GSTAR (1,1) Modeling with Time-Correlated Errors for Geoelectric Resistivity Log Data in Pontianak City
Abstract
Planting of concrete piles on the soil surface must reach a layer of rock/soil that is hard enough for the building to stand firmly. Rock/soil layers can be studied through geoelectric resistivity log data. We require tools with high prices and need a complicated process to obtain such data. Therefore, a mathematical model is developed to explore geological formations using a space-time model to overcome these problems. The generalized space-time autoregressive (GSTAR) model can be applied to the resistivity data. However, this data correlates with each rock layer. Therefore, we develop a GSTAR model for time-correlated errors. In our study, the parameter index, usually for a concrete time, is applied to the relative time in the form of rock layers. This research uses geoelectric resistivity log data at six locations in Pontianak City, namely Untan 1, Untan 2, Untan 3, Jl. Sawo, Jl KPM Permai, and Gg. Beringin. The GSTAR(1,1) model with time correlation error results in an average RMSE value of 9.51605 Ωm. In addition, we obtain that the most profound peat soil depth is 17.9 m from the surface and is located in the Untan 3.
Keywords: GSTAR (1,1); martingale difference; peat soil; resistivity; time-correlated error.
Abstrak
Penanaman tiang pancang beton pada tanah gambut harus mencapai lapisan batuan/tanah yang cukup keras agar bangunan dapat berdiri kokoh. Lapisan batuan/tanah dapat dipelajari melalui data log resistivitas geolistrik yang memerlukan alat yang mahal dan proses yang rumit untuk mendapatkan datanya. Untuk mengatasi permasalahan tersebut, dibuatlah model matematika untuk mengeksplorasi formasi geologi menggunakan model ruang-waktu. Salah satu model yang dapat diaplikasikan adalah generalized space-time autoregressive (GSTAR). Pada umumnya, data ini memiliki korelasi antarlapisan batuan. Oleh karena itu, pada penelitian ini dikembangkan model GSTAR untuk galat yang berkorelasi waktu. Indeks parameter yang biasanya menggunakan waktu konkret, pada penelitian ini diterapkan pada waktu relatif berupa lapisan batuan. Model ini disebut GSTAR dengan galat berkorelasi waktu. Data yang digunakan adalah data resistivitas geolistrik pada enam lokasi di Kota Pontianak Indonesia yang dinamakan Untan 1, Untan 2, Untan 3, Jl. Sawo, Jl KPM Permai, dan Gg. Beringin. Hasil menunjukkan bahwa model GSTAR(1,1) dengan galat berkorelasi waktu berhasil mengestimasi nilai resistivitas geolistrik di keenam lokasi tersebut dengan nilai rata-rata geometri dari RMSE sebesar 9,51605 Ωm. Selain itu, model ini pun berhasil memperkirakan kedalaman tanah gambut terdalam (dari permukaan tanah) yang terletak di lokasi Untan 3 yaitu 17,9 m.
Kata Kunci: GSTAR(1,1); pembeda martingale; tanah gambut; resistivitas; galat berkorelasi waktu.
2020MSC: 62P30
Keywords
References
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DOI: 10.15408/inprime.v4i2.26263
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