A mollifier approach to seismic data representation

The extension of the seismic bandwidth to lower frequencies enhances impedance contrasts that can be poorly represented by the broadband acquisition wavelet. Furthermore, long filters that are used to shape the wavelet of processed data can cause issues with noise, phase and interference between seismic events. In this paper, we use a mathematical technique known as mollification to resolve impedance variations with the highest detail allowed by the bandwidth of the data. The mollifier is integrated and windowed to match the low-frequency content of the data to yield a convenient conversion to relative impedance. Synthetic data created from wedge models show that the windowed mollifier provides an improved representation of the impedance profile. This is replicated by application to an acoustic well log and a regular seismic dataset recorded in the Southern North Sea as well as a broadband dataset recorded in the North Sea.