# Inversion-Based Deblending in Common Midpoint Domain Using Time Domain High-Resolution Radon
## 1 Introduction  
The quest for efficient seismic data acquisition is a well-known challenge in geophysical exploration. Simultaneous acquisition, also known as blended acquisition, stands as a solution, offering a method that significantly reduces the time spent in the field by concurrently firing multiple sources. This technique, which was initially proposed by [PERSON] [1] for vibroseis acquisition and later expanded by [PERSON] et al. [2], [PERSON] [3] for marine environments, allows for the interference of sources at acquisition time which are subsequently separated during processing. Despite its time-saving advantages, existing models and algorithms for deblending such data often come with limitations.  
This study is motivated by the need to address these limitations and to enhance the accuracy and efficiency of seismic data deblending. Current methods, including random firing and phase encoding, have paved the way for approaches to data acquisition. However, the deblending process remains a significant bottleneck, with two predominant schools of thought: the denoising-based approach [4], which focuses on erratic and random noise attenuation, and the inversion-based approach [5], which seeks to reconstruct the signal by inverting the blending process. This paper will mainly focus on processing data from the random firing approach.  
The introduction of small random delays to the source firing times, as suggested by [PERSON] [6], is a critical step in the deblending process. Pseudo-deblending involves remapping the blended shots to zero firing time and duplicating frames according to the number of simultaneous sources. This manipulation due to the random delays rendersthe interference from neighbouring sources as random noise in some of the common data domains, leaving only the target signal for recovery as coherent events. Pseudo-deblended data then show incoherent structures within the common midpoint gather (CMP), common receiver gather (CRG), and common offset gather (COF) domains, thus facilitating the deblending process. There are various methods to exploit the incoherency of blending noise, such as the separation work by [PERSON] and [PERSON] [7] and subsequent techniques such as Stolt Radon denoising [8], SSA filtering [9], denoising using a space-varying median filter [10], preconditioning with a discrete curvelet filter [11], and preconditioning with robust thresholding in the FK domain [12], each with their own advantages and drawbacks, often struggling with either issues in effectively distinguishing between signal and noise (source interference) for the denoising approaches or highly expensive and complex transform operators for the inversion-based approaches.  
This paper introduces an inversion-based deblending approach utilizing the CMP domain, which promises a high-speed solution using a Radon transform operator. The utilization of the hyperbolic Radon transform for deblending serves multiple functions and significantly aids in the recovery of the seismic signal. Given the intrinsic nature of seismic acquisition, the acoustic responses emanating from the Earth's interior manifest as hyperbolic arrivals at the surface. The hyperbolic Radon transform, by aggregating data based on hyperbolic trajectories, is ideally suited for mapping seismic data. Opting for the CMP domain over the traditional CRG domain method allows for the employment of a more streamlined version of the Radon transform operator, resulting in reduced runtimes.