# Unveiling Accurate Seismic Imaging through the Advanced Target-Oriented Kirchhoff Migration Method
## 1 Introduction  
Despite the existence of various advanced seismic migration approaches, pre-stack depth migration continues to hold its position as the most widely implemented technique. The challenges associated with this method and potential solutions are still subjects of ongoing discussion [1; 2]. Indeed, pre-stack depth migration holds particular importance, especially when confronted with lateral velocity variations within the overburden section. It has the capability to yield more precise images with an elevated signal-to-noise ratio compared to post-stack migration [3; 4; 5; 6]. Consequently, it is proven advantageous for performing amplitude versus offset (AVO) analysis [6; 7; 8; 9], facilitating fluid identification, and hydrocarbon reservoir characterization. Nonetheless, despite the growth in computing power, performing a full-scale 3D pre-stack depth migration remains challenging due to the extensive processing time and substantial demand on computing memory and storage. Thus, in an effort to make 3D pre-stack depth migration feasible for fast migration, it is essential to implement a target-oriented migration scheme. This approach aims to generate enhanced seismic data that are more manageable to process and capable of illuminating the target area efficiently, even beneath complex overburden conditions during the exploration geophysics activity. Ideally, 3D target-oriented pre-stack depth migration involves the calculation of reflectivity images exclusively for the identified target zones, aligning with the study's objectives and focusing on the specific area of interest. This target-oriented imaging approach leads to a reduction in the turnaround time required for 3D seismic imaging [10; 11; 12]. The concept has been a subject of discussion in the literature since the 1990s and gained further traction in the 2000s, as researchers began seeking solutions to address the computational demands of 3D seismic imaging. Nevertheless, the full potential of target-oriented imaging has not been fully exploited thus far. In 2003, [PERSON] and [PERSON] [13] presented their findings on a target-oriented version of least-squares migration (LSM) using Kirchhoff migration. In order to reduce computational costs in LSM, they identified the target area and executed LSM solely within a smaller subset of the data. However, a concern emerged because the proposed scheme did not incorporate the overburden effect, consequently impacting the precision of the migrated image. Furthermore, they exclusively evaluated the target-oriented least-squares migration scheme using post-stack datasets. Later, as Reverse Time Migration (RTM) made significant advancements in seismic processing and imaging, [PERSON], and [PERSON] (2004) [14] introduced reverse time datuning to address the computational costs associated with acquiring RTM images. This concept was later implemented on 3D synthetic data by [PERSON] et al. (2007) [15]. Even so, people's perception remains that computing RTM demands significant computational cost. The latest study conducted by [PERSON] et al. (2018) [16] showcased the benefits of Gaussian beam migration to fulfill the demands of target-oriented imaging through the application of a modified ray-tracing scheme. Even though they successfully formulated a target-oriented imaging algorithm, the proposed method still required a huge number of computations due to the ray calculations. In a different application of target-oriented imaging, the patched Green's function (PGF) technique was used by [PERSON] et al. (2022) [17] to reduce the computational cost of imaging problems based on wave equation. Indeed, this indicates that research on target-oriented imaging is still in progress, with ongoing efforts to identify appropriate solutions for effectively imaging the target area. In this paper, we delved into the Kirchhoff migration method for implementing target-oriented imaging. This method might be the oldest migration technique and possesses the simplest approximation for accurate seismic imaging.