Research Progress on Joint Inversion of Dynamic Geodetic

and Geophysical Data

School of Geodesy and Geomatics, Wuhan University

Xu Caijun

Contents

Trend of Joint Inversion5

Determination of Functional Model and Effective Algorithm

2

Determination of Relative Weight and Refining Stochastic Model

3

Application to Earthquake Study4

Meanings of Geodetic Inversion1

Forward and Inversion Problems

Geophysical Inversion

1 、 Meanings of Geodetic Inversion

Predict the results according to the general principles (model) with related conditions (initial conditions and boundary conditions).

Reconstruct the mathematical and physical models according to the observations through the appropriate methods.

A branch of geophysics that speculate the spatial variation of the physical state and structure of Earth's interior media using the observed physical phenomena on surface.

Joint Inversion of Geodesy and GeophysicsJoint inversion of geophysical geodetic inversion or geophysical geodetic.

An inverse problem to solve both the kinetic parameters and the physical parameters of the medium, covers the most basic issues of geophysics and geodesy.

Geodetic Inversion Application of high-precision and high-resolution geodetic measurements data for the geophysical problems. Geodetic inversion is the core issue of the geodetic disciplines in-depth study of earth science.

According to the geodetic observations, geophysical and geological data, obtain the geodynamic models and parameters from the inversion using the prior models. Or study the movement of active faults and blocks from the inversion of surface observations to explore the relations between crustal movement and earthquake and evaluate seismic and geological hazards.

Initiation and development of geodetic and geophysical inversion in China

Since the 1970s, appearance of concept of geodetic inversion and its wide applications

In the 1950s and 1960s, beginning of geodetic data involved in the geophysical inversion

In 1957and1958, Japanese scientists K. Kasahara studied natural properties of seismic origin and physical conditions of fault using seismology and geodesy data. Byerly, P. (1958) calculate the seismic energy using geodetic data.

M. Matsu’ura (1977) discussed the use of geodetic data in inversing fault, clearly put forward the concept of geodetic inversion, discussed in detail the mathematical models and formulas of geodetic inversion, and researched the 1927 Tango earthquake. Okada(1985,1992) and Okubo(1992) derived the classic formula of the surface displacement and gravity changes caused by underground fault based on dislocation theory, which have been widely applied in the coseismic deformation modeling and inversion study, negative dislocation theory research, as well as non-seismic deformation.

In 1975, Chen YT studied the source process of the 1966 Xingtai earthquake based ground deformation (horizontal and vertical displacement field), and in 1979, modeled the 1976 Tangshan earthquake with geodetic data.Zhao SR (1991) developed a theory of dynamic geodetic inversion and physical interpretation starting from the basic equations of solid mechanics.

The development process

Inverse Method

Inverse Model

Data Source

Single Geodetic data

Many kinds of geodetic data, as well as many types of (geodetic, geophysical, geological, etc.) observational data

Continuous

Discrete

Linear inversion

Non-linear inversion

With the extensive application of GNSS, of InSAR and satellite gravity technology and other space geodetic techniques in the geophysics, the interdisciplinary scope is greatly expanded and we can explore the dynamic processes of the earth interior, such as:

Plate motion

Tectonic

Earthquake

Earth Rotation

Glacier

Sea-level changes

Mantle convection etc

Long time series of dynamic geodetic data provides new means for geodynamic research. The joint inversion of dynamic geodetic data and geophysical data has become the hot and advanced topics of present-day geodesy.

2 、 Determination of Functional Model and Effective Algorithm

Linear model of joint inversion

Non-linear model of joint inversion

2 2 2

1 2

Tgeodesy geodesy geodesy

geophysics geophysics geophysics

simu simu prior

obs obs obs

obs obs obs

D P DWRSS

D P D

M M M

20 0( )

1

geodesy geodesygeodesy

geophysics geophysicsgeophysics

prior prior

d dG

d dGM

or

M MI

Linear inverse method

Non-linear inverse method

Simple, mature, high-speed, and accuracy evaluation

Abnormal coefficient matrix

Regularization method, singular value decomposition method, ridge estimation et al.

Simulated annealing algorithm, Parallel simulated annealing inversion methods, fast inversion method of simulated annealing, genetic algorithm, the adaptive hybrid global inversion algorithm, the new method of nonlinear programming, two-phase non-linear inversion method, the interval algorithm et al.

Extended Network Inversion Filter （ ENIF）

From linear system to non-linear system

Comparison with NIF method, ENIF method significantly improves spatial and temporal resolution of state space parameters and has lower computational cost.

State space parameters and smoothing factors directly resolved

Principal component analysis-based inversion method （ PCAIM）

Centralized data

Principal component analysis

Selection of number of useful components

Determination of il

Time evolution of geophysical process

3 、 Determination of Relative Weight and Refining Stochastic Model

Equally weight

Weighted by a priori variance of observed datasets

Weighted by trial and error procedure

Refine Stochastic model by Variance Component Estimation

Ti i iV PV

1 1

ˆm m m mS W

2

11 12 1 1 1 1

2

22 2 2 2 2 2

1 1

2

1

ˆ, ,

T

m o

T

m o

m m m m

T

mm om m m m

s s s V PV

s s V PVS W

s V PV

i 2 1

o ii

cˆˆ P

P

2 2 2

o o o1 2 iˆ ˆ ˆ

1 1 1v G s d

2 2 2v G s d

n n nv G s d

………

P1 P2 ……. Pn

2

1o 2

2o 2

on…….

1

2

3

4

If step 4 is yes, stop iteration; or re-run steps 2 and 3.

Steps of Variance Component Estimation

Geodynamic mechanism?

Which information do we want to know when an earthquake occur?

4 、 Application to Earthquake Study

Time and rupture process? Where?

The modern observation techniques for seismic activity monitoring such as seismic waves, GPS, InSAR, Gravity, Strong motion instrument and so on.

Satellite Gravity observation

Surface Gravity observation

台湾地区布设的全球最密集的地动仪

Graphic illustration of dislocation model for the seismic research

Difficulties of seismic inversion and the advantages of the joint inversion

Because of the high degree of complexity and specificity of the active faults and seismic activity , for any inversion problem, there maybe not only one solution. And single observation data can not be effectively constrain on model for seismic parameters inversion;

For the earthquake source rupture process study, due to different data, different fault model and different algorithm that can lead to different inversion results, so we need to establish a joint inverse model.

Jointly using multiple observation data to inverse kinematic rupture model has such advantages:

undergoing mutual verification and error data removed, and then obtaining more precise measurements;

increase the model's a priori information to improve the robustness of model solutions;

obtain a higher resolution of data and model.

Methods of determing weight scalingfactors for geodetic-geophysical joint inversion,

（ 2009, J.Geodyn.）

Our group’s working for the joint inversion

Contemporary Crustal Deformation in Sichuan-Yunnan Region from GPS and Gravity

Data (2009, Geomatics and Information Science of Wuhan University)

Our group’s working for the joint inversion

Multi-track SAR data and GPS observation for joint inversion in Wenchuan earthquake, develop an method to determine the weighting factor in inversion model

Our group’s working for the joint inversion

Our group’s working for the joint inversion

A preliminarycombined inversion using multi-observations

Examples and processing of international seismic joint inversion

From this article we can know the author combine the geodesy observation and broadband teleseismic data to determine the fault parameters, inverse the slip distribution depend on time the rupture process

Examples and processing of international seismic joint inversion

Compare the fault parameter inverse by teleseismic waveform with InSAR, so as to obtain an more reasonable geophysics result!

Examples and processing of international seismic joint inversion

The inversion results obtained using different means of observation there are differences, mainly due to the different spatial and temporal resolution data acquisition, the obtained deformation is different! Through joint inversion people can better explain the different result from the different data sources (This article use the equal weight to joint inversion)

Examples and processing of international seismic joint inversion

Use the geological and seismic waves as a priori information, we can effectively constrained inverse the rupture of the large earthquake sequence by InSAR observations.Joint inversion can have a strong constrain for inversing a complexity of the multi-branch fault system ruptured!

Examples and processing of international seismic joint inversion

5 、 Trend of Joint Inversion with Danaymic Geodetic and Geophysical Data

1 、 Data source fusing technology and extraction of the time-varying deformation field

     The integration of the data source with different spatial and temporal resolution; the integration of geodetic data with different physical properties; the integration of geophysical data and geodetic data; inversion with constraint by adding geological data;     Geodetic observations of surface deformation typically contain the impact of non-tectonic deformation. One can use a new timing analysis methods, such as Principal component analysis-based inversion method (PCAIM), Extended Network Inversion Filter (ENIF), and the Kalman filter, to extract tectonic deformation signals from a long time series, high-noise observations.

2 、 New mode of joint inverse model

Functional model：

If the a priori information is not accurate, or mastering the law of the systematic errors or model errors is not through, or system error and model error are complex, semi-parametric method and the total least squares method can take into account the observational error and model error. Thus, one can establish inversion function model using semi-parametric method and the total least squares method.

During the inversion of the active faults, seismic parameters and rupture process, for fault geometry model, and the underground medium properties, etc., one can create the inversion model with equality constraints or inequality constraints (probability inequality).

Stochastic model: To fix the appropriately relative weight among different types, different resolution observations, one can use the following technologies:

a) Helmert variance-covariance component estimation method is used to determine the weight matrix of the various types of observations, and refine the stochastic model

b) When study active faults, seismic parameters and rupture process, the smoothing constraint can be considered as a virtual observations and the rigorous theory of Helmert variance component estimation method can be used to determine the relative weights. Based on these, one can use the Helmert variance-covariance component estimation Bayesian approach to do the following inversion.

3 、 Development of effective global inversion algorithm

Dynamic geodesy and geophysical joint inversion is a nonlinear optimization process, involving many types of data, a number of model parameters, multiple extreme values , multiple constraints, multiple priori information and non-continuous features.

Development of effective global inversion algorithm: Combinational algorithm

4 Develop the dynamic geodesy geophysical data joint inversion software platform, carry out the earth geophysical data dynamic measurement joint inversion application research。

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