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Estimation of seismic local slope using Hilbert transform noise correction method
Estimación de la pendiente local a través del método de corrección de ruido con la transformada de Hilbert
DOI:
https://doi.org/10.15446/esrj.v28n1.112425Keywords:
Seismic local slopes calculation, Seismic wave numerical simulation, Geophysical exploration, Plane-wave destruction filter, Automatic normal moveout (ANMO) (en)Cálculo de pendientes locales sísmicas, simulación numérica de onda sísmica, exploración geofísica, filtro de destrucción de ondas planas lineales (es)
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In seismology, the local slope is essential for various seismic forward and inversion methods, including seismic migration imaging, seismic tomography, structure prediction, and other core seismic data processing methods. However, high-frequency random noise is unavoidable in real seismic data. Therefore, a robust estimation of event-slope attributes becomes important under high-frequency random noise. This research explores a robust and efficient method for estimating local slopes. The relationship between the frequency response of the Hilbert transform and Fourier transform is analyzed. The derivative operator constructed by the Hilbert transform can effectively weaken the effect on the energy enhancement of the high-frequency random noise. Minimizing the quadratic function of the proportionality factors was used to obtain the proportionality factors of the noise correction. Finally, the Hilbert transform and noise correction derived a new linear plane-wave destruction filter operator. The linear operator can effectively estimate the seismic events' local slope with high-frequency random noise. The calculation results of the numerical examples show that the linear plane-wave destruction filter estimation local slope method proposed in this study has high calculation accuracy and efficiency.
En seismología, la pendiente local es esencial para varios métodos de inversión y directos como las imágenes de migración sísmica, tomografía sísmica, predicción de estructura y otros métodos de procesamiento de información sísmica. Sin embargo, la alta frecuencia del ruido aleatorio es inevitable en la información sísmica real. Pero también una estimación robusta de los atributos de un evento relacionados a la pendiente se vuelve determinante ante las condiciones de ruido aleatorio de alta frecuencia. Este trabajo busca explorar un método robusto y eficiente para la estimación de pendientes locales. Con este objetivo se analizó la relación entre la frecuencia de respuesta de la transformada de Hilbert y la de Fourier. El operador derivado construido con la transformada de Hilbert puede debilitar efectivamente el efecto del mejoramiento de energía en el ruido aleatorio de alta frecuencia. La minimización de la función cuadrática de los factores de proporcionalidad se aplicaron en la corrección del ruido. Finalmente, un nuevo operador de filtro de destrucción de ondas planas lineales se derivo de la transformada de Hilbert y de la corrección del ruido. El operador lineal puede estimar efectivamente la pendiente local de los eventos sísmicos con ruido aleatorio de alta frecuencia. El cálculo de los resultados de los ejemplos numéricos muestran que el método de estimación de pendientes locales basada en el filtro de destrucción de ondas planas lineales propuesto en este estudio tiene una alta exactitud de cálculo y eficiencia.
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