Improvement and application of ESPAC method based on cross-correlation spectrum adaptive segmental fitting technology

Abstract

As a convenient and efficient passive-source geophysical method, microtremor exploration is widely used. The traditional Extended Spatial Autocorrelation (ESPAC) method tends to generate high-frequency cross-artifacts with sparse arrays. Although the Modified ESPAC (M-ESPAC) method can eliminate these artifacts, its inversion depth (less than twice the array radius) is much lower than ESPAC’s 3–5 times. To resolve this contradiction, this paper proposes a Further Modified ESPAC (FM-ESPAC) method based on cross-correlation spectrum adaptive segmental fitting. First, it defines the first intersection frequency f₀₁ between the cross-correlation curve and the frequency axis as the adaptive segmentation threshold. Then, adaptive segmental fitting is performed using f₀₁: the low-frequency band (f ≤ f₀₁) adopts ESPAC’s zero-order Bessel function J₀ fitting to retain low-frequency responses, while the high-frequency band (f > f₀₁) uses M-ESPAC’s analytic signal and first-kind zero-order Hankel function H₀⁽¹⁾ fitting to eliminate cross-artifacts. Finally, the array-averaged dispersion spectrum is obtained via superposition and normalization. Simulation experiments (triangular/linear arrays) and practical cases (Enshi geothermal exploration, Antarctic ice sheet detection) verify that FM-ESPAC not only eliminates high-frequency cross-artifacts but also inherits ESPAC’s low-frequency information to ensure inversion depth, showing significant advantages in the case of sparse arrays and insufficient spatial sampling.