Signal Apparition

date
Dec 31, 2021
slug
10050
status
Published
tags
SeismicExploration
summary
type
Post
notion image
以传统三震源为例，
一源按照(..., 1, 1, 1, 1, 1, 1, ...)激发，周期为1
二源按照(..., 1, A, 1, A, 1, A, ...)激发，周期为2
三源按照(..., 1, 1, A, 1, 1, A, ...)激发，周期为3
“Wavefield signal apparition” is a new method to sample time-discrete signals that allows for the separation of interfering signals from multiple sources. The theory of wavefield signal apparition is discussed in detail in a companion paper (Robertsson et al., 2016, submitted to EAGE). Essentially, by changing a well-sampled conventional source sequence (…,1,1,1,1,1,…), where the wavefield in the spectral fk-domain is present in a cone around the spatial wavenumber 𝑘 = 0, to the source sequence (…,1,A,1,A,1,…) where A is any function independent of spatial positions, the wavefield in the spectral 𝑓𝑘-domain will be present in two cones: one around 𝑘 = 0 and the other around the Nyquist wavenumber . Then, in simultaneous shooting, where the combined source sequences (…,1,1,1,1,1,…) and (…,1,A,1,A,1,…) are used, the data from the (…,1,A,1,A,1,…) sequence will be solely apparent and isolated in the cone around the Nyquist wavenumber. The data from the two source sequences thus can be separated in the fk-domain.
Figure 1: Top left: Marine seismic model used to generate synthetic data for the simultaneous source separation example. Data are recorded on the seabed 150m below the sea surface at 𝑥=3500m. Two source profiles are acquired simultaneously. Source ‘A’ shoots regularly, from left to right. Source ‘B’ fires periodically, with a 10ms time-delay at every alternate shot position, and is moved from right to left. Top right: Synthesized simultaneous source data, shown in the common receiver domain. The horizontal axis refers to the coordinate of source ‘A’. Bottom left: 𝑓𝑘 spectrum of simultaneous source data. The cone centred around 𝑘 = 0 contains data from both sources, while the cones centered around the Nyquist wavenumber ±𝑘! contain only information from source ‘B’. Thus, the data from source ‘B’ is perfectly known in the 𝑓𝑘 domain. Bottom right: Separated simultaneous source data (for source ‘A’).
Figure 1: Top left: Marine seismic model used to generate synthetic data for the simultaneous source separation example. Data are recorded on the seabed 150m below the sea surface at 𝑥=3500m. Two source profiles are acquired simultaneously. Source ‘A’ shoots regularly, from left to right. Source ‘B’ fires periodically, with a 10ms time-delay at every alternate shot position, and is moved from right to left. Top right: Synthesized simultaneous source data, shown in the common receiver domain. The horizontal axis refers to the coordinate of source ‘A’. Bottom left: 𝑓𝑘 spectrum of simultaneous source data. The cone centred around 𝑘 = 0 contains data from both sources, while the cones centered around the Nyquist wavenumber ±𝑘! contain only information from source ‘B’. Thus, the data from source ‘B’ is perfectly known in the 𝑓𝑘 domain. Bottom right: Separated simultaneous source data (for source ‘A’).
A 25Hz Ricker wavelet is used to simulate data at a receiver station. The data are acquired sufficiently densely to avoid spatial aliasing according to the geometry shown in Figure 1. The simultaneous source data with the apex to the left were generated by source ‘A’ shooting regularly (with source sequence (…,1,1,1,1,1,…)). The data with the apex to the right were generated by source ‘B’ shooting with the periodic sequence (…,1,A,1,A,1,…) where A represents a time delay: ; we have selected T=10ms which gives on every second recording a somewhat “fuzzy” appearance of this part of the data.
The data are transformed to the fk-domain, where the data generated from source ‘B’ are solely present in the cone around the Nyquist number . These data are isolated and properly scaled (with a function depending on the function A) before inverse Fourier transforming the source ‘B’ data to time-space domain. Here, they are subtracted from the originally acquired simultaneous source data, recovering the source ‘A’ data. As seen in Figure 1, the result is excellent and, apart from limited numerical artifacts at the top and bottom (related to windowing of data before the temporal Fourier transform), no signal leakage from source ‘B’ is visible.
 
reference: Wavefield signal apparition, Part II: Applications

© Wen Bo 2021 - 2022