Differential‐equation‐based seismic data filtering

Suppressing noise and enhancing useful seismic signal by filtering is one of the important tasks of seismic data processing. Conventional filtering methods are implemented through either the convolution operation or various mathematical transforms. We describe a methodology for studying and implementing filters, which, unlike conventional filtering methods, is based on solving differential equations in the time and space domain. We call this differential‐equation‐based filtering (DEBF). DEBF does not require that seismic data be stationary, so filtering parameters can vary with every time and space point. Examples with two‐dimensional (2-D) synthetic and field seismic data demonstrate that the DEBF method accomplishes the desired time‐ and space‐varying temporal and move‐out filtering at lower cost than conventional frequency‐wavenumber‐domain filtering. The computational advantage in 3-D would be much greater.