Time-Spectral Analysis for 4D Data Q-Controlled Calibration

Monitoring viscosity changes from time‐lapse seismic attenuation: case study from a heavy oil reservoir

“…The method is derived similarly to that of Dasgupta and Clark (), Wang (), Lecerf et al . (), and Blanchard et al . () by assuming a propagating wave whose amplitude as a function of frequency and depth is given by with magnitude where f is the frequency, z is the depth, k is the wavenumber, t is time, is the input source amplitude, is the amplitude of the recorded signal as a function of frequency and depth, is the geometrical spreading factor (assumed to be real as is standard in seismic processing), and is the frequency‐dependent attenuation coefficient.…”

“…4DRSM estimates attenuation between t 1 and t 2 in each survey separately and does not require the attenuation above the reservoir, γ 1 , to be the same between the two surveys as in Lecerf et al . (). In our analysis we thus do not require precise balancing of the amplitude (and spectrum) between the baseline and the monitor traces as the balancing filter cancels during the relative ratio estimation (i.e., , where F is the balancing filter between the baseline and monitor traces).…”

“…The method is derived similarly to that of Dasgupta and Clark (1998), Wang (2003), Lecerf et al (2006), and Blanchard et al (2009) by assuming a propagating wave whose amplitude as a function of frequency and depth is given by…”

“…It separates the effect of attenuation from geometric spreading and is first presented for laboratory measurements of rocks by Toksöz et al . () and adjusted for VSP and surface seismic in many studies (e.g., Hauge ; Badri and Mooney, Feustel and Young ; Chen and Sidney ; Dasgupta and Clark ; Sun and Castagna ; Hedlin Mewhort and Margrave ; Mateeva ; Wang ; Carter ; Vasconcelos and Jenner ; Matsushima ; Rickett ; Lecerf, Rogers, and Lefeuvre ; Reine, Clark, and van Der Baan ; Clark et al . ; Blanchard et al ., ; Reine et al .…”

“…The spectral ratio method is a common technique to estimate the attenuation (Q -factor) of the medium. It separates the effect of attenuation from geometric spreading and is first presented for laboratory measurements of rocks by Toksöz et al (1979) and adjusted for VSP and surface seismic in many studies (e.g., Hauge 1981;Badri andMooney, 1987 Feustel andYoung 1994;Chen and Sidney 1997;Dasgupta and Clark 1998;Sun and Castagna 2000;Hedlin Mewhort and Margrave 2001;Mateeva 2003;Wang 2003;Carter 2003;Vasconcelos and Jenner 2005;Matsushima 2006;Rickett 2006;Lecerf, Rogers, and Lefeuvre 2006;Reine, Clark, and van Der Baan 2009;Clark et al 2009;Blanchard et al, 2009;Reine et al 2012a,b). Note that, for surface seismic data, near surface effects make the measurements of attenuation even more difficult and less reliable.…”