Use of the “shape-of-anomaly” data misfit in

3D inversion by planting anomalous densities

Leonardo Uieda

Valéria C. F. Barbosa

Difference in shape

Scale factor: d i=α g i

Scale factor: d i=α g i

SOA=√∑i=1

N

(α g i−d i)2

Scale factor: d i=α g i

SOA=√∑i=1

N

(α g i−d i)2

minSOA α=∑i=1

N

g i d i

∑i=1

N

g i2

d , g α SOA

Predicted (model)

Observed

Planting anomalous densities

g i (observed)

mesh

seed

d i (predicted)

Choose the best:

φ=√∑i=1

N

(g i−d i)2

min of Γ=φ+μθ

&

compactness

Choose the best:

φ=√∑i=1

N

(g i−d i)2

min of Γ=SOA+μθ

&

Exchange for shape-of-anomaly

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Γ=φ+μθ Γ=SOA+μθ SOASOA

Synthetic tests

SOA

SOA

SOASOA

SOASOA

SOA

SOA

SOASOA

SOA

SOA

SOASOA

Redenção granite

Bouguer anomaly

Outcrop

Oliveira et al.(2008)

Bouguer anomaly

~ 6 km

Oliveira et al.(2008)

Bouguer anomaly

Seed at 3km ~ 6 km

SOA Known outcrop

SOA

Outcrop at wrong place

Known outcrop

SOA

Outcrop at wrong place

~ 9 km

Known outcrop

SOA

SOA

Outcrop at right place

SOA

Outcrop at right place

~ 6 km

5

SOA SOA

5

SOA SOA

6 km

In conclusion

SOA SOA

SOA SOA

SOA SOA

SOA SOA