**1. Introduction**

The increasing complexity of geological structures necessitates advancements in oil and gas exploration and development technologies, making multiple suppression an essential and challenging problem to address. The presence of multiples interferes with the identification of primary reflections, reducing the signal-to-noise ratio of seismic data, compromising the accuracy and reliability of seismic imaging, and potentially leading to erroneous interpretations and source rock investigations. Consequently, effective suppression of multiples is crucial for enhancing seismic data quality and facilitating oil and gas exploration and development. In northwest China, there are abundant resources of oil and natural gas. However, the complexity of its geological features and strong reflective interfaces in underground media, such as rock mounds, coal seams, basalt, etc., can generate strong internal multiples. The understanding

**Citation:** Xiao, M.; Xie, J.; Wang, W.; Liu, W.; Sun, J.; Jin, B.; Zhang, T.; Zhao, Y.; Wang, Y. Application of Iterative Virtual Events Internal Multiple Suppression Technique: A Case of Southwest Depression Area of Tarim, China. *Appl. Sci.* **2023**, *13*, 8832. https://doi.org/10.3390/ app13158832

Academic Editors: Guofeng Liu, Zhifu Zhang and Xiaohong Meng

Received: 11 March 2023 Revised: 22 May 2023 Accepted: 31 May 2023 Published: 31 July 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of internal geological structures is constrained. Therefore, the demand for effective suppression of seismic multiples is very urgent.

Seismic multiples are generally classified into two categories based on the location of reflective layers: surface-related multiples and internal multiples. Surface-related multiples exhibit relatively stronger energy, particularly in offshore seismic data. Consequently, numerous researchers have focused on predicting and suppressing surface-related multiples, resulting in the maturation of suppression techniques for this category. In 1992, Verschuur et al. employed the concept of series expansion to decompose the seismic wavefield into primaries and multiples of all orders, effectively suppressing surface-related multiples [1]. This method obviates the need for subsurface geological model information, is a data-driven method, delivers superior results in field data processing, and exhibits high computational efficiency. Many geophysicists have expressed interest in and conducted research on this approach, leading to its widespread adoption in the exploration and development field. In 2009, Van Groenestijn and Verschuur proposed using sparse inversion to estimate primaries, eliminating the requirement for adaptive matched subtraction and near offset extrapolation [2,3]. This advancement significantly optimized the traditional surface-related multiple elimination (SRME) methods. In 2015, Ma et al. developed a suppression method for 3D surface-related multiples [4]. This technique assumes that the multiple contribution trace set corresponding to each seismic record in 3D seismic data is hyperbolic, enabling multiple predictions and suppression in 3D seismic data through sparse inversion. In 2022, Zhu et al. introduced a least squares datum continuation method for suppressing surface-related multiples within the least squares inversion theoretical framework [5]. This approach targets seafloor-separated up- and down-wave records, and, without multiple separation or fractional extraction, iterative inversion yields pre-stack seismic data from virtual observations on the seafloor, enhancing the resolution of effective signals and improving seismic imaging quality.

In comparison to surface-related multiples, internal multiples exhibit smaller differences in frequency, stacking velocity, and normal moveout (NMO) correction, making their suppression more challenging. In 1998, Jakubowicz introduced a data-driven method for internal multiple suppression [6]. This approach directly employs surface observed seismic data to construct internal multiples, enhancing computational efficiency. However, the method necessitates the accurate selection of primary reflection events from seismic data, which is difficult to implement in complex field data. In 2005, Berkhout and Verschuur proposed an internal multiple prediction method based on common focus technology, which is grounded in wavefield extrapolation [7,8]. This method is better suited to complex geological conditions but relies on a velocity model, limiting its application in field data. In 2006, Weglein et al. presented the inverse scattering series method based on the point scattering model [9]. As a data-driven, wave equation-based method, it does not require prior information such as velocity models. However, the method involves substantial computation and is only effective for near offsets, making it insufficient for current data processing demands. In 2013, Ypma and Verschuur introduced an internal multiple suppression method based on sparse inversion [10]. This approach minimizes the damage caused by adaptive matched subtraction to primary signals and effectively protects effective waves. Nevertheless, the method still entails considerable computation and yields unstable wavelets, complicating large-scale field data processing. In 2015, inspired by Marchenko's imaging method, Meles et al. proposed a self-focusing-based Marchenko internal multiple suppression method [11]. This technique does not require accurate velocity models, only an inaccurate macro velocity model to forward direct waves. Subsequently, direct waves and original data are used to construct the up- and down-going Green functions for relevant virtual source points, generating the associated internal multiples. However, this method demands significant computation due to the need for virtual source points at various depths, making it difficult to apply widely to large scale, complex structured seismic data. In 2018, Zhang and Staring proposed a one-step internal multiple suppression method based on Marchenko's

self-focusing approach, also known as the data domain internal multiple suppression method [12]. This technique does not require macro velocity models for direct wave estimation and directly outputs primaries without internal multiples. However, this method imposes high requirements on the observation system, and its large-scale application in field data remains limited. In 2020, Zhang et al. applied the Marchenko internal multiple suppression method to field seismic data processing, achieving favorable results [13]. Nonetheless, in low signal-to-noise ratio scenarios, energy may not be sufficiently focused, rendering the Marchenko internal multiple suppression method ineffective. In 2022, Zhang et al. compared the self-focusing-based Marchenko method for internal multiple suppression with the data domain method [14]. In the same year, Zhang et al. introduced a multiple suppression method based on self-attention convolutional auto encoders [15]. This method can reduce artificial cost, reduce dependence on unknown prior information, and improve data processing efficiency.

In 2006 and 2009, Ikelle proposed a virtual seismic event construction method to predict internal multiples [16,17]. This approach does not require prior information, such as velocity models or subsurface structures, enabling accurate internal multiple predictions. However, this method requires sequential extraction of primaries to construct internal multiples generated by relevant layers, which increase the computational complexity. In 2013, Wu et al. utilized a multi-channel L1 norm adaptive matching algorithm to suppress multiples, considering the differences in amplitude and phase between virtual event method-predicted internal multiples and actual internal multiples, achieving favorable results in model data [18]. In 2018, Liu et al. introduced an adaptive virtual event method to address the excessive dependency on the matching algorithm in the traditional virtual event method, enhancing internal multiple suppression capabilities [19]. Although researchers have improved and modified the virtual event method to address various issues, the traditional virtual event method still requires sequential internal multiple constructions on subsurface interfaces, incurring high computational costs for seismic data derived from complex structures and making primary extraction difficult. To overcome this challenge, we propose an iterative virtual event method. Compared to the traditional virtual event method, the iterative virtual event technique incorporates an iterative calculation process, mitigates the influence of false frequencies generated by data space convolution on predicted multiple models, and significantly improves computational efficiency. When applied to actual onshore post-stack seismic data from the southwest depression of the Tarim Basin, our method effectively suppresses internal multiples that are challenging to eliminate in pre-stack traces, emphasizes the energy of deep effective waves, and further enhances the quality of seismic profiles.

The paper is organized as follows. After the introduction, we provide an overview of the study region. Subsequently, we present the theory of virtual events for internal multiple eliminations, followed by synthetic and field data experiments that validate the effectiveness of our approach. Finally, we draw conclusions based on detailed analyses and discussions.
