Enhancing in search of Milankovitch cycles from stratigraphic record using convex optimization algorithm

Accurately identifying Milankovitch cycles has been a significant challenge in cyclostratigraphic studies, as it is essential for improving geochronology. This manuscript focuses on developing a method that distinguishes Milankovitch cycles from sedimentary noise to enhance stratigraphic precision. Despite their often-conspicuous magnitude, these periodicities frequently intertwine with noise, posing a challenge for conventional spectral analysis. Therefore, to address this issue, we have developed an algorithm that enhances the resolution of the Milankovitch signal by employing convex optimization in spectral analysis. To evaluate the effectiveness of this new algorithm, we applied it to four distinct types of local stratigraphy where the Milankovitch signal has been confirmed. These include the stratigraphic sections in the middle Miocene molluscan beds of Java and the Mahakam Delta, Pleistocene sediments of Hominin Flores, and the Towuti Lake in Sulawesi Island, Indonesia. Our findings demonstrate the preservation of all targeted signals, with a confidence level surpassing 99%. By setting the significance level to 1%, we can reject the null hypothesis, which assumes noise or the absence of a Milankovitch signal in the stratigraphic data being tested. The absence of deviations from the identified periodicities further strengthens the Milankovitch signal, underscoring the robustness of our algorithm. However, we acknowledge that achieving optimal results still hinges on the accurate selection of the initial parameters z and λ.