Local covariance modeling using gravity anomaly data

Öz

Covariance functions are essential in statistical modeling and optimal estimation theory. In local applications, constructing a suitable covariance model is particularly critical, as it should reflect the specific characteristics of the region under investigation. This study addresses how an analytical covariance model can be adapted for a specific region of interest by estimating its parameters through the empirical power spectral density of the gravity anomaly. The model involves two parameters: a scale parameter that relates to the correlation length and a variance parameter. These parameters are derived by fitting a power-law model to the empirical PSD of the gravity anomaly, assuming that high-frequency components of the gravity field follow such a power-law behavior. A parameter set is determined for a region in the USA, and the resulting model is validated with real airborne gravity gradient data using the Least-Squares Collocation method. The results demonstrate that the quantities estimated using the proposed covariance model show good agreement with the observed gravity gradients, confirming the model's suitability for high-resolution local applications. The main contribution of this work is to demonstrate how covariance modeling can be tailored for local applications, thereby enabling more accurate estimation of gravity field-related quantities.

Anahtar Kelimeler

• Power spectral density
• Power-law model
• Covariance model parameters

Gravite anomali verileriyle yerel kovaryans modellemesi

Öz

Kovaryans fonksiyonları, istatistiksel modelleme ve optimal tahmin teorisinde temel bir öneme sahiptir. Yerel uygulamalarda uygun bir kovaryans modeli oluşturmak özellikle önemlidir, çünkü bu model incelenen bölgenin özgün özelliklerini yansıtmalıdır. Bu çalışma, analitik bir kovaryans modelinin belirli bir bölgeye nasıl uyarlanabileceğini, gravite anomalilerinin ampirik güç spektral yoğunluğu üzerinden parametrelerinin tahmin edilmesi yoluyla ele almaktadır. Model iki parametre içerir: korelasyon uzunluğuyla ilişkili bir ölçek parametresi ve bir varyans parametresi. Bu parametreler, gravite alanının yüksek frekans bileşenlerinin bir güç yasası davranışı sergilediği varsayımıyla, gravite anomalilerinin ampirik PSD’sine bir güç yasası modeli uydurularak elde edilir. ABD’deki bir bölge için parametre seti belirlenmiş ve elde edilen model, gerçek hava kaynaklı gravite gradyan verileri kullanılarak En Küçük Kareler Kollokasyonu yöntemi ile doğrulanmıştır. Sonuçlar, önerilen kovaryans modeli kullanılarak tahmin edilen değerlerin gözlemlenen gravite gradyanlarıyla iyi bir uyum gösterdiğini ve modelin yüksek çözünürlüklü yerel uygulamalar için uygunluğunu doğrulamaktadır. Bu çalışmanın temel katkısı, kovaryans modellemenin yerel uygulamalara nasıl uyarlanabileceğini göstermesi ve böylece gravite alanıyla ilişkili niceliklerin daha doğru tahmin edilmesini sağlamasıdır.

Anahtar Kelimeler

• Güç spektral yoğunluğu
• Güç yasası modeli
• Kovaryans model parametreleri

Kaynakça

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