Methods and systems for processing microseismic data
Methods and systems for processing microseismic waveforms. The methods and systems provide determining a measure of waveform fit in the frequency-domain comprising constructing, in the frequency-domain, at least one of an amplitude misfit functional and a cross phase functional between arrivals; and estimating source parameters and/or model parameters.
1. A method of processing microseismic data, comprising:
acquiring three-component microseismic waveform data with at least one receiver;
determining a measure of waveform fit in the frequency-domain comprising:
constructing, in the frequency-domain an amplitude misfit functional wherein constructing includes utilizing time reversal determined by a matrix inversion;
estimating source parameters and/or model parameters; and
displaying microseismicity results using estimated source parameters and/or model parameters; and
further comprising a joint χ 2 likelihood function comprising the amplitude misfit functional and a cross-phase functional, constructed in the frequency-domain wherein constructing includes utilizing time reversal determined by a matrix inversion, with a multivariate prior probability distribution; and maximizing or sampling a posterior probability function using global search techniques.
2. A method of processing microseismic data according to claim 1 , wherein the matrix inversion is determined from wavefield parameters.
3. A method of processing microseismic data according to claim 1 , further comprising rotating the waveform data to a geographical East, North, Up (ENU) coordinate system.
4. A method of processing microseismic data according to claim 1 , wherein the microseismic waveform data are acquired by a plurality of three-component geophones.
5. A method of processing microseismic data according to claim 1 , wherein the microseismic waveform data are acquired during a hydraulic fracturing operation.
6. A method of processing microseismic data according to claim 1 , wherein the microseismic waveform data are acquired during a perforation operation.
7. A method of processing microseismic data according to claim 1 , further comprising determining one or more source functions in the frequency-domain using:
d
(
x
j
,
ω
)
=
∑
k
=
1
3
u
k
(
ω
)
S
kj
T
kj
G
kj
ⅇ
ⅈω
t
kj
ⅇ
-
π
t
kj
/
Q
kj
(
f
+
i
2
f
π
ln
(
f
/
f
r
)
)
h
kj
wherein:
d is the waveform data acquired by a plurality of three-component geophones at locations x;
ω is angular frequency;
k represents three different wave types (P, Sv, Sh);
j is receiver index;
u k (ω) is displacement source function for the kth wave type;
S kj is source radiation amplitude;
T kj is total transmission loss along the ray;
G kj is geometrical spreading;
t kj is arrival time;
Q kj is the time-weighted harmonic average of (isotropic) Q values along the ray;
f r is reference frequency for absorption modeling due to Q, the frequency at which there is no phase dispersion; and
h kj is the polarization vector at the receiver.
8. A method of processing microseismic data according to claim 1 , wherein the amplitude misfit functional is:
χ
a
2
=
1
N
ω
∑
ω
[
d
(
ω
)
-
d
^
(
ω
)
2
/
σ
^
a
2
(
ω
)
]
wherein:
d is data recorded by a network of three-component geophones;
{circumflex over (d)} is data generated using estimated source functions u k (ω);
ω is angular frequency;
N ω is the number of frequencies; and
σ
^
a
2
(
ω
)
=
1
M
∑
m
=
1
M
d
(
ω
)
2
/
SNR
.
9. A method of processing microseismic data according to claim 1 , further comprising generating a joint posterior probability function of a model vector m using:
p(m|d,I)∝e (−(χ d 2 +χ m 2 )/2)
wherein:
d is the waveform data acquired by a plurality of three-component geophones at locations x;
I is prior model distribution information;
χ
d
2
=
[
α
·
χ
a
2
+
(
1
-
α
)
·
χ
p
2
]
·
N
r
;
and
χ
m
2
=
∑
i
(
m
i
-
μ
i
)
2
/
σ
i
2
,
where μ is the expected value and σ is the standard deviation.
10. A method of processing microseismic data according to claim 1 , further comprising generating images of reflection interfaces between a source location and receivers comprising:
determining one or more source functions in the frequency domain using time reversal;
deconvolving three-component residuals; and
migrating the deconvolved residuals using a calibrated velocity model to derive locations of reflection interfaces.
11. A method of processing microseismic data according to claim 1 , further comprising calibrating a velocity model using absolute arrival times recorded from a perforation shot.
12. A method of processing microseismic data, comprising:
acquiring three-component microseismic waveform data with at least one receiver;
determining a measure of waveform fit in the frequency-domain comprising:
constructing, in the frequency-domain an amplitude misfit functional wherein constructing includes utilizing time reversal determined by a matrix inversion;
estimating source parameters and/or model parameters;
displaying microseismicity results using estimated source parameters and/or model parameters;
determining a joint χ 2 likelihood function over a three-dimensional (3D) map for each time window of data, wherein the joint χ 2 likelihood function comprises the amplitude misfit functional and a cross-phase functional, constructed in the frequency-domain wherein constructing includes utilizing time reversal determined by a matrix inversion, with a multivariate prior probability distribution;
maximizing or sampling a posterior probability function using global search techniques for each time window of data; and
displaying the 3D map as a movie of time evolution of the spatial distribution of coherent, time-reversed seismic energy.
13. A method of processing microseismic data, comprising:
acquiring three-component microseismic waveform data with at least one receiver;
determining a measure of waveform fit in the frequency-domain comprising:
constructing, in the frequency-domain a cross-phase functional between arrivals wherein constructing includes utilizing time reversal determined by a matrix inversion;
estimating source parameters and/or model parameters; and
displaying microseismicity results using estimated source parameters and/or model parameters.
14. A method of processing microseismic data according to claim 13 , wherein constructing a cross-phase functional between arrivals comprises constructing a spectral coherence functional averaged over frequency.
15. A method of processing microseismic data according to claim 13 , wherein the cross-phase functional between arrivals is:
χ
p
2
=
(
1
-
〈
γ
xy
2
〉
)
·
SNR
wherein:
SNR is signal-to-noise ratio;
γ
xy
(
f
)
2
=
S
xy
2
S
x
S
y
;
and
p represents phase.
16. A system of processing microseismic data according to claim 13 , wherein the at least one three-component geophone comprises a plurality of three-component geophones.
17. A system of processing microseismic data according to claim 13 , wherein the system is configured or designed for hydraulic fracturing operations.
18. A system of processing microseismic data according to claim 13 , wherein the system is configured or designed for perforation operations.
19. A system of processing microseismic data according to claim 13 , wherein the system is configured or designed for permanent or passive monitoring operations.
20. A system of processing microseismic data according to claim 13 , wherein the system is configured or designed for cross-well operations.