The W transform with a chirp-modulated window

A high-resolution time–frequency spectrum is desirable for processing and interpreting seismic data. The W transform is a method that effectively preserves the resolution in the low-frequency region of the time–frequency spectrum of nonstationary seismic signals. To further increase the energy concentration of the time–frequency spectrum estimated with the W transform, we propose to combine the W transform with a chirp-modulated window. The chirp rate in the chirp-modulated window can control the rotation of the window in the time–frequency plane to achieve a better match with the time–frequency spectrum. The chirp rate in the modified W transform can be directly determined with the estimated instantaneous frequency. It has been shown that the W transform with a chirp-modulated window maintains the resolution of the time–frequency spectrum and improves the energy concentration around the dominant frequency against noise. To speed up the computational process of the W transform with a chirp-modulated window, we formulate the transform as a matrix-vector multiplication, which can be accelerated by using graphics processing unit computations. The application of the modified algorithm to synthetic and field data indicates that the frequency anomalies can be easily identified with the modified W transform.