Inversion-based directional deconvolution to remove the effect of a geophone array on seismic signal

The geophone array, as a directivity filter, has been widely used in seismic data acquisition for suppressing noises and alias-free sampling, and its negative effects have long been recognized by analyzing its response to harmonic waves. We extended the analysis by considering its effects on seismic signals, especially on amplitude variation with offset (AVO). Taking the ratio of the array length to the dominant wavelength as a reference, we analyzed the attenuations of the peak amplitude and the peak frequency with the incident angle for the Ricker wavelet. When an array with a ratio of 1.0 is used, the peak amplitude and the peak frequency decay to around 50% and 80% respectively at an angle of 40°. The effect of an array is directivity-dependent, and it acts on the seismic record as a nonstationary filter. We present an inversion-based solution to remove the directional effects. On the approximation of the horizontal stratified medium, the horizontal velocity of the seismic reflection can be concisely expressed in terms of its reflection time, offset, and rms velocity, which facilitates the implementation of directional deconvolution. The method was tested using model-based and logging-based synthetic data.