2d and 3d density block models creation based on isostasy usage

Corr. Member of RAS, Prof. Petr Martyshko1,2

Dr. Igor Ladovskii1

Denis Byzov1

Alexander Tsidaev1,2

1Bulashevich Institute of Geophysics, Yekaterinburg, Russia2Yeltsin Ural Federal University, Yekaterinburg, Russia

2D and 3D Density Block Models Creation Based on Isostasy Usage

REIT'2017: 1st International Workshop on Radio Electronics & Information Technologies

Gravity survey (gravimetry)Field of gravitational force has tension approximately equal to

g = 9.8 m/s2

But this value is not a constant. All the masses around have impacts on the tension value. And the biggest impact is from the masses below the Earth surface level.

So the gravity field is dependent on densities of the Earth rocks.

Interpreting measured gravity field values, one can try to restore possible density distribution under the Earth surface.

0. Background

Image: PBG Ltd.

0. Background

Isostasy is the state of gravitational equilibrium between Earth's crust and mantle such that the crust "floats" at an elevation that depends on its thickness and density.

Definition: Wikipedia, CC BY-SA 3.0Image: Tasa Graphic Arts

Study area of Urals and neighboring regions with positionsof deep seismic sounding profiles

Profiles:

1) Agat-2 2) Globus3) Quartz4) V. Nildino – Kazym5) Rubin-16) Syktyvkarsk7) N. Sosva – Yalutorovsk8) Krasnolelinsk9) Granit – Rubin-210) Polar-Urals transsect

1. Initial data

mGal

Seismic-density model along the “Quartz” profile

1. Initial data

Density and velocity values are interconnected by function (Ladovskii et al., 2013).

Model with homogeneous mantle and observed (violet) and model (red) gravity fields(model created using Mishenkina-Krylov technique)

=9,80665 m/s2 is mean value of gravity acceleration.

∆ 𝑃 (𝑥 , 𝑧 )=𝑃 (𝑥 ,𝑧 )− 𝑃0 (𝑧 )=𝑔𝑎∫𝑧

0

(𝜌 (𝑥 ,𝜁 )− 𝜌0 (𝜁 ) )𝑑𝜁❑

Lithostatic pressure anomalies

The lithostatic anomaly is defined as difference between the lithostatic and hydrostatic pressures on given depth level.

Lithostatic pressure is calculated by values of fitted densities. Hydrostatic pressure is calculated by mean density value on every hypsometric level.

For every depth value the deviation of lithostatic pressure from its mean (hydrostatic) value is calculated.

2. Lithostatic anomalies (2D)

Lithostatic pressure cut along the “Quartz” profile


Lateral variability of ∆P on supposed level of isostatic compenstation (80 km). ΔР pressure amplitude is around 600 bar:

Lithostatic pressure ∆P distribution:kB

ar

Compensating function


To rearrange mantle density to satisfy isostatic equilibrium condition on the level of 80 km we introduced compensating function.

Compensator shows which density value should be added (or subtracted) to the layer between Mohorovicic discontinuity HM and the lower boundary of layer H.

Selected mantle blocks


Densities ofmantle blocks

Lithostaticanomalies

for model withblock mantle

Compensating function

Cut with selected mantle blocks


Zeroes of lithostatic model match with resulting mantle blocks position


3D case

3. Initial model

Anomaly gravity field and tectonic scheme of Urals

3. Initial model

Sysolsk vault (SV), Mezensk syneclise (MC), Komi-Perm vault (KPV), Timan ridge (TR), Izhma-Pechora depression (IPD), Omra-Luza saddle (OLS), PechoraKolvinsk zone (PKZ), Horeyversk basin (HVB), Pre-Urals deflection (PUD), Urals uplift (UU), Near-Urals deflection (NUD), East-Urals uplift (EUU), East-Urals deflection (EUD), Nadym block (NB), Zauralsk uplift (ZU), Hantymansiysk middle uplift (HMU)

mGal

Common method to create tectonic schemes is to analyze the gravity field. But depth information cannot be extracted this way.

Initial 3D density model

Interpolated density model(with map of tectonic structures)

Spatial position of profiles

3. Initial model

The dependence of the initial approximation model average density from the depth

g/cm3

km

1¿ 𝜌𝑚𝑖𝑛 (h )=min𝑥 , 𝑦

𝜌 (𝑥 , 𝑦 , h )

2¿ 𝜌𝑚𝑎𝑥 (h )=max𝑥 ,𝑦

𝜌 (𝑥 , 𝑦 , h )

- average density of the model at the depth h

4. Refined density model

Direct gravity problem

mGal

1

1) 3D density model of the initial approximation

2) Observed gravity field

3) Calculated gravity field of the initial model

4) Difference field

g/cm³

2

3

4


“Upward” continuation process (integral formula):

dxdyhyx

yxghhg ∫∫

23))()((

)0,,(2

),,( 222

z=0

z=-h

z=h

Splitting the field difference on density model layers

),,()4)()((

),,(22

23222 hgdxdy

hyxhyxgh

∫∫

Field at the height (+h) – a known quantity

Field at the depth (-h) – unknown quantity

,)4)()((

),(22

23222 Udxdy

hyxyxuh

∫∫

(𝐾 +𝜶𝐸 )𝑢=𝑈

“Downward” continuation process (integral equation):


Transformation of the field difference on heights with step 1 km

∆ 𝑔 ,mGal

40 km

80 km

0 km

Field of layer below H = 00 km

g[-72; 101]



∆ 𝑔 ,mGal


g[-24; 44]

40 km

80 km

0 km



∆ 𝑔 ,mGal


g[-43; 51]

40 km

80 km

0 km



∆ 𝑔 ,mGal


g[-15; 15]

40 km

80 km

0 km



∆ 𝑔 ,mGal


g[-8; 7]

40 km

80 km

0 km



mGal

g/cm3

Resulting 3D model with fitted densities

Anomaly lithostatic pressure


Gravity anomalies contain integral information on density inhomogeneities for all lithosphere depth levels. Thus, blocks selected by the gravity field could not be split by depth. Moreover, these blocks are usually invisible in horizontal maps of density distribution.

We propose to use integral characteristics: masses of prismatic elements of 3D density grid. For each depth level, masses of prisms located above are calculated and the sum then converted to lithostatic pressure. In lithostatic model the blocks of Earth crust become mode visible and can be traced on different depth levels.

Similarly to 2D case, we introduce anomaly lithostatic pressure as difference between a lithostatic pressure and the hydrostatic one, calculated on given depth.

∆ 𝑃 (𝑥 , 𝑦 , 𝑧 )=𝑃 (𝑥 , 𝑦 ,𝑧 )− 𝑃0 (𝑧 )=𝑔𝑎∫𝑧

0

(𝜌 (𝑥 , 𝑦 , 𝜁 )−𝜌0 (𝜁 ) )𝑑𝜁❑

6. Lithostatic model

Bar

Lithostatic pressure model for study region

Lithostatic anomaly model cut at depth of 10 km


Bar



Bar

Horizontal cuts of density model (left image in each pair) mapped to horizontal cut of the lithostatic model (right image in pair) with overlapped map of tectonic structures.

I – Timan Ridge, II – East Urals Deflection

7. Result

8. Conclusion

• Matching of 3D lithostatic model with density model allowed us to select large deep inhomogeneities in the upper lithosphere.

• Distribution of lithostatic pressure on horizontal cuts qualitatively matches the map of tectonic structures, which was created by potential fields.

• Block structures positions coincides with the deep fault boundaries of collision structures: East boundary of Timan ridge, Pechora-Kolvinsk zone, Near-Urals Deflection, Western edge of Tagil deflection (Main Urals Fault) and zone of East-Urals uplift and East-Urals deflection conjunction.

• Such a separation of continual density model to separate layers and blocks of different organization level allows one to build seismic-gravity model of layers and blocks for the Earth crust in a study region.

Conclusion

9. Literature

Ladovsky, I.V., Martyshko, P.S., Druzhinin, V.S., Byzov, D.D., Tsidaev, A.G., Kolmogorova V.V.: Methods and results of crust and upper mantle volume density modeling for deep structure of the Middle Urals region. Ural Geophysical Messenger. 2(22), 31-45 (2013) [in Russian]

Martyshko, P.S., Ladovskii, I.V., Byzov, D.D.: Solution of the Gravimetric InverseProblem Using Multidimensional Grids. Doklady Earth Sciences. 450, Part 2, 666-671 (2013)

Martyshko, P.S., Ladovskiy, I.V., Byzov, D.D.: Stable methods of interpretation of gravimetric data. Doklady Earth Sciences. 471, Issue 2, 1319{1322 (2016)

Martyshko, P.S., Ladovskiy, I.V., Fedorova, N.V., Byzov, D.D., Tsidaev, A.G.: Theory and methods of complex interpretation of geophysical data. UrO RAN, Ekaterinburg (2016) [in Russian] http://igeoph.net/book.pdf

http://igeoph.net/book.pdf

Thank you for your attention

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2d and 3d density block models creation based on isostasy usage

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