Ratios in Higher Order Statistics (RHOS) values of Seismograms for Improved Automatic P-Phase Arrival Detection

In this paper we present two new procedures for automatic detection and picking of P-wave arrivals. The first involves the application of kurtosis and skewness on the vector magnitude of three component seismograms. Customarily, P-wave arrival detection techniques use vertical component seismogram which is appropriate only for teleseismic events. The inherent weakness of those methods stems from the fact that the energy from P-wave is distributed among horizontal and vertical recording channels. Our procedure, however, uses the vector magnitude which accommodates all components. The results show that this procedure would be useful for detecting/picking of P-arrivals from local and regional earthquakes and man-made explosions. The second procedure introduces a new method called “Ratios in Higher Order Statistics (RHOS).” Unlike commonly used techniques that involve derivatives, this technique employs ratios of adjacent kurtosis and skewness values to improve the accuracy of the detection of the P onset. RHOS can be applied independently on vertical component seismogram as well as the vector magnitude for improved detection of P-wave arrivals.

💡 Research Summary

This paper presents a significant advancement in automated seismic signal processing by introducing two novel methodologies for improving the detection and precise picking of P-wave arrival times, a critical task in seismology.

The core innovation addresses a fundamental limitation of traditional methods. Many existing automatic pickers rely solely on the vertical component of seismograms, which is effective only for teleseismic events where P-waves arrive nearly vertically. For local and regional earthquakes, seismic energy is distributed across both horizontal and vertical components, rendering single-component methods suboptimal. To overcome this, the authors’ first procedure utilizes the vector magnitude of the three-component seismogram (v = √(x²+y²+z²)). This composite signal incorporates energy from all directions. This vector magnitude is then normalized within sliding time windows to standardize the scale and suppress amplitude variations from ground motion. The skewness and kurtosis (third and fourth-order statistical moments) of each normalized window are computed. Background noise exhibits near-zero skewness and kurtosis, while the arrival of a P-wave creates a highly non-Gaussian, asymmetric distribution, causing sharp peaks in these Higher Order Statistics (HOS). The time of these peaks provides an initial estimate of the P-arrival.

The second, and more groundbreaking, contribution is the introduction of the “Ratios in Higher Order Statistics (RHOS)” technique. The initial pick based on the HOS peak often lags behind the true P-wave onset by a few samples. Previous correction schemes, like the PAI-S/K method, used the point of maximum slope (derivative) on the HOS curve just before the peak. This paper proposes a superior correction mechanism. The key insight is that the most drastic change in HOS values occurs precisely at the moment the P-wave breaks through the background noise. To capture this change, the method calculates the absolute ratio of adjacent HOS values (Right-Hand-Side value / Left-Hand-Side value) within the sliding window. The maximum of this RHOS value pinpoints the actual onset time with high accuracy.

The paper validates both procedures using real broadband seismic data from various networks archived at the IRIS Data Management Center, encompassing events at local and regional distances (50-1400 km) with different noise levels. The results demonstrate clear improvements: 1) Using the vector magnitude provides a more robust signal for P-detection in local/regional contexts compared to the vertical component alone. 2) The RHOS-based correction method yields more accurate and consistent arrival time estimates than the traditional maximum-derivative approach. Crucially, corrections derived from skewness and kurtosis via RHOS agree with each other (e.g., both suggesting an 11-sample correction in the provided example), whereas derivative-based corrections from the older method were inconsistent (suggesting 5 and 1 samples for skewness and kurtosis, respectively).

In conclusion, this research establishes a robust and generalizable framework for automatic P-phase picking. It successfully integrates three-component information, enhances signal features through normalization, and implements a mathematically sound and accurate correction principle via RHOS. While applicable to all distance ranges, this method offers a particularly powerful tool for improving analysis accuracy for local and regional earthquakes and explosions, where conventional single-component techniques are inherently limited.