Low frequency passive seismic interferometry for land data

Ambient seismic wavefield

In 2007, Saudi Aramco initiated an experiment aiming to detect and characterize microseismic energy for reservoir monitoring (Jervis and Dasgupta, 2009). The surface array consisted of 225 buried 3-component stations placed in a $15$ by $15$ grid with station spacing of $200$ m, spanning an area $3$ km by $3$ km.

geometry Figure 1. Geometry of the Aramco passive experiment; 225 stations (denoted by triangles) placed in a 15 by 15 grid. The geographic North is indicated by $\mathbf{N}$ . Open triangles denote stations turned into virtual sources for Figures 7 and 8. Lines denote receiver lines for sections shown in Figure 7.

Stanford University received a nearly continuous raw data record spanning 48 hours divided over 3 days, starting on day 1 at 18:00 ending on day 3 at 18:00. Only vertical components were used, after removing the arithmetic mean over $30$ s time windows. The 48 hours of passive data were analyzed for their spectral characteristics. A frequency domain amplitude spectrogram averaged over the entire array is shown in Figure 2. Most energy was recorded between $2$ Hz and $12$ Hz and varies in a daily pattern with higher energy during the daylight hours and less energy at night. Figure 3 shows the frequency-domain amplitude spectrum, averaged for all recordings during the hour from 20:00 to 21:00 on day 1, drawn as curve (a). We identify a peak at very low frequencies, below 1 Hz.

spectra1d-48-z
Figure 2. Frequency-domain amplitude spectrum averaged over the array as a function of time for 48 hours. White grid lines denote 6 hour blocks. a) Frequency-domain amplitude spectrum between 0 Hz and $100$ Hz; b) frequency-domain amplitude spectrum between 0 Hz and 20 Hz; the black line denotes the frequency of the low-pass filter applied before interferometry.

specbandpassed
Figure 3. Normalized frequency-domain amplitude spectrum, averaged over the array and data recorded between 20:00 and 21:00 on day 1. Curve (a) is the spectrum of the original data record, curve (c) is the spectrum after low-pass filtering for interferometry and curve (b) is the spectrum of the data after band-pass filtering for beam-forming.

To help determine what kind of seismic energy composes the low-frequency spectrum, the frequency-wavenumber ($f-k_x-k_y$ ) domain spectra were computed. A cross section through a cube of frequency-wavenumber spectra averaged over all recordings during the hour from 20:00 to 21:00 on day 1 is shown in Figure 4. The panel in the upper right corner of Figure 4 denotes a beam-forming experiment (see below). A cross section through a cube of frequency-wavenumber spectra averaged over all recordings between 11:00 and 12:00 on day 2 is shown in Figure 5. Both cross-sections only show frequencies below 6 Hz; above 6 Hz no wave modes could clearly be identified. Up to 6 Hz most of the energy resides in the (Rayleigh) surface wave modes. The fundamental mode becomes aliased above 3 Hz. Between 20:00 and 21:00 on day 1 most energy comes from the west, while from 11:00 to 12:00 on day 2 most energy comes from the north. (The directionality of the tails in the frequency-wavenumber spectra is controlled by the sign of the Fourier transformations.) Another common technique to characterize directionality in a wavefield is beam-forming. This was performed, after bandpass filtering between 1 Hz and 3.5 Hz, by computing linear $\tau-p$ transformations over both directions. A beam is formed by averaging the amplitude in the $(\tau-p)$ domain over a certain $\tau$ -window. (Note $\tau$ denotes the interception times and $p$ denotes the slownesses of the stacking lines of the $\tau-p$ transformation in $(t,x)$ domain). The beams shown in the upper right corners of Figures 4 and 5 show that the fundamental mode travels with a slowness of slightly less than 1 ms/m (corresponding to a velocity of slightly greater than 1000 m/s). A higher mode visible in the frequency-wavenumber domain of Figure 4 can be observed (faintly) to travel with a slowness under 0.4 ms/m (corresponding with a velocity greater than 2500 m/s). Studying averaged frequency-wavenumber domains for other hours shows that the ambient seismic field at frequencies below 6 Hz is generally incident from the west and/or north.

MDspectra1
Figure 4. Cross-sections through frequency-wavenumber spectra cube and averaged over the data recorded between 20:00 and 21:00 on day 1. The top right panel contains a beam-forming experiment for the frequency band of 1 Hz to 3.5 Hz.

MDspectra2
Figure 5. Cross-sections through frequency-wavenumber spectra cube and averaged over the data recorded between 11:00 and 12:00 on day 2. The top right panel contains a beam-forming experiment for the frequency band of 1 Hz to 3.5 Hz.

Low frequency passive seismic interferometry for land data