This process establishes rigorous mathematical foundations for objective function construction [90].

The workflow implements iterative model perturbation techniques to progressively approximate sample data distributions, ultimately yielding high-resolution inversion results. Under Bayesian constraints, optimal statistical sampling prioritizes wells with high similarity metrics and spatial proximity to build initial models [91]. High-resolution well-seismic joint simulation achieves interwell reservoir prediction with seismic waveform constraints, simultaneously improving vertical and lateral resolution (Figure 7).

4.2. SOM-Based Seismic Attribute Clustering Analysis

Seismic attribute analysis can effectively predict sandbody distribution, but numerous studies have demonstrated that single seismic attributes exhibit low correlation coefficients with drilled sandstone thickness, making it challenging to achieve precise interpretations for thin-layer sandbodies. To address this limitation, an optimized fusion approach for seismic attributes is adopted to enhance their correlation with sandstone thickness [92].

The key to thin-layer sandbody characterization lies in effective sandbody identification. Self-Organizing Maps (SOM), an unsupervised neural network method, is widely utilized in seismic attribute analysis for feature extraction, clustering, and visualization. By extracting multiple attributes representing geological characteristics and applying SOM to cluster attributes with similar data features, a three-dimensional spatial visualization of attribute “hollow maps” can be generated, significantly improving sandbody boundary identification [93]. Combined with high-resolution seismic inversion techniques, this approach reduces the interpretative ambiguity in seismic inversion, thereby enhancing the precision of sandbody boundary delineation [94].

The primary workflow involves seismic attribute optimization and SOM network configuration. In this study, five interbedded seismic attributes were extracted from the 2nd sand layer of the Dong’erxia Subsection in the Huanghekou Sag: Root Mean Square Amplitude (RMS), Total Energy (TE), Average Energy (AE), Amplitude Envelope (ENV), and Peak Amplitude (PA). These attributes exhibit strong correlations with sandstone thickness [95]. A rectangular network structure was selected for SOM, comprising two neural layers: an input layer and a competitive layer. The competitive layer adopted a 10 × 10 grid structure, containing 100 neurons. Each neuron in the grid occupies a specific spatial position [96]. The five optimized attributes were assigned as inputs to the network, with each neuron receiving a five-dimensional input vector corresponding to the five seismic attributes. When an input is presented, the neuron with the smallest Euclidean distance to the input vector is designated as the winner (WTU) (Figure 8) [97]. This is determined by calculating the distance between the weight vectors (W) of all neurons and the input vector (X):

$$dj=\sqrt{{\displaystyle \sum _{i=1}^N{{\displaystyle (Wji-Xi)}}^2}}$$

(2)

dj: The distance between the weight vectors (Wji) and input vectors (Xi)

Wji = (W11, W22, ..., Wpn), j = 1, 2, ..., p,i=1, 2, ..., n (where p is the total number of neurons in the network) represents an ordered sequence of weight values, forming an internal representation of the neural network

Xi = (x1, x2, ..., xn),i=1, 2, ..., n denotes an ordered input sequence, where each seismic attribute can be viewed as an independent coordinate axis in the data space.

The competitive learning mechanism ensures that the winning neuron and its neighboring neurons adjust their weights iteratively, thereby preserving the topological relationships within the input data. The two-dimensional grid of the competitive layer represents the topological structure after dimensionality reduction, with Wji serving as the corresponding image of Xi [98]. The winning neuron and its neighboring neurons adjust their weight vectors to approach the input data, a process controlled by a neighborhood function (typically implemented using the Mexican Hat Wavelet, also known as the Ricker wavelet) [99]. The mathematical expression of this neighborhood function is as follows.

$$\Lambda (r)={{\displaystyle e}}^{{\displaystyle \frac{{{\displaystyle d}}^2}{{{\displaystyle 2\sigma }}^2}}}$$

(3)

ʌ: Neighborhood weight

r: Neighborhood radius

σ: Controls the decay rate (larger σ results in smoother weight distribution)

d: Distance function (Manhattan distance is adopted due to its sparse dimensionality independence, strong robustness, and emphasis on local abrupt features).

Based on the distribution of each attribute across SOM neurons, the correlations between attributes are analyzed and optimized, where adjacent neurons represent regions with similar attribute combinations [100]. The color patterns and clustering results on the two-dimensional grid can indicate seismic facies associated with sand body boundaries, with each seismic facies possessing clear physical and geological significance [101].

4.3. Technical Workflow for Thin-Bedded Sandbody Boundary Delineation

For the Lower E₃d₂ Sub-member, an optimized analysis was conducted by integrating seismic facies characteristics and well logging data. Earthquake attributes insensitive to seismic facies were excluded, and those with similar data features were evaluated using correlation and clustering analysis to select optimal seismic attributes. Three types of seismic attributes capable of characterizing the distribution of thin sand bodies were extracted: envelope attributes, main peak attributes, and amplitude energy (Figure 9a). By examining individual attributes, boundaries were delineated using artificial intelligence-based SOM (Self-Organizing Map) clustering to group data with consistent features. Subsequently, well-seismic calibration was employed to determine the threshold for sand body distribution (Figure 9b). After hollowing out non-sand bodies, the spatial distribution of the Lower Member of the Second East Sandstone Formation was sculpted (Figure 9(c-1)). This approach enhances the visibility of beach-bar sand body distribution and provides clearer identification and delineation of sand body edges compared to using single attributes alone.

The attribute hollowing-out map of the Lower E₃d₂ Sub-member (Figure 9(c-1)) reveals that the study area can be primarily divided into three regions: red, yellow, and green. The number of colors corresponds to the identified clustering types. Based on potential sedimentary environments, green is defined as areas with thin sand bodies near the sandstone pinch-out boundaries, red represents thicker sand bodies marking the main body of the beach-bar, and yellow indicates a transition zone where sand body thickness gradually decreases. Sandstones are concentrated in the southern part of the central strike-slip zone, the central uplift zone, and the development of the northwestern sub-sag, exhibiting sheet-like and domal distributions overall.

SOM-based seismic multi-attribute clustering and waveform inversion analysis reveal significant amplitude anomalies on both the east and west sides of the key area, with the anomalies extending in a north-south direction. The central and northern parts exhibit weak amplitudes. Inversion slices show high-resistance anomaly features in the northern parts of well areas C3-1-a and C4-3-a, as well as in the northern part of well area C4-3-a, with irregular dome-shaped boundaries of the anomaly zones. Combining single-well data and geological understanding, waveform inversion was used to predict the cumulative thickness of the Lower E₃d₂ Sub-member, resulting in a thickness map of sandbody distribution (Figure 9(c-2)). Sandstone layers have developed in the southern part of the central strike-slip zone, the central uplift zone, and the northwestern sub-sag, with thicknesses ranging from 4 m to 12 m. Thick sandbodies are concentrated near wells B8-2-a and C4-4-b in the eastern part of the study area, extending in a near NE-SW direction, while the southwestern part has a large sandbody distribution area with thinner thicknesses (4–8 m) and a sheet-dome shape. The sandbody distribution range is consistent with the structural highs on the top surface map of the Lower E₃d₂ Sub-member, indicating the potential for oil and gas exploration in the target area.

The inversion thickness map shows that the sandbody thicknesses in well areas C3-1-a, C4-3-a, and B8-2-a are relatively thick and gradually thin out toward the surrounding areas. The pinch-out lines of the sandstone thickness and the boundaries of the high-amplitude anomaly regions of the attributes show a high degree of coincidence. Based on the prediction of sandbody thickness, combined with litho-electric characteristics and seismic response features, three microfacies types of the beach-bar system in the HHK Sag are identified: bar body, beach body, and beach edge. The bar body has a sandbody thickness of approximately 8–14 m, the beach body 3–8 m, and the beach edge 0–3 m. The specific characteristics are shown in Figure 9d.

The integration of Self-Organizing Maps (SOM) machine learning theory and Seismic Meme Inversion (SMI) waveform inversion methodology addresses the limitations of low vertical resolution in seismic data volumes and multi-solution ambiguity in seismic interpretation. This fusion enables the precise delineation and identification of thin-layer sandbody boundaries under conditions of sparse well data.

5. Applications and Discussion

5.1. Geological and Geophysical Characteristics

During the Paleogene sedimentary period of the lower E₃d₂ Formation in the HHK Depression, the study area was situated within a lacustrine transgressive system tract (TST) characterized by braided-river delta-bar depositional systems. Quantitative analysis of individual sandbody dimensions (thickness and frequency) reveals that the thin-bedded beach-bar facies in the lower Ed₂ Formation predominantly consist of gray, fine-grained feldspathic litharenite, lithic feldspathic sandstone, feldspathic sandstone, and litharenite, with localized siltstone interbeds (Figure 10a). The lower Ed₂ member of the Paleogene succession in the study area exhibits a distinctive stratigraphic architecture characterized by thin-bedded sandstone packages intercalated within thick mudstone sequences (Figure 10a). Individual sandstone beds range from 3 to 8 m in thickness, typically comprising 1–2 discrete layers vertically separated by mudstone intervals exceeding 100 m in cumulative thickness. This vertical stacking pattern manifests a “thin-bedded sandstone-thick mudstone” alternation, indicative of low accommodation/sediment supply conditions.

The quartz content within the sand bodies ranges from 29.0% to 46.0% (average: 36.2%), while feldspar content varies from 29.0% to 41.0% (average: 34.8%). The proportion of lithic fragments falls between 25.0% and 33.0% (average: 29.75%). The cumulative probability curve exhibits a segmented pattern of two to three segments, with an average particle size (Mz) of 0.474 mm and a skewness (Sk) of 0.922. The saltation fraction content ranges from 30% to 50%, while the suspension fraction content exceeds 50%. The phi (ϕ) value at the intersection between the saltation and suspension fractions ranges from 2.5 to 3.5, indicating that the fine cutoff point skews toward finer sizes. This suggests a reduced proportion of the saltation fraction and a greater overall content of suspension, indicative of pronounced suspension sedimentation and wave action (Figure 10b). The sorting of particles is classified as good to moderate, while the roundness ranges from moderate to sub-rounded, with grains primarily exhibiting point-to-line contacts (Figure 10c).

Thick-layered beach-bar sand bodies typically display natural potential (SP) and natural gamma (GR) curves characterized by large amplitude and exhibiting funnel-shaped or boxy profiles. Conversely, thin-layered beach-bar sand bodies present natural potential (SP) curves with medium to low amplitudes, displaying finger-like profiles, while the natural gamma (GR) curves reveal a fine-toothed, finger-like configuration (Figure 10d). The seismic facies of the beach-bar deposits within the study area are characterized by moderate to good continuity, with parallel to subparallel reflector configurations and medium to strong amplitude reflections. Thicker sand bodies exhibit seismic facies distinguished by high continuity and strong amplitude reflections, whereas thinner sand bodies demonstrate seismic facies characterized by moderate continuity and medium strength amplitude reflections (Figure 10e).

5.2. Results of Rock Physics Analysis

This study investigates a 3D seismic survey area (400 km²) with 23 wells distributed unevenly. To assess the validity of the waveform indicator inversion algorithm under sparse-well conditions, we conducted an inversion experiment using an uneven well network: 12 wells were selected for inversion (training set), while 11 wells served as independent validation data (

Table 2. Sandstone thickness values of the Lower E₃d₂ Sub-member for the Participant Well and Verification Well, calculated through well log interpretation and inversion prediction.

Participant Well	Sandstone Thickness/m		Verification Well	Sandstone Thickness/m
	Well Log Interpretation	Inversion Prediction		Well Log Interpretation	Inversion Prediction
B7-2-b	1.3	0.5	B8-2S-b	1.8	2.3
B7-2-d	1.5	3.2	C4-2-a	8	7.6
B7-2-a	2.4	1.1	C-5-b	4.5	3.9
C4-3-bD	2.9	3.4	B7-2-e	4.6	2.6
C4-4-e	2.9	3.3	C4-1-a	5.3	5.6
C4-3-a	3.0	5	B6-5-a	5.6	7.1
B7-2-c	3.1	1.8	B7-4-a	7.3	6
C4-5-a	3.6	4.6	B7-4-b	7.7	8.5
B8-3-b	4.3	5.8	B8-2-a	8.8	10.0
C3-1-a	16.5	14.3	C4-4-c	10.1	9.1
C4-4-a	5.7	6.8	C4-2-bA	12.3	8
B7-5-a	8.8	6.3

, Figure 11c).

Pearson’s correlation coefficient was used to separately compute correlation values between well log-derived and inversion-predicted sandstone thicknesses for both the participant and verification wells (Figure 11a). The P-wave impedance inversion results (Figure 11b) demonstrate strong consistency with both the training and validation wells, yielding high correlation coefficients (R² = 0.927 for training wells, R² = 0.821 for validation wells).

The inversion successfully resolves thin sandstone layers (3–8 m) and accurately captures their lateral variations, as evidenced by the clear identification of layer boundaries in the impedance profile, consistency between predicted sandstone thickness (from inversion) and log-derived measurements, and effective delineation of lateral facies transitions matched by seismic reflectivity patterns. These results confirm that the waveform indicator inversion method provides reliable lateral resolution (≥3 m) for lithological characterization in complex reservoirs with sparse well coverage.

To further validate the precision of the waveform-based inversion method in identifying thin sandstone layers, we extracted well-site curves using well C4-3-a as an example (Figure 12). The first purple curve in Figure 12 represents the measured DT curve, the second blue curve corresponds to the measured GR curve, and the third curve (IMP) is the inversion result. The inversion-derived wave impedance profile (waveform indicator inversion result) shows high consistency with the measured curves. By applying a sandstone discrimination threshold, the lithological interpretation of the inversion results aligns well with the actual well logging interpretations, accurately identifying sandstones with thicknesses of 1.8–3.0 m (Figure 12).

5.3. Cross-Section Inversion Results

A comparative analysis of well-linked cross-sections and inversion profiles in the Lower Second Member of the Dongying Formation reveals that, due to boundary constraints in the study area, sandbody boundaries extend outward, and thin sand layers (3–8 m) are stably distributed. The inversion profile clearly delineates effective sandbodies in individual wells, with accurate prediction of sandbody pinchouts (Figure 13).

Petrophysical analysis and application results demonstrate that the seismic waveform-indicated inversion technique can identify 1.8–3.0 m-thick thin sandstone layers, with a mean match rate of 90.2% (95% CI: 87.5–92.7%, n = 12) for participating wells and 81.5% (95% CI: 76.8–85.3%, n = 11) for validation wells, based on bootstrap resampling with 1000 iterations. Additionally, the waveform-based facies-controlled constrained inversion exhibits robustness to well distribution constraints, as evidenced by spatial cross-validation results, while maintaining geological consistency.

To address the uncertainty in thin-layer sand body prediction, this study attempts to integrate waveform-indicated inversion with SOM. By employing facies-controlled inversion and uncertainty propagation analysis, the goal is to control reservoir prediction errors within 10%, enhance vertical resolution, improve thin-layer identification accuracy, and reduce ambiguity in thin-layer predictions. However, significant room for innovation remains. Future efforts could further explore deep learning domains and real-time uncertainty feedback mechanisms to enhance exploration reliability under complex geological conditions.

5.4. Planar Sedimentary Microfacies

Through the integrated application of geological understanding with SOM multi-attribute optimization and waveform-indicated inversion techniques, a detailed characterization of beach-bar sedimentary microfacies in the Lower E₃d₂ Sub-member of the study area was conducted, identifying three microfacies types: bar body, beach body, and beach edge. Two distinct patterns emerge in microfacies boundary delineation: a sparsely drilled area in the western sector and a relatively well-drilled region in the eastern sector of the focus area.

Based on geological characteristics and depositional system analysis, the eastern sector primarily employs well-controlled waveform-indicated inversion for microfacies boundary characterization. This approach involves: determining microfacies types at well locations through single-well facies analysis combined with logging facies characteristics, supported by sandstone core samples and lithological analysis; delineating sandbody extension boundaries using inversion profiles to objectively represent sedimentary microfacies distribution.

For the western low-well-density area, a comprehensive methodology was implemented. Geological–seismic attribute analysis guided the creation of SOM-processed attribute hollow maps for the Lower E₃d₂ Sub-member. Seismic characteristics from drilled areas were analogously applied to undrilled zones. Integrated analysis incorporating geological data, acoustic impedance inversion, and SOM multi-attribute optimization established micro-facies assemblage relationships of beach-bar sandbodies, enabling effective sedimentary microfacies characterization in the undrilled western sector.

The planar distribution characteristics of the beach-bar sedimentary microfacies are as follows:

Eastern Beach-bar: Near the B8-2-a well at the northern boundary, the sandbody is relatively thick and the bar body is well-developed, with the same extension direction as the western beach-bar. The outer beach body extends in the SW-NE direction along the direction of lake wave reworking. One large-scale and two small-scale beach bodies develop to the south, with the beach edge surrounding the beach body in a south-north strip-like distribution (Figure 14).

Western Beach-bar: Near the C3-1-a well, the sandbody is relatively thick and the bar body is well-developed, showing an enhanced northward extension trend. A large-scale beach body is present in the form of a wide strip, and a smaller-scale beach body is developed in the north in the form of a narrow strip. The beach edge develops around the beach body, showing a near-NS strip-like distribution (Figure 14).

6. Conclusions

• The lithological types in the study area predominantly consist of sandstone, siltstone, mudstone, limestone, and dolomite. A single logging curve is inadequate for reservoir identification. Therefore, a lithology indicator curve was developed to effectively identify sandstone, utilizing a cutoff value of less than 83. Subsequently, seismic waveform inversion was employed to predict thin sand bodies, which can be identified vertically at depths of 3 to 8 m and laterally with distinct boundaries. The validation results of the inversion demonstrate a coincidence rate exceeding 90% with the participating wells and over 80% with the verification wells.
• Guided by seismic sedimentary theory, a Self-Organizing Map (SOM)-based multi-attribute optimization analysis was conducted utilizing three seismic attributes sensitive to lithological characteristics: Root Mean Square Amplitude (RMS), Total Energy (TE), Average Energy (AE), Amplitude Envelope (ENV), and Peak Amplitude (PA). SOM operations were employed for correlation and clustering analyses to identify a subset of data that reflects lithological features. In conjunction with well-seismic calibration, a threshold for sandstone distribution was established, non-sandstone areas were excluded, and a spatial hollowing-out map of the Lower Member of the Second East Sandstone Formation was produced. The visual representation of this map, in comparison to single attributes, emphasizes the distribution of beach-bar sand bodies and facilitates clearer identification and delineation of the sandbody edges.
• Seismic waveform inversion, which embodies phase-controlled principles, operates independently of the quantity and distribution of wells. The Self-Organizing Map (SOM) algorithm is effectively employed for comprehensive attribute clustering analysis. The integration of these two techniques in the study of beach-bar microfacies within the Lower Member of the Second East Sandstone Formation in the HHK Depression reveals a strong correlation between sandstone thickness pinch-out lines and the boundaries of attribute amplitude anomalies. By predicting sandbody thickness through waveform inversion and integrating litho-electric characteristics with seismic responses, three microfacies types are delineated: bar body, beach body, and beach edge. The thickness of the bar body sandbody is approximately 8 to 14 m, the beach body ranges from 3 to 8 m, and the beach edge measures between 0 and 3 m.
• Guided by geological principles and seismic sedimentology theory, high-resolution waveform indicator inversion is employed in well-controlled areas to enhance the accuracy of thin-sandstone predictions. In regions lacking well control, Self-Organizing Map (SOM) based seismic attribute clustering mitigates the limitations of inversion precision by clarifying the spatial distribution of sand bodies. This integrated methodology addresses two critical challenges in seismic interpretation: the low vertical resolution of seismic data and the complexities associated with lithological identification. By combining the high-resolution capabilities of waveform inversion with the pattern recognition advantages of SOM clustering, this approach offers a novel solution for predicting thin sandstones and delineating boundaries in sparsely sampled areas.