Processing seismic data by nonlinear stacking
Seismic data processing using one or more non-linear stacking enabling detection of weak signals relative to noise levels. The non-linear stacking includes a double phase, a double phase-weighted, a real phasor, a squared real phasor, a phase and an N-th root stack. Microseismic signals as recorded by one or more seismic detectors and transformed by transforming the signal to enhance detection of arrivals. The transforms enable the generation of an image, or map, representative of the likelihood that there was a source of seismic energy occurring at a given point in time at a particular point in space, which may be used, for example, in monitoring operations such as hydraulic fracturing, fluid production, water flooding, steam flooding, gas flooding, and formation compaction.
1. A computer program product stored in one or more non-transitory computer readable mediums for performing a method for use in well production or treatment, the method comprising:
receiving via a sensor a seismic data signal acquired in a formation, the seismic data signal including a microseismic data signal;
computing a non-linear stack of the seismic data signal having a non-linear weighting factor;
outputting the non-linear stack;
using the output non-linear stack to identify a microseismic event in time and space in an oilfield operation comprising one or more of hydraulic fracturing, fluid production, water flooding, steam flooding, gas flooding, or formation compaction, and
displaying an image of the formation based on the non-linear stack;
wherein the non-linear weighting factor is selected from a first group of a double phase, a double phase-weighted, a real phasor, and a squared real phasor.
2. The computer program product of claim 1 , wherein the non-linear weighting factor is a product of two factors selected from a second group including a phase, an n th root, the double phase, the real phasor, and the squared real phasor.
3. The computer program product of claim 2 , wherein the non-linear weighting factor is a product of more than two non-linear weighting factors from the second group.
4. The computer program product of claim 2 , wherein the non-linear weighting factor is a product of the double phase, squared real phasor, and n th root.
5. The computer program product of claim 2 , wherein the non-linear stack of the seismic data signal comprises a linear summation of the seismic data signal weighted by an instantaneous phase of the seismic data signal.
6. The computer program product of claim 5 , wherein the non-linear stack of the seismic data signal is calculated according to an equation of the form:
y
P
(
t
)
=
1
L
∑
i
=
1
L
exp
{
j
x
,
i
(
t
)
}
,
where y P (t) is the non-linear stack of the seismic data signal, L is a number of traces, i denotes different receiver signals, j is √{square root over (1)}, and x,i (t) is an instantaneous phase.
7. The computer program product of claim 2 , wherein an n th root stack of the seismic data signal comprises a nonlinear summation of the seismic data signal weighted by the n th root of the seismic data signal.
8. The computer program product of claim 7 , wherein the n th root stack of the seismic data signal is calculated according to an equation of the form:
y NR ( t,n )=sgn[ u ( t,n )]| u ( t,n )| n ,
where u(t,n) is the n th root stack, sgn[u(t, n)] is a sign or signum function, and y NR (t,n) is a product of sgn[u(t, n)] and u(t,n).
9. The computer program product of claim 2 , wherein computing the non-linear stack of the seismic data signal comprises computing a double-phase-weighted stack of the seismic data signal.
10. A computer program product stored in one or more non-transitory computer readable mediums for performing a method for use in well production or treatment, the method comprising:
receiving via a sensor a seismic data signal acquired in a formation, the seismic data signal including a microseismic data signal;
computing a phase-weighted n th root stack of the seismic data signal according to the form: y PWNR (t, m, n)=[y P (t)] m y NR (t, n), where y PWNR (t,m,n) is the phase-weighted n th root stack, y P (t) is a non-linear stack of the seismic data signal, m is a user selected parameter, and y NR (t,n) is a product of the nth root stack and a sign or signum function,
outputting the non-linear stack;
using the output non-linear stack to identify a microseismic event in time and space in an oilfield operation comprising one or more of hydraulic fracturing, fluid production, water flooding, steam flooding, gas flooding, or formation compaction, and
displaying an image of the formation based on the non-linear stack.
11. The computer program product of claim 10 , wherein computing the phase-weighted n th root stack of the seismic data signal further comprises computing a double phase-weighted n th root stack of the seismic data signal.
12. The computer program product of claim 11 , wherein the double phase-weighted n th root stack comprises a product of a double phase-weighted stack of the seismic data signal and an n th root stack of the seismic data signal.
13. The computer program product of claim 10 ,
wherein a phase stack factor of the phase-weighted n th root stack is calculated according to an equation of the form:
y
p
(
t
)
=
1
L
∑
i
=
1
L
exp
{
j
x
,
i
(
t
)
}
;
and
wherein an n th root stack factor of the phase-weighted n th root stack is calculated according to an equation of the form:
y NR ( t,n )=sgn[ u ( t,n )]| u ( t,n )| n ,
where L is a number of traces, i denotes different receiver signals, j is x,(t) is an instantaneous phase, sgn[u(t, n)] is the sign or signum function.
14. A system for acquiring seismic data and processing seismic data, the system comprising:
a seismic acquisition apparatus disposed at a formation that acquires the seismic data via a receiver; and
a data processing apparatus configured to:
receive via a sensor a seismic data signal acquired in the formation, the seismic data signal including a microseismic data signal;
compute a phase stack of the seismic data signal;
compute an n th root stack of the seismic data signal;
compute a phase-weighted n th root stack, wherein the phase-weighted n th root stack comprises the products of factors selected from the phase stack and the n th root stack;
output the phase-weighted n th root stack; and
use the output phase-weighted n th root stack to identify a microseismic event in time and space in an oilfield operation comprising one or more of hydraulic fracturing, fluid production, water flooding, steam flooding, gas flooding, or formation compaction; and
a display apparatus configured to display an image of the formation based on the phase-weighted n th root stack.
15. A system for acquiring seismic data and processing seismic data, the system comprising:
a seismic acquisition apparatus that acquires the seismic data; and
a data processing apparatus configured to:
receive a seismic data signal acquired in an Earth formation;
compute a phase stack of the seismic data signal;
compute an n th root stack of the seismic data signal;
compute a phase-weighted n th root stack, wherein the phase-weighted n th root stack is a product of the phase stack and the n th root stack; and
using one or more of the computed phase stack, n th root stack, or phase-weighted n th root stack to identify a microseismic event in time and space in an oilfield operation comprising one or more of hydraulic fracturing, fluid production, water flooding, steam flooding, gas flooding, or formation compaction.