Leonardo Uieda
August 15, 2011
360

# 3D gravity inversion by planting anomalous densities

August 15, 2011

## Transcript

1. ### 3D gravity inversion by planting anomalous densities Leonardo Uieda and

Valéria C. F. Barbosa August, 2011 Observatório Nacional

Outline
6. ### Inverse Problem Planting Algorithm Synthetic Data Forward Problem Inspired by

René (1986) Outline
7. ### Inverse Problem Planting Algorithm Synthetic Data Real Data Forward Problem

Inspired by René (1986) Outline

11. ### Observations of g z Group in a vector: g= [g

1 g 2 ⋮ g N ] N×1 = observed data g Surface of the Earth

14. ### = observed data g Assume caused by anomalous sources Δρ

Density contrast =

model
18. ### Right rectangular prisms Parametrize the gravitational effect Discretize into M

elements Homogeneous density contrast jth element Linearize (Nagy et al., 2000) Interpretative model p j
19. ### Arrange M density contrasts in a vector: Parametrize the gravitational

effect Discretize into M elements p= [p 1 p 2 ⋮ p M ] M×1 Parameter vector Linearize Interpretative model
20. ### Discretize into M elements Parametrize the gravitational effect p j

=Δρ Prisms with not shown p j =0
21. ### Discretize into M elements Parametrize the gravitational effect g≈d Prisms

with not shown p j =0 p j =Δρ
22. ### Discretize into M elements Parametrize the gravitational effect g≈d Predicted

data Prisms with not shown p j =0 p j =Δρ
23. ### Discretize into M elements Parametrize the gravitational effect Gravitational effect

is linear d=∑ j=1 M p j a j g≈d Predicted data Prisms with not shown p j =0 p j =Δρ
24. ### Discretize into M elements Parametrize the gravitational effect Gravitational effect

is linear d=∑ j=1 M p j a j Density contrast of jth prism g≈d Predicted data Prisms with not shown p j =0 p j =Δρ
25. ### Discretize into M elements Parametrize the gravitational effect Gravitational effect

is linear d=∑ j=1 M p j a j g≈d Predicted data Effect of prism with unit density Prisms with not shown p j =0 p j =Δρ
26. ### Discretize into M elements Parametrize the gravitational effect Gravitational effect

is linear g≈d Predicted data d=∑ j=1 M p j a j =A p Prisms with not shown p j =0 p j =Δρ
27. ### Discretize into M elements Parametrize the gravitational effect Gravitational effect

is linear g≈d Predicted data Parameter vector d=∑ j=1 M p j a j =A p Prisms with not shown p j =0 p j =Δρ
28. ### Discretize into M elements Parametrize the gravitational effect Gravitational effect

is linear g≈d Predicted data Jacobian (sensitivity) matrix d=∑ j=1 M p j a j =A p Prisms with not shown p j =0 p j =Δρ
29. ### Discretize into M elements Parametrize the gravitational effect Gravitational effect

is linear g≈d Predicted data Column vector of A d=∑ j=1 M p j a j =A p Prisms with not shown p j =0 p j =Δρ

a j

38. ### Minimize difference between and g d r=g−d Residual vector Data­misfit

function: ϕ( p)=∥r∥2 = (∑ i=1 N (g i −d i )2 )1 2
39. ### Minimize difference between and g d r=g−d Residual vector Data­misfit

function: ϕ( p)=∥r∥2 = (∑ i=1 N (g i −d i )2 )1 2 ℓ2­norm of r Least­squares fit

constraints

46. ### Constraints: 1. Compact no holes inside 2. Concentrated around “seeds”

Similar to René (1986)
47. ### Constraints: 1. Compact no holes inside 2. Concentrated around “seeds”

• User­specified prisms Similar to René (1986)
48. ### Constraints: 1. Compact no holes inside 2. Concentrated around “seeds”

• User­specified prisms • Given density contrasts ρs Similar to René (1986)
49. ### Constraints: 1. Compact no holes inside 2. Concentrated around “seeds”

• User­specified prisms • Given density contrasts • Any n° of ≠ density contrasts ρs Similar to René (1986) Not like René (1986)
50. ### Constraints: 1. Compact no holes inside 2. Concentrated around “seeds”

• User­specified prisms • Given density contrasts 3. Only • Any n° of ≠ density contrasts or p j =0 p j =ρs ρs Similar to René (1986) Not like René (1986)
51. ### Constraints: 1. Compact no holes inside 2. Concentrated around “seeds”

• User­specified prisms • Given density contrasts 3. Only • Any n° of ≠ density contrasts or p j =0 p j =ρs ρs 4. of closest seed p j =ρs Similar to René (1986) Not like René (1986)
52. ### ill­posed problem well­posed problem constraints ϕ( p)=∥r∥2 = (∑ i=1

N (g i −d i )2 )1 2 Minimize data misfit Minimize goal function Γ( p)=ϕ( p)+μθ( p)
53. ### ill­posed problem well­posed problem constraints ϕ( p)=∥r∥2 = (∑ i=1

N (g i −d i )2 )1 2 Minimize data misfit Minimize goal function Γ( p)=ϕ( p)+μθ( p) Regularizing parameter
54. ### ill­posed problem well­posed problem constraints ϕ( p)=∥r∥2 = (∑ i=1

N (g i −d i )2 )1 2 Minimize data misfit Minimize goal function Γ( p)=ϕ( p)+μθ( p) Regularizing function
55. ### ill­posed problem well­posed problem constraints ϕ( p)=∥r∥2 = (∑ i=1

N (g i −d i )2 )1 2 Minimize data misfit Minimize goal function Γ( p)=ϕ( p)+μθ( p) Regularizing function μ = tradeoff between fit and regularization
56. ### Regularization: θ( p)=∑ j=1 M p j p j +ϵ

l j β Γ( p)=ϕ( p)+μθ( p)
57. ### Regularization: θ( p)=∑ j=1 M p j p j +ϵ

l j β Γ( p)=ϕ( p)+μθ( p) Similar to Silva Dias et al. (2009)
58. ### Regularization: θ( p)=∑ j=1 M p j p j +ϵ

l j β Γ( p)=ϕ( p)+μθ( p) ϵ = avoid singularity l j = distance between jth prism and seed β = how much compactness (3 to 7) Similar to Silva Dias et al. (2009)
59. ### Regularization: θ( p)=∑ j=1 M p j p j +ϵ

l j β Γ( p)=ϕ( p)+μθ( p) For p j ≠0:
60. ### Regularization: θ( p)=∑ j=1 M p j p j +ϵ

l j β Γ( p)=ϕ( p)+μθ( p) distance from seeds For p j ≠0:
61. ### Regularization: θ( p)=∑ j=1 M p j p j +ϵ

l j β Γ( p)=ϕ( p)+μθ( p) distance from seeds regularizing function For p j ≠0:
62. ### Regularization: θ( p)=∑ j=1 M p j p j +ϵ

l j β Γ( p)=ϕ( p)+μθ( p) distance from seeds regularizing function Imposes: • Compactness • Concentration around seeds For p j ≠0:
63. ### Constraints: 1. Compact 2. Concentrated around “seeds” 3. Only or

p j =0 p j =Δρs 4. of closest seed p j =Δρs Regularization
64. ### Constraints: 1. Compact 2. Concentrated around “seeds” 3. Only or

p j =0 p j =Δρs 4. of closest seed p j =Δρs Regularization Algorithm

69. ### Based on René (1986) Start with seeds known density contrast

& position Overview:
70. ### Based on René (1986) Start with seeds known density contrast

& position All other parameters set to 0 Overview:
71. ### Based on René (1986) Start with seeds All other parameters

set to 0 Iteratively grow Overview: known density contrast & position
72. ### Based on René (1986) Start with seeds All other parameters

set to 0 Iteratively grow add neighbor of seed Overview: known density contrast & position
73. ### Based on René (1986) Start with seeds All other parameters

set to 0 Iteratively grow add neighbor of seed accretion Overview: known density contrast & position
74. ### Based on René (1986) Start with seeds All other parameters

set to 0 Iteratively grow add neighbor of seed accretion Controlled by goal function and data misfit function Overview: Γ( p)=ϕ( p)+μθ( p) ϕ( p)=∥r∥2 = (∑ i=1 N (g i −d i )2 )1 2 known density contrast & position

78. ### Algorithm: Define interpretative model All parameters zero g = observed

data Interpretative model
79. ### Algorithm: seeds N S Define interpretative model All parameters zero

g = observed data Interpretative model
80. ### Algorithm: seeds N S Define interpretative model All parameters zero

Include seeds Prisms with not shown p j =0 Seeds
81. ### Algorithm: seeds N S Define interpretative model All parameters zero

Include seeds Compute initial residuals r(0)=g−d(0) Prisms with not shown p j =0
82. ### Algorithm: Residual vector seeds N S Define interpretative model All

parameters zero Include seeds Compute initial residuals r(0)=g−d(0) Prisms with not shown p j =0
83. ### Algorithm: Observed data seeds N S Define interpretative model All

parameters zero Include seeds Compute initial residuals r(0)=g−d(0) g = observed data Prisms with not shown p j =0
84. ### Algorithm: Predicted by seeds seeds N S Define interpretative model

All parameters zero Include seeds Compute initial residuals r(0)=g−d(0) g = observed data d = predicted data Prisms with not shown p j =0
85. ### Algorithm: seeds N S Define interpretative model All parameters zero

Include seeds Compute initial residuals r(0)=g−d(0) g = observed data d=∑ j=0 M p j a j d = predicted data Prisms with not shown p j =0
86. ### Algorithm: seeds N S Define interpretative model All parameters zero

Include seeds Compute initial residuals r(0)=g−d(0) g = observed data d=∑ j=0 M p j a j Many=0 d = predicted data Prisms with not shown p j =0
87. ### Algorithm: seeds N S Define interpretative model All parameters zero

Include seeds Compute initial residuals r(0)=g−d(0) g = observed data d=∑ s=1 N S ρ s a j S d = predicted data Prisms with not shown p j =0
88. ### Algorithm: seeds N S Define interpretative model All parameters zero

Include seeds Compute initial residuals r(0)=g− (∑ s=1 N S ρ s a j S ) Prisms with not shown g = observed data d = predicted data p j =0
89. ### Algorithm: Density contrast of sth seed seeds N S Define

interpretative model All parameters zero Include seeds Compute initial residuals r(0)=g− (∑ s=1 N S ρ s a j S ) Prisms with not shown g = observed data d = predicted data p j =0
90. ### seeds N S Algorithm: Define interpretative model All parameters zero

Include seeds Compute initial residuals r(0)=g− (∑ s=1 N S ρ s a j S ) Column vector of A Prisms with not shown g = observed data d = predicted data p j =0
91. ### seeds N S Algorithm: Define interpretative model All parameters zero

Include seeds Compute initial residuals r(0)=g− (∑ s=1 N S ρ s a j S ) Prisms with not shown g = observed data d = predicted data Neighbors Find neighbors of seeds p j =0

p j =0
94. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: p j =0
95. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit ϕ( p)=∥r∥ 2 p j =0
96. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =0
97. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) j = chosen j p j =0
98. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =ρ s j = chosen j p j =0 (New elements)
99. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =ρ s j = chosen j p j =0 (New elements) new predicted data
100. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =ρ s j = chosen Update residuals r(new)=g−d(new) p j =0 (New elements) new predicted data j
101. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =ρ s j = chosen Update residuals r(new)=g−d(new) p j =0 (New elements) new predicted data j d(old)+ effect of j
102. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =ρ s j = chosen Update residuals r(new)=g−d(new) p j =0 (New elements) new predicted data j d(old)+ effect of j ∑ s=1 N S ρs a j S p j a j +
103. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =ρ s j = chosen Update residuals r(new)=g−d(new) p j =0 (New elements) new predicted data j d(old)+ effect of j ∑ s=1 N S ρs a j S p j a j +
104. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =ρ s j = chosen Update residuals r(new)=g−∑ s=1 N S ρs a j S − p j a j p j =0 (New elements) new predicted data j
105. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =ρ s j = chosen Update residuals r(new)=g−∑ s=1 N S ρs a j S − p j a j p j =0 (New elements) new predicted data j { r(0)
106. ### Prisms with not shown Growth: Try accretion to sth seed:

Choose neighbor: 1. Reduce data misfit 2. Smallest goal function ϕ( p)=∥r∥ 2 Γ( p)=ϕ( p)+μθ( p) p j =ρ s j = chosen Update residuals p j =0 (New elements) new predicted data j r(new)=r(old )− p j a j
107. ### Prisms with not shown Growth: None found = no accretion

Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: p j =0
108. ### Prisms with not shown Growth: None found = no accretion

Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: Variable sizes p j =0
109. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: p j =0
110. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: p j =0 (New elements) j
111. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0
112. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0
113. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0 (New elements) j
114. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0 (New elements) j
115. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0 j
116. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0 j
117. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0 j
118. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0 j
119. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0 j
120. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0 j
121. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No p j =0
122. ### Prisms with not shown Growth: None found = no accretion

N S Try accretion to sth seed: 1. Reduce data misfit 2. Smallest goal function p j =ρ s j = chosen Update residuals r(new)=r(old )− p j a j Choose neighbor: At least one seed grow? Yes No Done! p j =0
123. ### Advantages: Compact & non­smooth Any number of sources Any number

of different density contrasts No large equation system Search limited to neighbors
124. ### Remember equations: r(0)=g− (∑ s=1 N S ρs a j

S ) r(new)=r(old)− p j a j Initial residual Update residual vector
125. ### Remember equations: r(0)=g− (∑ s=1 N S ρ s a

j S ) r(new)=r(old)− p j a j Initial residual Update residual vector No matrix multiplication (only vector +)
126. ### No matrix multiplication (only vector +) Remember equations: r(0)=g− (∑

s=1 N S ρ s a j S ) r(new)=r(old)− p j a j Initial residual Update residual vector Only need some columns of A
127. ### No matrix multiplication (only vector +) Remember equations: r(0)=g− (∑

s=1 N S ρ s a j S ) r(new)=r(old)− p j a j Initial residual Update residual vector Only need some columns of A Calculate only when needed
128. ### No matrix multiplication (only vector +) Remember equations: r(0)=g− (∑

s=1 N S ρ s a j S ) r(new)=r(old)− p j a j Initial residual Update residual vector Only need some columns of A Calculate only when needed & delete after update
129. ### No matrix multiplication (only vector +) Remember equations: r(0)=g− (∑

s=1 N S ρ s a j S ) r(new)=r(old)− p j a j Initial residual Update residual vector Only need some columns of A Calculate only when needed Lazy evaluation & delete after update
130. ### Advantages: Compact & non­smooth Any number of sources Any number

of different density contrasts No large equation system Search limited to neighbors
131. ### Advantages: Compact & non­smooth Any number of sources Any number

of different density contrasts No large equation system Search limited to neighbors No matrix multiplication (only vector +) Lazy evaluation of Jacobian
132. ### Advantages: Compact & non­smooth Any number of sources Any number

of different density contrasts No large equation system Search limited to neighbors No matrix multiplication (only vector +) Lazy evaluation of Jacobian Fast inversion + low memory usage

km

X 1 km

1 km X 1 km
137. ### • Sources = 1 km X 1 km X 1

km Depth=0.8 km
138. ### • Sources = 1 km X 1 km X 1

km Depth=1.6 km Depth=0.8 km
139. ### • Sources = 1 km X 1 km X 1

km • Data set = 375 observations Depth=1.6 km Depth=0.8 km
140. ### • Sources = 1 km X 1 km X 1

km • Area = 5 km X 3 km • Data set = 375 observations Depth=1.6 km Depth=0.8 km
141. ### • 0.05 mGal Gaussian noise • Sources = 1 km

X 1 km X 1 km • Area = 5 km X 3 km • Data set = 375 observations Depth=1.6 km Depth=0.8 km
142. ### • Interpretative model = 151,875 prisms • Prisms = 66.7

m X 66.7 m X 66.7 m

145. ### • Used 2 seeds • With corresponding density contrasts •

Placed in center of sources
146. ### Δρ=0.5 g/cm3 • Used 2 seeds • With corresponding density

contrasts • Placed in center of sources
147. ### Δρ=1.0 g/cm3 Δρ=0.5 g/cm3 • Used 2 seeds • With

corresponding density contrasts • Placed in center of sources

150. ### Inversion result • compact • concentrated around seeds • recover

correct geometry of sources
151. ### Predicted data Inversion result • compact • concentrated around seeds

• recover correct geometry of sources
152. ### Predicted data Observed data Inversion result • compact • concentrated

around seeds • recover correct geometry of sources
153. ### Predicted data Observed data Inversion result • compact • concentrated

around seeds • fits observations • recover correct geometry of sources
154. ### Predicted data Observed data On laptop with 2.0 GHz •

375 data • 151,875 prisms • Total time≈4.4 min

158. ### Cana Brava complex (CBC) & Palmeirópolis sequence (PVSS) After Carminatti

et al. (2003)
159. ### Cana Brava complex (CBC) & Palmeirópolis sequence (PVSS) • Outcropping

• North of Goiás • Tocantins Province • Amazonian & São Francisco cratons After Carminatti et al. (2003)
160. ### Cana Brava complex (CBC) & Palmeirópolis sequence (PVSS) Gravimetric data:

• 132 observations • Residual Bouguer • Max 45 mGal After Carminatti et al. (2003)
161. ### Cana Brava complex (CBC) & Palmeirópolis sequence (PVSS) Previous interpretation:

After Carminatti et al. (2003) • Carminatti et al. (2003) • PVSS • CVC • Max depth Δρ=0.27 g/cm3 Δρ=0.39g/cm3 ≈6 km
162. ### Cana Brava complex (CBC) & Palmeirópolis sequence (PVSS) Previous interpretation:

After Carminatti et al. (2003) • Carminatti et al. (2003) • PVSS • CVC • Max depth Δρ=0.27 g/cm3 Δρ=0.39g/cm3 ≈6 km Test this hypothesis
163. ### Assign seeds Green: z=0 km Δρ=0.27g/cm3 Blue: z=2 km Δρ=0.27g/cm3

Red: z=0 km Δρ=0.39 g/cm3 Total = 269 Assign seeds
164. ### Interpretative model Size: 120 km X 50 km X 11

km 480,000 prisms Prism size: 500 m X 500 m X 575 m

174. ### Inversion result ≈6km Max depth Agree with previous interpretation Compact

Fits observations
175. ### Inversion result On laptop with 2.0 GHz • 132 data

• 480,00 prisms • Total time≈3.75 min

177. ### • New 3D gravity inversion • Multiple sources • Interfering

gravitational effects • Abrupt density­contrast distribution • No matrix multiplication • No need to solve large linear systems • Ideal for: ore bodies, intrusions, salt domes, etc Conclusions
178. ### • Developed for gravity gradients • Presented at EAGE 2011

preliminary results • To be presented at SEG 2011: • Final results • Robust method to handle non­targeted sources Previous and future work