## 4 Principles of Technical Methods
### Seismic Waveform Inversion  
Seismic resolution is divided into two aspects: vertical resolution and lateral resolution. [PERSON] 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 \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Core Advantages** & **Limitations** & **Applicable Scenario** \\ \hline Traditional deterministic & High vertical resolution, & Low lateral & Preliminary exploration of \\ impedance inversion & fast computation & resolution, multiple & well-controlled areas \\ \hline Seismic Waveform & High resolution, multi-data & Complex computation, & Detailed prediction of \\ Inversion & integration & data sensitivity & complex reservoirs \\ \hline SOM & Unsupervised clustering, & Limited capability in & Attribute classification and \\  & low computational & handling nonlinear & real-time processing \\  & demand & structures & \\ \hline Kriging & Spatial modeling, & Complex & \\  & uncertainty quantification & computation, model & Heterogeneous attribute \\  & & dependency & interpolation \\ \hline Single-attribute & & Singular information, poor & Rapid screening and \\  & thresholding & adaptability & simple environments \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative Analysis of Geophysical Methods [80; 81; 82; 83; 84; 85; 86]. similarity metrics and spatial proximity to build initial models [91].