Geodetically Accurate InSAR Data Processor for Time Series Analysis

Howard Zebker, Piyush Shanker, Cody Wortham, Scott Hensley

Stanford University and Jet Propulsion Laboratory

Modern applications need better geodetic accuracy

• InSAR and time series methods (PS, SBAS) require precise SLC alignment from a variety of orbits

• Merging SAR data with other types needs geolocated and orthorectified products

• Processing many scenes (typically dozens) of one area needs to be efficient and on the desktop

Need for new processor

• Existing processing packages largely geodetically inaccurate

• Pixels placed at wrong place

• Lots of resampling to find offsets, and this is where many processors fail

• Now have precise orbits

• Multicore processors have untapped cycles we can use to speed up processing time

Approach

• Use precise orbits to find exact (~10 cm error) satellite position

• Choose a reference orbit for multiple scenes so images are nearly aligned – small offsets

• Reference orbit not physically realizable without constant acceleration, so it’s “virtual”

• Use motion compensation method to make spacecraft “fly” on chosen trajectory

• Be careful to keep geometrical info throughout

Definitions for orbital geometry

Reference orbit

Orbit track projected on reference sphere

Coordinate origin at center of sphere with local Earth radius of curvature

Point to be imaged

Instantaneous squint angle

Remember the basics

Phase and range relations

Doppler relations

Focus and position equations in our geometry

SCH coordinate system

rc – local radius of curvature, not Earth radius

s – along track distanceon local sphere from reference point

c – across-track distance on local sphere

h – height above local sphere

Geometry for motion compensation distance and phase

Actual satellite positionSatellite position on reference orbit at same squint direction

(Figure is projection of imaging geometry onto the reference sphere)

Finding the position on the reference orbit for an actual spacecraft location

Motion compensation distance calculation

Motion compensation baseline is difference between actual range r’ and reference orbit range r

Motion compensation algorithmDerivation of reference distance r:

Mocomp distance and phase corrections:

Phase history for mocomped scatterer

Compare phase histories for ract(t) and r(t)

Focus corrections

Quadratic phase correction from processing at wrong distance:

Frequency domain phase term from range-varying motion compensation phase:

Topographic correction

• Processor computes SLCs assuming perfectly spherical Earth

• No easy closed form solution for position so use iterative method to find pixel location in 3-space

• Apply phase correction based on pixel elevation

Iterative topography correction

Topographic phase correction:

Impulse response

Impulse resolution: 5.3 m range, 4.0 m azimuth

Figure for mocompbaseline of 1500 m(InSAR baseline 3km)

Single look complex image of SFO

Geodetic accuracy – Pinon Flat Corner Reflector Locations

Latitude Longitude Latitude LongitudeMeasurement (deg) (deg) error (m) error (m) Reflector aligned with ascending orbit InSAR location, 33.61233 -116.4570 9 -18unregistered image

InSAR location, 33.61215 -116.4567 -11 9registered image

Ground GPS 33.61225 -116.4568 -- --survey Reflectors aligned with descending orbit InSAR location, 33.61215 -116.4579 -11 0unregistered image

InSAR location, 33.61213 -116.4577 -13 18registered image

Ground GPS 33.61225 -116.4579 -- --Survey

InSAR location, 33.60729 -116.4517 -9 9unregistered image

InSAR location, 33.60727 -116.4516 -11 18registered image

Ground GPS 33.60737 -116.4518 -- --survey

Geodetic accuracy – Image offsets from SRTM DEM

Range offset Azimuth offset Additional stretch

Scene at center (m) at center (m) Range (m) Azimuth (m)

Ventura -15.8 18.2 9.4 15.2

Hawaii -21.5 24.0 14.1 25.4

Iceland 2.0 2.9 44.0 29.4

Ventura, CA – Atmospheric phases

Hawaii – deformation plus atmosphere

Iceland – significant ionospheric artifact

Correlation images

Ventura Hawaii Iceland

Computational efficiency

• Implemented on multicore desktop using F90 and Python scripting

• Computational modules parallelized with OpenMP

• Typical ALOS interferogram ~2-4 minutes

• Working with JPL to produce a package to be distributed to community

• At present we use a standalone version compiled under *nix

Summary

• InSAR and time series analysis requires precise image pixel locations

• Imprecise locations make processing slow and unreliable

• With precise orbits, motion compensation, and particular geometry processor equations are fairly simple and efficient to compute

• Accuracies of 10 m easy to achieve, probably 1 m with further development