## 1 Introduction
[PERSON] [11] has further improved supervised convolutional neural networks (CNN)-based network architecture implementation for elastic properties estimation using an abundance of real well logs and seismic data from the Sleipner Vest study area on the Norwegian Continental Shelf. A different approach was suggested by [PERSON] et al. [12]. They proposed a unique neural network method that can map full-stack seismic data into a broader frequency spectrum before mapping into impedance. Different approaches that attempt to incorporate prior knowledge such as synthetic datasets input for deep learning network training to increase the space of the solution was introduced among others by [PERSON] et al. [13; 14]. They implemented a series of CNN layers to train synthetic datasets that use facies information built upon prior knowledge of physics, geology, and geostatistics. The approach was successfully applied in a real dataset with decent prediction accuracy while using a predictive network trained based on a synthetic labeled dataset. [PERSON] [15] proposed a similar method utilizing a hybrid theory-guided data science (TGDS) model which contains a series of dense neural networks (DNN) as a predictive network and statistical rock physics-based synthetic labeled well and seismic dataset training input. The approach was successfully applied to the North Sea dataset to predict elastic and reservoir properties comparable to those obtained from deterministic inversion. Most examples mentioned earlier utilize relatively simple deep learning model architectures such as CNN and DNN to establish the predictive network. These simple model architectures tend to be saturated easily and can lead to accuracy degradation and vanishing gradient as we increase the layers. Deeper architecture, like U-Net, can be implemented to solve the problem. For instance, the U-Net architecture has been successfully utilized by [PERSON] [16] as self-supervised deep learning to obtain low-frequency envelope data as part of the nonlinear seismic full waveform inversion process. The proposed nonlinear operator can mitigate the typical issue of initial model dependency while achieving stable convergence. Besides U-Net, there are other attempts to utilize more complex deep learning network architecture, such as the Generative Adversarial Network (GAN) for seismic impedance inversion, as proposed by [PERSON] [17]. The proposed method successfully predicts acoustic impedance with much higher resolution and at a better consistency than conventional deep learning inversion. However, the testing is only limited to synthetic data environments and requires extensive data labeling for training. The traditional approach to deep learning application requires abundant data availability for network training to produce a promising predictive network. The application of these approaches for elastic property prediction in a green field or frontier exploration where (well) data is limited and sparse becomes less practical. Application of theory-based synthetically generated data can be helpful when dealing with sparse data environments. However, the predictive network models may encounter issues in mimicking the actual seismic data characteristic, for instance, due to amplitude scaling, dynamic frequencies content, phase shift, and embedded noises. This data domain discrepancies (synthetic and real data characteristics) will significantly deteriorate the prediction accuracy of elastic properties. Inspired by the works of [13; 14; 15; 18], we attempt to establish a reliable seismic inversion method that integrates prior knowledge into deep learning network architecture to estimate elastic properties from seismic with better accuracy. The approach includes synthetic data generation from a set of rock physics knowledge, which is called the rock physics library, and building a combination of U-Net and ResNet-18 architecture. The rock physics library is a compilation of pseudo-well logs and seismic datasets that simulate the true subsurface reservoir condition.