Though these omens are often cited in the reports of a network of observers established

Though these omens are often cited in the reports of a network of observers established

 throughout the Assyrian empire in the 7th century BC, they seem to have lost their popularity late in the period of the Persian domination of Mesopotamia (ending in the 4th century BC). During the later period new efforts were made, in a large number of works called Diaries, to find the correct correlations between celestial phenomena and terrestrial events. Before this development, however, portions of the older omen series were transmitted to Egypt, Greece, and India as a direct result of Achaemenid domination (the Achaemenian dynasty ruled in Persia from 559 to 330 BC) of these cultural areas or of their border regions.The evidence for a transmission of lunar omens to Egypt in the Achaemenian period lies primarily in a demotic papyrus based on an original of about 500 BC. 

A more extensive use of Mesopotamian celestial omens is attested by the fragments of a book written in Greek in the 2nd century BC and claimed as a work addressed to a King Nechepso by the priest Petosiris. From this source, among others, the contents of Enūma Anu Enlil were included in the second book of the Apotelesmatika, or “Work on Astrology” (commonly called the Tetrabiblos, or “Four Books”), by Ptolemy, a Greek astronomer of the 2nd century AD; the first book of an astrological compendium, by Hephaestion of Thebes, a Greco-Egyptian astrologer of the 5th century AD; and the On Signs of John Lydus, a Byzantine bureaucrat of the 6th century.

 Yet another channel of transmission to the Greeks was through the Magusaeans of Asia Minor, a group of Iranian settlers influenced by Babylonian ideas. Their teachings are preserved in several Classical works on natural history, primarily that of Pliny the Elder (c. AD 23–79), and the Geoponica (a late collection of agricultural lore).In various Middle Eastern languages there also exist many texts dealing with celestial omens, though their sources and the question as to whether they are directly descended from a Mesopotamian tradition or are derived from Greek or Indian intermediaries is yet to be investigated. 

Of these texts the most important are those ascribed to Hermes Trismegistos by the Harranians and now preserved in Arabic, the Book of the Zodiac of the Mandaeans (a Gnostic sect still existing in Iraq and Khuzistan), the Apocalypse, attributed to the biblical prophet Daniel (extant in Greek, Syriac, and Arabic versions), and The Book of the Bee in Syriac.The transmission of Mesopotamian omen literature to India, including the material in Enūma Anu Enlil, apparently took place in the 5th century BC during the Achaemenid occupation of the Indus valley. The first traces are found in Buddhist texts of this period, and Buddhist missionaries were instrumental in carrying this material to Central Asia, China, Tibet, Japan, and Southeast Asia.

 But the most important of the works of this Indian tradition and the oldest extant one in Sanskrit is the earliest version of the as-yet-unpublished Gargasamhita (“Compositions of Garga”) of about the 1st century AD. The original Mesopotamian material was modified so as to fit into the Indian conception of society, including the system of the four castes and the duty of the upper castes to perform the samskaras (sanctifying ceremonies).