## 1 Introduction  
Remote sensing methods are often the only way to investigate specific archaeological sites (e.g., Reference [1]). One of them is the muon radiography method for probing sizable solids and constructions, based on the analysis of absorption and scattering of cosmic muon fluxes on their way through the substance of the investigated object. The first experiment investigating an archaeological site with the help of muons of cosmic origin was the study of the Pyramid of Khafre in Egypt by the group of the Nobel prize winner [PERSON] [2; 3]. Recently, a successful attempt to study another archaeological object, the Khufu pyramid, was undertaken by an international team of scientists from Japan, France and Egypt in 2016-2017 within the framework of the ScanPyramids project [4]. The result of the studies performed with emulsion track detectors was the discovery of a new unknown chamber, which is the first great breakthrough in the Cheops pyramid investigation since the XIXth century, without any damage to the construction. This sensational result, confirmed by the electronic instrumentation, demonstrated the success of the muon radiography method based on emulsion detectors in the study of archaeological objects. Our experiment was carried out in spring 2018 by collaborators from the National University of Science and Technology Moscow Institute of Steel and Alloys, \"MISiS\", Lebedev Physical Institute of RAS, Skobeltsyn Institute of Nuclear Physics of Moscow State University; Institute of History, Archaeology and Ethnography of Dagestan Scientific Centre of RAS, and Dagestan State University, with the participation of the Agency for the Protection of Cultural Heritage of the Republic of Dagestan. The aim was to clarify the possibility of investigating the selected archaeological site by using the muon radiography method, to determine the optimal exposure, number, size and arrangement of the detectors employed and to obtain the first images of the object by nuclear emulsions. The object of study was an underground cross-shaped dome construction oriented to the cardinal directions, located in the citadel of Naryn-Kala in ancient Derbent. The construction built from local shell-imestone is about 11 meters high and extends for 14.8 m from south to north and 13.4 m from west to east (Figure 1). The segments (arms) of the cross-shaped construction are about 4.7 m wide, three arms are about 4.2 m long, and the fourth (northern) one is over 6 m long. The arms are covered with ogival vaults, and above the central part a wire frame of the dome 5 m in diameter is located. In some historical and reference literature this construction is mentioned as an underground reservoir for water, as it was in XVII-XVIII centuries (see, e.g., Reference [5]). At the same time, it was suggested that this construction was originally an early Christian church established during V-VI A.D, [6; 7] or a Zoroastrian temple of fire [8]. The construction is almost completely hidden by a cultural layer; on the modern surface, only a fragment of the half ruined dome and the back end of the northern section (arm) with a window are seen (Figure 1). Specialists emphasize the need to study this structure by using non-invasive methods (without destruction of the cultural layer) [9]. Its investigation by traditional methods, such as archaeological excavations, is rather problematic, as nobody knows how the walls of the building exposed to the long-time action of water would behave when released from the ground. Moreover, massive diggings would disturb the existing historical landscape of the citadel and reveal the adjacent architectural complexes of various medieval periods, requiring preservation and conservation. Under such conditions, the method of muon radiography seems to be the only possible approach to study this architectural and archaeological site.