## 1 Introduction  
The fracture reservoir is an important type of carbonate reservoir in the Tarim Basin [1]. Due to the complexity of carbonate fracture reservoirs, the large variation in morphology and parameters, and the influence of tectonic factors, difficulties are encountered in clarifying the seismic response characteristics, which creates ambiguity in the seismic prediction of reservoirs. On seismic migration profiles, fractured reservoirs exhibit anomalous bright spots and short-axis, low-frequency strong reflections, which are common features of the Ordovician carbonate formations in the Tarim Basin [2; 3; 4]. These bright spots are finite in height and consist of one to three peaks and valleys that visually seem like a string of beads. Therefore, they are called the string of bead-like response (SBLR) in seismic explorations [5]. Fracture reservoirs within the Tarim Basin include tectonic fracture-type reservoirs and cave-top collapse fracture development zones, which are distributed in the form of beaches and belts, and dissolution joints formed by karst action, which are in the form of near-vertical or high angles. Fractured reservoirs are widely distributed in carbonate formations and often exhibit non-standard beaded pie, strip, or cluttered reflection features on the seismic migration profiles [6; 7; 8; 9]. Local fracture distribution exhibits strong transverse or longitudinal inhomogeneity [10; 11]. Fracture and karst suture systems are the main pore spaces in reservoirs [12]. In practical seismic exploration, the attributes of amplitude and frequency are used with better results for carbonatite seam-hole reservoirs [13; 14; 15; 16]. The essence of the SBLR is the convergence of seismic diffraction from finite-scale fractured reservoirs during the migration process. It is generally considered to be the result of reflection and multi-wave interference between fracture edges, including the top, bottom, and sides of the fracture. The large impedance difference between the fractured reservoir and its surroundings and the limited size of the fractured zone are the two most important factors contributing to the SBLR. Fractures generally consist of soft and porous fills and fluids surrounded by dense carbonate rocks. Low-dipping-angle fractured reservoirs are beach bodies with limited thicknesses, even comparable to the wavelength of seismic waves. Therefore, the bright spots generates on the seismic profile are limited in the vertical direction. Wave propagation within a fracture should be described by the diffraction theory rather than the ray theory. A fracture can be considered as a combination of numerous thin layers, and the SBLR is the stack of all the thin layers of diffraction waves. Established numerical simulations and real seismic data have shown that the seismic reflected characteristics such as the amplitude and frequency of the SBLR are affected by the tectonic morphology, internal structural parameters, surrounding geology, and total volume [17; 18; 19; 20; 21; 22; 23; 24]. The SBLR, as an indicator of high-quality reservoirs, has become the main drilling target for current exploration and production in the Tarim Basin [25]. In localized exploration, targeting the SBLR has a success rate of over 80% in hydrocarbon exploration [26]. The widespread development of fractures in the Tarim Basin has an important and positive impact on oil and gas production [27]. Correctly recognizing the correspondence between the SBLR and fractures will contribute to the efficient drilling of target fractured reservoirs and is a significant issue which needs to be addressed urgently in the exploration of oil and gas reservoirs in the Tarim Basin. Seismic physical simulation is a good method to investigate the characteristics of the SBLR [28]. In the real strata, the seismic profile characteristics of fractured reservoirs are affected by numerous factors, while the structure and parameters are not well defined, which is not conducive to targeted research with seismic profile data [29].