US 11,307,320 B2 · Expedient processing and waveform inversion of seismic data

Abstract

A method for expediently processing and inverting elastic wave data to reduce the amount of data and to determine a physical properties model of the material medium and a source properties model. The data are processed to generate waveforms containing the phase difference between compressional- and shear-wave arrivals using auto-correlation, cross-correlation, or deconvolution of said data sensed at each of an arrangement of sensors, whereby said lengthy elastic wave data records are reduced substantially in time. Said waveform data are thereafter inverted using waveform inversion by modifying the source term in the equation of motion, wherein the source term is mathematically expressed as a product of time-independent source properties volume defined at every location in space within said material medium and a space-independent source-time function, whereby no prior knowledge of the number of sources, spatial distribution of source location, source amplitude, or source focal mechanism is needed.

Claims12

Dependent claims

A method for compressing the amount of elastic wave data, for eliminating the source-time functions, and for simulating composite impulse responses, comprising the steps of:

(a) recording elastic wave data in at least one spatial location that includes at least one directional component of particle displacement, velocity, or acceleration and said elastic data originating from at least one source selected from the group consisting of man-made and natural sources, and
(b) using at least one operation selected from the group consisting of auto-correlation, cross-correlation, and deconvolution, on said elastic data, thereby generating waveforms containing the phase difference between compressional-wave mode and slow-shear-wave mode, or any two different elastic wave modes, selected from the group consisting of compressional-wave mode, fast-shear-wave mode, and slow-shear-wave mode, and
(c) discarding the acausal part, and
(d) truncating the causal part at a predetermined time value ascertained by the maximum expected time interval between the said elastic wave modes originating from said sources,
whereby said elastic wave data are compressed, and
whereby either the phase or both the amplitude and phase of the source-time functions of sources generating said elastic waves are eliminated, and whereby the said computed waveform at each sensor represents the composite impulse response between the sources and the said sensor.

3 more elements

A system for compressing the amount of elastic wave data, for eliminating the source-time functions, and for simulating composite impulse responses, comprising:

(a) a data recording system comprising of one or more computers, data recording hardware, and one or more elastic wave sensors that include at least one directional component of particle displacement, velocity, or acceleration, that record elastic wave data in at least one spatial location and said elastic data originating from at least one source selected from the group consisting of man-made and natural sources, and
(b) a processor that uses at least one operation selected from the group consisting of auto-correlation, cross-correlation, and deconvolution, on said elastic data, thereby generating waveforms containing the phase difference between compressional-wave mode and slow-shear-wave mode, or any two different elastic wave modes, selected from the group consisting of compressional-wave mode, fast-shear-wave mode, and slow-shear-wave mode, and
(c) wherein the processor further discards the acausal part, and
(d) wherein the processor further truncates the causal part at a predetermined time value ascertained by the maximum expected time interval between the said elastic wave modes originating from said sources,
whereby the system compresses said elastic wave data, and
whereby the system eliminates either the phase or both the amplitude and phase of the source-time functions of sources generating said elastic waves, and whereby the system simulates the composite impulse response between the sources and each sensor.

3 more elements

A method for efficient imaging of acoustic or processed elastic wave data using the inhomogeneous acoustic wave equation

m
⁡
(
x
)
⁢
∂
2
⁢
u
⁡
(
x
,
f
)
∂
t
2
-
∇
2
⁢
u
⁡
(
x
,
t
)
=
f
⁡
(
x
,
t
)
,
where x represents space, t is time, m(x) represents the material medium properties, μ(x,t) is the wavefield that may be a scalar or a vector field, ƒ(x,t) represents the sourcing function in space and time, said method comprising the steps of:
(a) modifying said sourcing function in said inhomogeneous acoustic wave equation to the mathematical product of a time-independent source attribute defined at every location in space within said material medium and a space-independent source-time function given by
m
⁡
(
x
)
⁢
∂
2
⁢
u
⁡
(
x
,
t
)
∂
t
2
-
∇
2
⁢
u
⁡
(
x
,
t
)
=
A
⁡
(
x
)
⁢
S
⁡
(
t
)
,
where S(t) is the said space-independent source-time function, A(x) represents the said time-independent source attribute,
(b) recording acoustic wave data or using wave data obtained through processing in at least one spatial location, and
(c) generating an initial source attributes model and an initial material medium properties model, said initial source attributes model optionally comprising only null values at all spatial locations within said material medium, and
(d) simulating synthetic wave data using the source properties model and the material medium properties model, and
(e) computing an objective function that is a measure of the discrepancy between said simulated wave data and said recorded or pre-processed wave data, and
(f) computing the gradients of said objective function with respect to the source attributes model and material medium properties model given by
ℊ
A
⁡
(
x
)
=
∫
0
T
⁢
u
†
⁡
(
x
,
T
-
t
)
⁢
S
⁡
(
t
)
⁢
dt
,
⁢
and
⁢
⁢
ℊ
m
⁡
(
x
)
=
m
†
⁡
(
x
)
⁢
∫
0
T
⁢
u
†
⁡
(
x
,
T
-
t
)
⁢
∂
2
⁢
u
⁡
(
x
,
t
)
∂
t
2
⁢
dt
,
where μt represents the adjoint wavefield, gA(x) is the gradient of said objective function with respect to said source attributes model, gm(x) is the gradient of said objective function with respect to said material medium properties model, and mt(x)=2/V(x)3 if m(x)=V(x), and mt(x)=−2/V(x) if m(x)=1/V(x), and mt(x)=−1 if m(x) 1/V(x)2, and
(g) updating said source attributes model and said material medium properties model using
A(x)updated=A(x)−αaAgA(x),
and
m(x)updated=m(x)−αmgm(x),
where A(x)updated is the updated source attributes model, m(x)updated is the updated material medium properties model, αA and αm are one-dimensional minimizers of said objective function along vectors A(x)−αAgA(x) and m(x)−αmgm(x), respectively, optionally replaced by the Hessian or the pseudo-Hessian, and
(h) optionally iterating steps (d)-(g) at least once more, wherein said updated source attributes model and said updated material medium properties model of step (g) arc used in step (d) to simulate synthetic wave data, thereby resulting in a further updated source attributes model and a further updated material medium properties model.

173 more elements

A system for efficiently imaging acoustic or processed elastic wave data using the inhomogeneous acoustic wave equation

m
⁡
(
x
)
⁢
∂
2
⁢
u
⁡
(
x
,
t
)
∂
t
2
-
∇
2
⁢
u
⁡
(
x
,
t
)
=
f
⁡
(
x
,
t
)
,
where x represents space, t is time, m(x) represents the material medium properties μ(x,t) is the wavefield that may be a scalar or a vector field, ƒ(x,t) represents the sourcing function in space and time, said system comprising:
(a) a processor that modifies said sourcing function in said inhomogeneous acoustic wave equation to the mathematical product of a time-independent source attribute defined at every location in space within said material medium and a space-independent source-time function given by
m
⁡
(
x
)
⁢
∂
2
⁢
u
⁡
(
x
,
t
)
∂
t
2
-
∇
2
⁢
u
⁡
(
x
,
t
)
=
A
⁡
(
x
)
⁢
S
⁡
(
t
)
,
where S(t) is the said space-independent source-time function, A(x) represents the said time-independent source attribute,
(b) a data recording system comprising of one or more computers, data recording hardware, and one or more acoustic wave sensors that record acoustic wave data in at least one spatial location, or a data storage drive containing wave data obtained through processing in at least one spatial location, and
(c) wherein the processor further generates an initial source attributes model and an initial material medium properties model, said initial source attributes model optionally comprising only null values at all spatial locations within said material medium, and
(d) wherein the processor further simulates synthetic wave data using the source properties model and the material medium properties model, and
(e) wherein the processor further computes an objective function that is a measure of the discrepancy between said simulated wave data and said recorded or pre-processed wave data, and
(f) wherein the processor further computes the gradients of said objective function with respect to the source attributes model and material medium properties model given by
ℊA
⁡
(
x
)
=
∫
0
T
⁢
u
†
⁡
(
x
,
⁢
T
-
t
)
⁢
S
⁡
(
t
)
⁢
dt
,
⁢
and
⁢
⁢
ℊ
m
⁡
(
x
)
=
m
⁡
(
x
)
⁢
∫
0
T
⁢
u
†
⁡
(
x
,
T
-
t
)
⁢
∂
2
⁢
u
⁡
(
x
,
t
)
∂
t
2
⁢
d
⁢
t
,
where μt represents the adjoint wavefield, gA(x) is the gradient of said objective function with respect to said source attributes model, gm(x) is the gradient of said objective function with respect to said material medium properties model, and mt(x)=2/V(x)3 if m(x)=V(x), and mt(x)=−2/V(x) if m(x)=1/V(x), and mt(x)=−1 if m(x)=1/V(x)2, and
(g) wherein the processor further updates said source attributes model and said material medium properties model using
A(X)updated=A(x)−αAgA(X)
and
m(x)updated=m(x)−αmgm(x),
where A(x)updated is the updated source attributes model, m(x)updated is the updated material medium properties model, αA and αm are one-dimensional minimizers of said objective function along vectors A(x)−αAgA(x) and m(x)−αmgm(x), respectively, optionally replaced by the Hessian or the pseudo-Hessian, and
(h) wherein the processor further optionally iterates steps (d)-(g) at least once more, by using said updated source attributes model and said updated material medium properties model of step (g) in step (d), thereby further updating said source attributes model and further updating said material medium properties model.

174 more elements

A method for efficient imaging of acoustic or processed elastic wave data using the frequency-domain inhomogeneous acoustic wave equation

−(m(x)ω2+Δ2)U(x,ω)=ƒ(x,ω),
where x represents space, ω is frequency, m(x) represents the material medium properties, U(x,ω) is the wavefield that may be a scalar or a vector field, ƒ(x, ω) represents the sourcing function in space and frequency, said method comprising the steps of:
(a) modifying said sourcing function in said frequency-domain inhomogeneous acoustic wave equation to the mathematical product of a frequency-independent source attribute defined at every location in space within said material medium and a space-independent source-time function given by
−(m(x)ω2+Δ2)U(x,ω)=A(x)S(ω),
where S(ω) is the said space-independent source-time function in the frequency domain, A(x) represents the said frequency-independent source attribute, and
(b) recording acoustic wave data or using wave data obtained through processing in at least one spatial location, and
(c) transforming said recorded acoustic or pre-processed elastic wave data into the frequency domain, and
(d) generating an initial source attributes model and an initial material medium properties model, said initial source attributes model optionally comprising only null values at all spatial locations within said material medium, and
(e) simulating synthetic wave data using the source properties model and the material medium properties model, and
(f) computing an objective function that is a measure of the discrepancy between said simulated wave data and said recorded or pre-processed wave data, and
(g) computing the gradients of said objective function with respect to the source attributes model and material medium properties model given by
gA(x)=Re{Ut,*(x,ω)S(ω)},
and
gm(x)=−Re{mt(x)ω2Ut,*(x,ω)U(x,ω)},
where Ut represents the adjoint wavefield, * represents complex conjugation, Re represents the real part of a complex vector, gA(x) is the gradient of said objective function with respect to said source attributes model, gm(x) is the gradient of said objective function with respect to said material medium properties model, and mt(x)=2/V(x)3 if m(x)=V(x), and mt(x)=−2/V(x) if m(x)=1/V(x), and mt(x)=−1 if m(x)=1/V(x)2, and
(h) updating said source attributes model and said material medium properties model using
A(X)updated=A(x)−αAgA(x),
and
m(X)updated=m(x)−αmgm(X),
where A(x)updated is the updated source attributes model, m(x)updated is the updated material medium properties model, αA and αm are one-dimensional minimizers of said objective function along vectors A(x)−αAgA(x) and m(x)−αmgm(x), respectively, optionally replaced by the scaled Hessian or the scaled pseudo-Hessian, and
(i) optionally iterating steps (e)-(h) at least once more, wherein said updated source attributes model and said updated material medium properties model of step (h) are used in step (e) to simulate synthetic wave data, thereby resulting in a further updated source attributes model and a further updated material medium properties model.

18 more elements

A system for efficiently imaging acoustic or processed elastic wave data using the frequency-domain inhomogeneous acoustic wave equation

−(m(x)ω2+Δ2)U(x,ω)=ƒ(x,ω),
where x represents space, w is frequency, m(x) represents the material medium properties, U(x,ω) is the wavefield that may be a scalar or a vector field, ƒ(x,ω) represents the sourcing function in space and frequency, said system comprising:
(a) a processor that modifies said sourcing function in said frequency-domain inhomogeneous acoustic wave equation to the mathematical product of a frequency-independent source attribute defined at every location in space within said material medium and a space-independent source-time function given by
−(m(x)ω2+Δ2)U(x,ω)=A(x)S(ω),
where S(ω) is the said space-independent source-time function in the frequency domain, A(x) represents the said frequency-independent source attribute, and
(b) a data recording system comprising of one or more computers, data recording hardware, and one or more acoustic wave sensors that record acoustic wave data in at least one spatial location, or a data storage drive containing wave data obtained through processing in at least one spatial location, and
(c) wherein the processor further transforms said recorded acoustic or pre-processed elastic wave data into the frequency domain, and
(d) wherein the processor further generates an initial source attributes model and an initial material medium properties model, said initial source attributes model optionally comprising only null values at all spatial locations within said material medium, and
(e) wherein the processor further simulates synthetic wave data using the source properties model and the material medium properties model, and
(f) wherein the processor further computes an objective function that is a measure of the discrepancy between said simulated wave data and said recorded or pre-processed wave data, and
(g) wherein the processor further computes the gradients of said objective function with respect to the source attributes model and material medium properties model given by
gA(x)=Re{Ut,*(x,ω)S(ω)},
and
gm(x)=−Re{mt(x)ω2Ut,*(x,ω)U(x,ω)},
where Ut represents the adjoint wavefield, * represents complex conjugation, Re represents the real part of a complex vector, gA(x) is the gradient of said objective function with respect to said source attributes model, gm(x) is the gradient of said objective function with respect to said material medium properties model, and mt(x)=2/V(x)3 if m(x)=V(x), and mt(x)=−2/V(x) if m(x)=1/V(x), and mt(x)=−1 if m(x)=1/V(x)2, and
(h) wherein the processor further updates said source attributes model and said material medium properties model using
A(x)updated=A(x)−αAgA(x),
and
m(x)updated=m(x)−αmgm(x),
where A(x)updated is the updated source attributes model, m(x)updated is the updated material medium properties model, αA and αm are one-dimensional minimizers of said objective function along vectors A(x)−αA gA(x) and m(x)−αm gm(x), respectively, optionally replaced by the scaled Hessian or the scaled pseudo-Hessian, and
(i) wherein the processor further optionally iterates steps (e)-(h) at least once more, by using said updated source attributes model and said updated material medium properties model of step (h) in step (e), thereby further updating said source attributes model and further updating said material medium properties model.

18 more elements

Dependencies are inferred from the claim text.

Expedient processing and waveform inversion of seismic data

Life of this patent

Expedient processing and waveform inversion of seismic data

Life of this patent

Abstract

Claims12