## 1 Introduction  
Sound propagation is influenced by the complex interference of reflection, refraction, transmission, and attenuation in ocean media [1]. Sonar systems when operating in marine environments are affected by sound propagation through physical parameters including the sound speed and density of seawater, geological parameters such as bottom topography and sediment types, and sea surface, which can cause reflections and scattering [1]. Prior studies have extensively covered the propagation of acoustic waves by physical and geological parameters, but few studies have explored biological parameters affecting sound propagation, such as fish schools [2]. Fish schools are randomly and largely distributed in the ocean and they are able to alter the sound propagation pattern [3,4]. Fish with swim bladders produce a large impedance difference compared with seawater, and the acoustic waves are scattered when passing through the fish body [5]. The propagation of acoustic waves is affected by the positions, orientations, and sizes of fish schools, which act as scatterers that attenuate incident waves. Fish schools result in acoustic energy loss, as the sound propagates through the water column [6, 7, 8]. Fish schools in the ocean are formed in various sizes and densities with a single fish school varying from a few hundred to tens of thousands of fish. In the case of a well-formed ocean area, very large fish schools are distributed and inhabited [9]. Therefore, the attenuation of fish schools cannot be ignored and needs to be investigated. Japanese horse mackerel (_Trachurus japonicus_) is one of the representative fish species that typically form schools [10]. This fish is a warm-flowing migratory fish and an important commercial species in the coastal waters of the Northeastern Pacific Ocean of Korea, Japan, Taiwan, and China [10]. According to fisheries' statistical data in Korea, about 43,053 tons of horse mackerels were cultured in 2019, which was 4.7% of the total amount of coastal and offshore fish culturing [11]. It continues to appear and inhabit the coasts of Korea, and the fishery volume gradually increased from 2014 to 2019 [11]. The horse mackerel forms small to large schools in the ocean, which are known to reach a maximum of 150 and 15 m in length and width, respectively [12; 13]. However, the acoustic characteristics of horse mackerel schools have never been measured. Some studies have shown the relationship between sound attenuation and fish populations at different frequencies through direct measurements of culture nets [14; 15] and net cages [5; 16], and indirect estimation methods [17; 18; 19]. [PERSON] (1973) performed ex situ attenuation measurements by using the direct sphere method from Northern anchovy (_Engraulis mordax_) at 1-20 kHz and measured the attenuation at relatively low frequency to observe the swim bladder resonance effects [5]. [PERSON] et al. (1983) and [PERSON] et al. (1985) measured attenuation by using the direct culture net method at 25, 50, 100, and 200 kHz from yellowtail (_Serola quinqueradita_), sea brems (_Pagrus major_), and spotted mackerel (_Somber australiscus_) [15; 16]. [PERSON] (1978) estimated the extinction cross-section using the indirect cage method and applied the parameter fitting method from Saithe (_Pollachius virens_) at 38 and 120 kHz [17]. [PERSON] et al. (1990) conducted the acoustic estimation of Pacific herring in sea pens for attenuation measurements at 420 kHz [19]. Other relevant research works were analyzed and reviewed by [PERSON] et al. (1992) [6]. [PERSON] (2005) conducted a study on estimating the number density from the attenuation of anchovy schools during the day and night at the mid-frequency range of 1-3 kHz in shallow water environments through transmission loss measurements [20]. [PERSON] and [PERSON] (2015) recently studied sound extinction by fish schools on the basis of the forward scattering theory [21]. However, these previous studies mainly focused on attenuation by individuals or schools of fish at high-frequency bands.