The Cyrenaica Method (CM) is an algorithm to transform the altered oxygen and carbon isotope curves patterns. The algorithm applies mathematical and statistical transformations to correct the pattern of any oxygen and/or carbon stable isotope data that was deformed during diagenesis. The algorithm is implemented to separate noise signature from the original signature of the oxygen and carbon stable isotope values, when applied on the Cyrenaican Miocene carbonate whole rock stable isotope (δ¹⁸O, δ¹³C) data of the stratigraphic field measured section A1 of 74 m thickness in the Cyrenaica region, northeastern Libya.

This work proves and carries a new discovery that the oxygen and carbon isotope data can be deformed and altered due to diagenesis but will never reset as many academic scientists think! Also, before going through any petrographical studies, the extracted noise signature from the altered raw data can be used to discover and determine the geological packages that are affected the most by the diagenetic processes (e.g., replacement, cementation, and dissolution) or any other external factors such as penecontemporaneous volcanic activity that could alter the original depositional signature of the stable isotopes. Moreover, the Cyrenaican Method will give the stable isotope studies that are based on the whole rock an advantage over those based on the fossils. The whole rock based stable isotope data combined with the Cyrenaica Method will be able to give both, extra information on the external factors (noise) and a cleaned original signature comparable in patterns and ranges to those obtained from the fossil based stable isotope data.

A1 of 74 m thickness is the detailed field measured section selected out of 29 measured sections along 130 km distance to represent the Miocene Ar-Rajmah Group carbonate sequence in Cyrenaica, northeastern Libya. The sampling interval frequency was every 0.5 m for whole rock stable isotope (δ¹⁸O, δ¹³C) chemostratigraphy, XRF trace, common elements analysis, and thin sections petrographic analysis.

Almost the entire Miocene record was preserved in the Ar-Rajmah Group as indicated by the carbon isotope data. Six main 3^rd–order sequences (S1–S6) arranged into two shallowing upward 2^nd–order super-sequences (SS1–SS2) to form the Ar-Rajmah Group carbonate succession of the Cyrenaican Miocene.   

In the study area, the Early Miocene stable isotope record is generally enriched in both δ¹⁸O and δ¹³C, the Middle Miocene is enriched in δ¹³C but depleted in δ¹⁸O, and the Late Miocene is depleted in both δ¹⁸O and δ¹³C. The altered Cyrenaican Miocene raw data revealed a wide range of the stable isotope values, where the δ¹⁸O data ranges from -9.2 to 3.7 ‰ VPDB, and the δ¹³C data ranges from -6.7 to 3.0 ‰ VPDB.

On the other hand, the outcomes of the Cyrenaica Method processed data of the Cyrenaican Miocene stratigraphic section A1 shows a more accurate and narrower range of the stable isotope values, where the δ¹⁸O data range from -1.7 to 2.2 ‰ VPDB, and the δ¹³C data range from -1.8 to 2.3 ‰ VPDB. These ranges of the cleaned and processed Cyrenaican Miocene stable isotope whole rock data are very comparable to the stable isotope fossil-based Miocene ranges (Zachos et al., 2001), the δ¹⁸O data range from 1.1 to 3.7 ‰ VPDB, and the δ¹³C data ranges from -1.3 to 2.4 ‰ VPDB.