Median filter behaviour with seismic data¹

Abstract

Abctract Median filters may be used with seismic data to attenuate coherent wavefields. An example is the attenuation of the downgoing wavefield in VSP data processing. The filter is applied across the traces in the ‘direction’ of the wavefield. The final result is given by subtracting the filtered version of the record from the original record. This method of median filtering may be called ‘median filtering operated in subtraction’. The method may be extended by automatically estimating the slowness of coherent wavefields on a record. The filter is then applied in a time‐ and‐space varying manner across the record on the basis of the slowness values at each point on the record. Median filters are non‐linear and hence their behaviour is more difficult to determine than linear filters. However, there are a number of methods that may be used to analyse median filter behaviour: (1) pseudo‐transfer functions to specific time series; (2) the response of median filters to simple seismic models; and (3) the response of median filters to steps that simulate terminating wavefields, such as faults on stacked data. These simple methods provide an intuitive insight into the behaviour of these filters, as well as providing a semiquantitative measurement of performance. The performance degradation of median filters in the presence of trace‐to‐trace variations in amplitude is shown to be similar to that of linear filters. The performance of median filters (in terms of signal distortion) applied obliquely across a record may be improved by low‐pass filtering (in the t‐dimension). The response of median filters to steps is shown to be affected by background noise levels. The distortion of steps introduced by median filters approaches the distortion of steps introduced by the corresponding linear filter for high levels of noise.

A seismic reflection image for the base of a tectonic plate

“…3a) an amplitude-enhancement smoothing method that is equivalent to a form of low-pass filter in both space and time. This is called a median filter 29 , which is a nonlinear digital filtering technique used to remove noise. A median filter replaces each data point in a data set with the median of the data points in a specified region centred on that data point.…”

“…Using a value of 8.5 km s 21 for v P at the base of recorded on 878 seismographs, with moderate and strong median filters. a, Low (1-15)-fold stack (fold 5 number of seismic traces that reflect from a common subsurface point that are stacked into a single trace) that has been processed with a median filter (Methods) that smooths traces in both space and time, and acts like a low-pass filter 29 . Plotted at approximate true scale with travel time on the left vertical axis, and approximate depth on the right vertical axis.…”

“…S g is the crustal refracted S wave. e, Shot gather for shot 11 with band pass filter [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] Hz that shows up the R2 reflector with its broad frequency content, and suppresses the low frequency R1 reflection. R sed and P m P represent reflections interpreted to come from the upper surface of the sediment channel on top of the oceanic crust, and from the Moho of the oceanic Pacific plate, respectively.…”

Filtros de echado recursivos

“…El problema de este tipo de filtrado, es que en su primera etapa, no rechaza totalmente la señal sísmica, de modo que perdemos información durante la sustracción. La determinación del ángulo variable de un evento hacia el que se realizará el filtrado se determina con base en un análisis autom ático de sem blanza (Duncan y Beresford, 1995). Para eliminar ruido incoherente, aprovechamos que la respuesta al impulso unitario del filtro de mediana es nula (Duncan y Beresford, 1995 En la figura 9 mostramos un ejemplo de este tipo de filtrado, aplicado a una sección proveniente de las costas europeas.…”

“…La determinación del ángulo variable de un evento hacia el que se realizará el filtrado se determina con base en un análisis autom ático de sem blanza (Duncan y Beresford, 1995). Para eliminar ruido incoherente, aprovechamos que la respuesta al impulso unitario del filtro de mediana es nula (Duncan y Beresford, 1995 En la figura 9 mostramos un ejemplo de este tipo de filtrado, aplicado a una sección proveniente de las costas europeas. Antes del filtrado, la sección presenta una gran cantidad de ruido aleatorio, mismo que dificulta la interpretación de los detalles estructurales en la parte inferior de la sección, así com o en los plegam ientos más someros.…”