Seismic exploration is an important tool to search for oil and gas. However, the presence of strong random noise greatly degrades the quality of seismic data and brings difficulty to image geological structure in the subsurface. In seismic denoising methods, seismic random noise is usually assumed to be stationary Gaussian noise without consideration of its nonstationarity in space. In the condition of the complex surface area, it is a challenge to suppress spatially nonstationary seismic random noise, i. e. the power of seismic noise is variable in different seismic traces, by using these denoising methods. On the basis of the spatially nonstationarity, we propose a method to suppress seismic random noise attenuation by using the rank-ordered absolute difference and radial time-frequency peak filtering method (ROAD-RTFPF). Radial time-frequency peak filtering (RTFPF) is an effective method to preserve seismic signals when suppressing random noise in seismic data at low signal-to-noise ratio (SNR). Based on the rank-ordered absolute difference (ROAD), we propose the ROAD-RTFPF method to suppress spatially nonstationary random noise in seismic data at low SNR. Firstly, we introduce the concept of spatially nonstationary random noise to describe such noise with spatially changing power. The correlation integral of resampled data on radial traces are analyzed to demonstrate the nonstationarity of seismic noise in space. Secondly, the property of the spatially nonstationary random noise on the radial traces is analyzed and then used to improve the performance of RTFPF. Therefore, on the basis of calculating the values of ROAD, we conduct local time-frequency peak filtering for the resampled data on radial traces with high ROAD, which indicates the nonstationary part of seismic random noise. RTFPF is then applied to the processed data on radial traces to further suppress the random noise in seismic data. We calculate the correlation integral, the rank-ordered absolute difference on field seismic random noise data, and compare the performance of the ROAD-RTFPF and RTFPF, taking synthetic seismic data and common shot point seismic record for example. We compare the correlation integral with spatially nonstationary and spatially stationary seismic records. The calculating results indicate that the spatially nonstationary seismic random noise has a smaller value of correlation integral than the stationary seismic random noise record on radial traces. For the spatially nonstationary seismic random noise record, the values of the ROAD become larger for some resampled data on a radial trace corresponding to nonstationary seismic traces. So we combine the ROAD to identify nonstationary random noise, which has higher ROAD than the other resampled noise on radial traces. The results of the synthetic seismic data and field common-short-point record show that the ROAD-RTFPF provides a satisfactory denoising and signal preserving performance for seismic data with spatially nonstationary random noise. It also shows that our method is superior to the RTFPF in suppression of spatially nonstationary random noise. The approach combining ROAD with radial time-frequency peak filtering method can effectively suppress the spatially nonstationary seismic random noise, which has small correlation integral on radial traces. On the radial traces, spatially nonstationary random noise appears as impulse noise in corresponding seismic traces with large power, so large values of ROAD can be used to identify the spatially nonstationary random noise. The ROAD-RTFPF can effectively attenuate spatially nonstationary random noise based on identification with ROAD and retain the advantage of the RTFPF in signal preservation.
