## 2 Methodology and Data
### High Precision and Wide Range XCH4 Fusion Dataset Construction
Finally, this study uses the Normalized Difference Water Index (_NDWI_) to extract the water body mask, with the formula defined as

\[NDWI=\frac{b(Green)-b(NIR)}{b(Green)+b(NIR)} \tag{4}\]

This index is calculated as the ratio of the difference between the _green_ and near-infrared (_NIR_) bands to their sum. The _NDWI_ is computed for each pixel in the image, and the pixels are then classified as water bodies based on a predefined water threshold. Pixels with an _NDWI_ value greater than the threshold are identified as water bodies. ### Construction of High-Resolution XCH\({}_{4}\) Fusion Dataset for Oil Fields

To obtain a high-resolution XCH\({}_{4}\) fusion dataset tailored to the needs of the oil and gas industry, we designed a method using \(\Delta\)XCH\({}_{4}\) retrieved from GF-5, combined with the GFEI prior emissions inventory. We reallocate the high-precision fusion dataset output by the LRF model grid by grid in specific areas, producing a 1 km resolution XCH\({}_{4}\) grid product. Based on the Beer-Lambert law, the increase in the column density of gas molecules \(\Delta\)XCH\({}_{4}\) will affect the observed spectrum:

\[x_{m}(i,j)=x_{r}(i,j)_{L\times 1}\cdot e^{-k_{L\times 1}\cdot\Delta XCH_{4}(i,j)} \tag{5}\]In Equation (5), \(x_{m}\) represents the radiance observed by the sensor, i.e., the observed spectrum; \(x_{r}\) represents the reference radiance; \(k\) denotes the absorption coefficient per unit gas concentration; \(i\) and \(j\) are the horizontal and vertical retrieval index coordinates in the two-dimensional hyperspectral image; and \(L\) is the length of each column in the image. To simplify the calculations, Equation (5) is expanded to a first-order approximation using the Taylor series. Since the GF-5 AHSI sensor collects data in a column-by-column scanning mode, the inversion is performed on each column as a unit, with the mean radiance of that column approximating the reference radiance. To obtain an accurate \(\Delta\)XCH4, we solve it using the least squares method. By minimizing the weighted sum of squared residuals between each spectral band's prior value (prior spectrum) and the observed value (observed spectrum), we can achieve the optimal estimate of the enhancement in the column density of each gas. The log-normal distribution improves the original matched filter, i.e., LMF, addressing the issues with residuals in the conventional matched filter (MF). By taking the logarithm of both sides of Equation (5) and performing least squares operations, we obtain the LMF matched filter detector:

\[\Delta XCH_{4}=\frac{\left(\ln(x_{m}(\lambda))-\ln(x_{r}(\lambda))\right)^{T} \!\!\sum^{-1}k}{k^{T}\!\!\sum^{-1}k}, \tag{6}\]

[PERSON] et al. proposed that iterative logarithmic matched filtering allows for the updating of mean and covariance matrices, which effectively reduces the contamination of the target signal by background statistics [13]. The column density enhancement values calculated using Equation 6 are used to update the mean and covariance matrices iteratively until convergence. Outliers are considered statistically significant if they exceed twice the noise level (2\(\sigma\) threshold, \(p<0.05\)). The iteration terminates either when no outliers are detected or when the number of iterations exceeds five. Subsequently, the final updated mean and covariance are used to obtain the 30 m resolution \(\Delta\)XCH4 image. In addition, this study utilized the GFEI emissions inventory ([[https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/HH4](https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/HH4) EUM&version=1.0]([https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/HH4](https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/HH4) EUM&version=1.0), accessed on 1 October 2024). Developed by Harvard University, GFEI assesses methane emissions. The inventory was compared with satellite results from the Global Atmospheric Methane Observation Satellite (GOSAT) and in situ observation platform (GLOBALVIEW).