In the process of oil and gas exploration and development, ultrasonic logging imaging technology visually displays the lithology, structure, fractures, pores, and other characteristics of the wellbore. This technology has been widely applied in the exploration and development of oil and gas resources. However, the low circumferential sampling rate negatively affects the imaging quality and resolution during drilling logging. To address the issues of low resolution and blurriness in ultrasonic logging images caused by these factors, as well as the limitation of existing super-resolution reconstruction algorithms that can only reconstruct fixed scales, this paper presents an Image Super-Resolution Reconstruction Network called Residual Dense Feature Aggregation (SR-RDFAN-LOG), which is specifically designed to improve ultrasonic logging image resolution. The proposed network consists of two stages, including encoding and decoding. In the encoding stage, a local feature extraction module is initially designed to integrate contextual features. Subsequently, a residual dense module is introduced for extracting deep features. Finally, a spatial attention module is constructed to focus on high-frequency details. In the decoding stage, a multilayer perceptron is used to decode the feature maps and achieve super-resolution reconstruction at arbitrary scales. The method is tested on an ultrasonic logging images test set with in-distribution scale factors of × 2 and × 4, and out-of-distribution scale factors of × 8 and × 16. When the scaling factors are × 2 and × 4, compared to the best-performing method, the peak signal-to-noise ratio (PSNR) increased by 0.4892 dB and 0.3849 dB, respectively, the structural similarity (SSIM) values increased by 0.0002 and 0.0012, respectively, and the learned perceptual image patch similarity (LPIPS) decreased by 0.0001 and 0.0008, respectively. Compared to the bicubic interpolation method, the LPIPS decreased by 0.0001 and 0.0008 at scale factors of × 8 and × 16, PSNR increased by 1.9614 dB and 2.1002 dB, respectively, and SSIM values increased by 0.0476 and 0.033, respectively. The LPIPS values decreased by 0.2233 and 0.1070, respectively. The experimental results demonstrate that our method outperforms other mainstream methods, achieves super-resolution reconstruction at arbitrary scale, and provides support for subsequent fracture-cave evaluation and oil and gas exploration.