Group A Wei Wang & Yongfei Wang

Oct. 28 2013

Modeling marine Magnetic anomalies

o  Background o  Basic theory for forward and inverse

problem o  Numerical results and inversion o  Conclusion

Outline

In the late 1950's, scientists mapped the present-day magnetic field generated by rocks on the floor of the Pacific Ocean. The volcanic rocks which make up the sea floor have magnetization because, as they cool, magnetic minerals within the rock align to the Earth's magnetic field. The intensity of the magnetic field they measured was very different from the intensity they had calculated.

Background

Figure-1 Oceanic structure Figure-2 Magnetic anomalies distribution and signals (http://volcano.oregonstate.edu/)

Sandwell,2001

Basic theory to calculate magnetic anomalies To calculate the anomalous scalar field on the sea surface due to thin magnetic stripes on the seafloor, we go back Poisson’s equation relating magnetic field to magnetization. ΔB = −∇U∇2U = 0∇2U = µ0∇•M

We define a scalar potential U and a magnetization vector M. The magnetic anomaly ΔB is the negative gradient of the potential. The potential satisfies Laplace’s equation above the source layer and is satisfies Poisson’s equation within the source layer.

Sandwell,2001

•  Use the following equation relating the fourier transform of the magnetic anomaly to the fourier transform of the magnetic timescale.

•  This earth filter attenuates both long and short wavelengths so it acts like a band-pass filter. In the space domain it modifies the shape of the square-wave reversal pattern as sketched in the following diagram.

Sandwell,2001

Numerical Results 1) Earth Filter

Sandwell, 2001

•  2). Skewness function:

•  Periodic function •  Different skewness values

•  3). Observed paleo-magnetic field

•  Symmetric pattern •  Skewness

•  4). Grid Search Method: •  Method:

– Separate the parameter domain into to grids – Minimum value of misfit function

•  Assumption: – Speading rate kept the same – Skewness kept the same

•  Three parameters: – Mean crust thickness: 1-9 km

•  Not sensitive, set to 3 km – Skewness: -180 – 180 degree

•  Grid 10 degree – Spreading rate: 30 – 70 km/my

•  Grid 2 km/my

•  5). Misfit function

•  a). Difference between observed and synthetic paleo-magnetic field.

•  b). Emphersize the phase difference to fit the polarity misfit.

L. Zhao & D. Helmberger 1993

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•  Misfit function value map

•  Best Fit Solution: –  Misfit function: 0.326 –  Skewness: -40 degree –  Spreading rate: 46 km/my

•  Repeat the experiment with half time range

•  Misfit function value map

•  Best Fit Solution: –  Misfit function: 0.62 ( almost double ) –  Skewness: 0 degree ( vary with time ) –  Spreading rate: 46 km/my ( not vary with time )

•  1. The synthetic and observation fit well within 10 my and misfit after 10 my

•  2. Mean crust thickness: 3 km (no constraint)

•  3. Spreading rate is 46 km/my •  4. Skewness is -40 degree,

– not located above the polarity

Conclusion

Discussion •  1. The two assumptions:

– The speading rate may be change a little ? – The skewness changes a lot?

•  2. Noise in data: – constrain the accuracy – constrain the meshes of grid search

•  3. Future-work – Change the skewness with time for better

accuracy