Seismic inversion for formation properties and attenuation effects
Method for inverting seismic data to obtain reflection properties by estimating or measuring ( 301 ) the source signature for the seismic data, then inverting ( 302 ) simultaneously for subsurface formation properties or reflection properties and for the amplitude attenuation and velocity dispersion effects integrated over the raypath from the source to the reflectors and to the receiver.
1. A computer-implemented method for inverting seismic data to obtain reflection properties of a subsurface region, comprising:
estimating or measuring a source signature for the seismic data; and
using the source signature, inverting the seismic data simultaneously for a subsurface formation or reflection property and for amplitude attenuation or velocity dispersion effects or both, integrated over a ray-path from source to reflectors and to a receiver;
wherein, at least the inversion is performed using a computer, and the inversion transforms the seismic data into an interpretable model of the subsurface region.
2. The method of claim 1 , wherein the seismic data are inverted for both amplitude attenuation and velocity dispersion effects, but the number of unknown variables in the inversion is reduced by using a causality assumption relating frequency dependence of the velocity dispersion to the amplitude attenuation.
3. The method of claim 1 , wherein the inversion uses a causality relationship to couple and thereby constrain values of the amplitude attenuation and the velocity dispersion effects determined by the inversion.
4. The method of claim 1 , further comprising using the subsurface formation properties or reflection properties or the amplitude attenuation or velocity dispersion effects for exploration for hydrocarbons.
5. The method of claim 1 , wherein the inversion assumes that reflections are sparse.
6. The method of claim 1 , wherein the subsurface formation or reflection property is acoustic velocity, acoustic impedance, or reflectivity.
7. The method of claim 1 , wherein the inversion is iterative and the seismic data being inverted are limited by a time window, with the window becoming progressively larger as the iterations progress, until in a last iteration the window includes an entire trace of seismic data.
8. The method of claim 1 , wherein the inversion comprises:
simulating synthetic seismic data using an assumed subsurface model of said formation or reflection property and a mathematical relationship describing acoustic wave propagation in a medium, then comparing the simulated seismic data to corresponding measured data from said seismic data to determine a degree of misfit, then adjusting parameters in the subsurface model to reduce the degree of misfit, and repeating until the misfit is less than a predetermined amount or other stopping condition is met.
9. The method of claim 8 , wherein the mathematical relationship represents the amplitude attenuation as a polynomial function of frequency raised to a power and the inversion determines coefficients of the polynomial.
10. The method of claim 8 , wherein the inversion is sparse spike inversion and the mathematical relationship can be expressed in the following form:
p
(
t
)
=
s
(
t
)
*
∑
k
=
1
N
z
k
F
(
α
k
-
τ
k
)
,
wherein p(t) is seismic response, meaning pressure or particle velocity or acceleration, as a function of time; s(t) is the estimated or measured source signature as a function of time; * represents the convolution operator; N subsurface reflectors are labeled by integer index k; z k is reflection coefficient for reflector k; and F(α k , τ k ) represents an earth filter for the subsurface region which is a function of effective attenuation α k and two-way travel time τ k from the source to reflector k and then to the receiver.
11. The method of claim 10 , wherein unknown quantities found in the inversion are α k , τ k , and z k .
12. The method of claim 10 , wherein said mathematical relationship, after being transformed into frequency domain, can be written as
P
(
ω
)
=
S
(
ω
)
*
∑
k
=
1
N
z
k
ⅇ
-
ω
α
k
τ
k
/
2
ⅇ
-
ⅈωτ
k
(
1
+
α
k
ln
(
ϖ
/
ω
)
/
π
)
where ω is a reference frequency greater than frequency ω, and α k =1/Q k , where Q k is an effective quality factor that is constant as a function of the frequency ω.
13. The method of claim 12 , wherein causality is assumed, and the velocity dispersion effects are expressed as a frequency-dependent time delay given by
Delay( f )=τ k (1+α k ln( ω /ω)/π)
where ω is a reference frequency greater than frequency ω=2πf.