seismic inversion and its types and geological model build and nonlinear and linear inverse theory and it application in geophysics

2. Formulation of Forward and Inverse
Problems for Different Physical Fields
 FORWARD PROBLEM: model {model parameters m} → data d.
 INVERSE PROBLEM: data d → model {model parameters m}.

3. Formulation of Forward and Inverse
Problems for Different Physical Fields
 In studying the geophysical methods, we should also take into account that the field can be
generated by some source. So we have to correct our chart accordingly
 FORWARD PROBLEM:
model {model parameters m, sources “s”} → data d:
d = As(m)
where As is the forward problem operator depending on a source “s.”

4. Formulation of Forward and Inverse
Problems for Different Physical Fields
 INVERSE PROBLEM:
{data d, sources “s”} → model {model parameters m}:
m = A s (d)
Or (m,s) = A (d)
−1

6. Formulation of Forward and Inverse
Problems for Different Physical Fields
 Inverse problems usually start with some procedure for predicting the response of a physical
system with known parameters.
 how can we determine the unknown parameters from observed data?

7. estimating the density of the material in a body

8. Measuring Volume and Mass

9. Computing
ρ

10. The Pernicious Effects of Errors
 For many purposes this story could end now.
 We have found an answer to our original problem (measuring the density of K).
 We don’t know anything (yet) about the short comings of our answer, but we haven’t had to do
much work to get this point. However, we, being scientists, are perforce driven to consider this
issue at a more fundamental level.

13. 2D Seismic surface wave Tomography
We want
A map of surface
wave velocity
We have
Average velocity
along seismic rays
Receivers Sources

15. (A)Geometry of the station
array.
(b) Records of ambient
vibrations at the stations.
(c) Dispersion curves with
error bars for different
time windows and array
geometries. (d) Swave
velocity profiles explaining
the dispersion curves. The
darkest models present
the lowest misfit values.

16. Travel time Inversion
 The traveltime of a seismic wave between source and receiver is solely dependent on the velocity
structure of the medium through which the wave propagates
 Therefore, subsurface structure in a seismic traveltime inversion is represented by variations in P
or S wave velocity
 The most appropriate choice will depend on the a priori information (e.g. known faults or other
interfaces), whether or not the data indicates the presence of interfaces (e.g. reflections, mode
conversions), whether data coverage is adequate to resolve the trade-off between interface
position and velocity, and finally, the capabilities of the inversion routine

17. Including Interfaces
 Velocity discontinuities are most
commonly included in velocity
models when the subsurface is
represented by sub horizontal
layers in Fig).
 In 2-D and 3-D traveltime inversion,
the use of layered
parameterizations has almost
exclusively been the domain of
reflection and refraction tomograph

18. Including Interfaces
 discontinuous at the joins between segments. Such
discontinuity may not be geologically realistic and
will create artificial shadow zones because incident
rays with very similar paths may depart from the
interface along very different paths if they intersect
the interface on either side of a point of gradient
discontinuity
 smooth interface

19. Solving the Inverse Step
 In traveltime tomography, the functional g is non-linear because the ray path depends on the
velocity structure.
 an inversion scheme should account for this non-linearity.
 The inversion step, which involves the adjustment of the model parameters m to better satisfy
the observed data dobs through the known relationship d = g(m), can be performed in a
number of ways.
 The three approaches to solving the inversion step that will be considered below are
backprojection, gradient methods and global optimization technique

20. Seismic inversion

21. Seismic inversion

22. Seismic inversion

23. Inversion
methods
Post-stack
Pre-stack
Model
Based
Recursive
Sparse
spike
Coloured
Elastic
Impedance
LMR
Simultaneous
Inversion methods
Stochastic

24. General
Forward
Model for
Inversion

25. Inverse
Model

26. AVO

27. Inverse Model
of The zero-angle model

28. Inverse Model
of The non zero-angle model
 Using the P-wave velocity, we can transform the
offset gathers shown earlier to angle gathers. There
are two ways in which AVO methods extract
reflectivity from angle gathers

29. The Zoeppritz Equations
To explain the amplitude change,
Zoeppritz derived the amplitudes of the
reflected and transmitted waves using
the conservation of stress and
displacement across the layer boundary,
which gives four equations with four
unknowns. Inverting the matrix form of
the Zoeppritz equations gives us the
exact amplitudes as a function of angle:

31. AVO

32. Model
Based
Inversion
32

33. Model
Based
Inversion

34. Model Based Inversion
o Optimally process the seismic data
o Build model from picks and
impedances
o Iteratively update model until output
synthetic matches original seismic
data.

35. Colored
Inversion

36. Colored
Inversion

37. Real Data Test – Inversion Results
ZPZS

39. AI – Vp/Vs
template

40. Rock Property Summary
 From well calibrations, seismic derived attributes can be used to discriminate between the
following rock/fluid classes:
 •Clean Gas Sands Low Pwave Impedance, Low Vp/Vs Ratio
 •Clean Water Sands High Pwave Impedance, Intermediate Vp/Vs Ratio
 •Laminated Gas Sands Reduced Pwave Impedance and Vp/Vs Ratio
 •Shales Increased Pwave Impedance, Intermediate to higher Vp/Vs Ratio

41. Rock Property Summary
•Acoustic Impedance Volume (Product of Velocity and Density) Porosity, Geometry and Lithology
•Shear Impedance Volume
–Lithology, Fluid
•Density Volume
–Fluid type and ‘fizz water’ discriminator
•Vp/Vs Volume or
•Poisson’s Ratio Volume
–Lithology, Fluid type, Net/Gross ratio’s
•Porosity Volume
•N/G and Sw Estimations

42. ZP AND VP /VS

43. Cross
plotting
Vp/Vs
against Zp
using the
log curves:
43This zone should
correspond to gas:

44. Gas Zone from log cross plot

45. Benefits of Inversion
 Lithology and Fluid Discrimination
 •Used for Reservoir Property Prediction
 •Best Tool for Reservoir Characterization
 •Best Method for Optimized Field Development
 •Increased Reflectivity in Shear Volume
 •Calibration to Well Data and Rock Properties
 •Increased Signal Bandwidth
 •Easier to Interpret

46. Final Inversion model