Zelt, C.A., and Zelt, B.C. 1995. Comparison of 2D and 3D inversion of wide-angle traveltime data in the presence of 3D structure. EOS, 76: 386.

Comparison of 2D and 3D Inversion of Wide-Angle Traveltime Data in the Presence of 3D Structure

Colin Zelt

Department of Geology and Geophysics

Rice University, Houston, Texas

Barry Zelt

Geotechnology Research Institute

Houston Advanced Research Center

The Woodlands, Texas




Presented at the 1995 Fall meeting of the AGU, San Francisco


INTRODUCTION

There are two reasons for performing 3D seismic experiments:

1. to image a 3D volume

2. to image a region or feature that cannot be "properly" imaged with 2D data (or a network of 2D data)

This poster considers the latter point in the case of crustal-scale velocity imaging using wide-angle traveltime data. Specifically, we consider whether the following statement can ever be justified:

"A 3D experiment is necessary because out-of- plane effects will significantly distort or degrade the results of any 2D experiment"

To address this, we have:

1. calculated noise-free synthetic traveltime data for 3D models which produce a large (but realistic) amount of out-of-plane ray bending for (1) a typical 2D crustal geometry and (2) various 3D geometries used in recent crustal experiments

2. performed 2D and 3D inversions and compared the 2D results with cross-sections through the 3D models

We also consider:

1. how the 3D geometries compare in their ability to produce an accurate image in the presence of strong 3D variations

2. how a simultaneous inversion of a network of 2D data compares to the results obtained from the 3D inversions


METHOD

1. upper-crustal velocity and reflector models which produce significant out-of-plane ray bending were selected

2. synthetic refracted and reflected traveltimes were calculated for a single-profile 2D experiment and several 3D geometries using a 3D finite difference traveltime method

3. the 2D profile data were inverted using two 2D methods: (1) a back-projection tomography method (for velocity) and (2) a layered, large-block damped least-square inversion (for velocity and interface depth)

4. the 3D data were inverted using two 3D methods: (1) a back-projection tomography method (for velocity) and (2) a finely-discretized interface inversion

5. comparison was made of the distortion in the 2D images caused by out-of-plane sampling with the error (i.e. lateral smearing) in 2D cross-sections through the 3D models

3D geometries.


Velocity Model

Velocity model.

Ray tracing for 2D geometry.

Traveltimes for 2D geometry.

Results of 3D inversions: vertical slices away from anomaly.

Results of 2D inversions.

Results of 3D inversions: vertical slices through center of anomaly.

Results of 3D inversions: vertical slices through center of anomaly.

Results of 3D inversion: horizontal slices.
Star geometry.
Triangle geometry.
Coarse grid geometry.
Fine grid geometry.


Simple Reflector Model

Simple reflector model.

Comparison of 2D and 3d inversions.

Results of 3D inversion.
Star geometry.
Triangle geometry.
Coarse grid geometry.
Fine grid geometry.


Complex Reflector Model

Complex reflector model.

Comparison of 2D and 3d inversions.

Results of 3D inversion.
Star geometry.
Triangle geometry.
Coarse grid geometry.
Fine grid geometry.


Network Inversion

Results of simultaneous 2D network inversion.

Comparison of 2D network and 3D fine grid inversions.


CONCLUSIONS

  • all 3D geometries tested provided a reasonable image of the strong velocity anomalies and reflector topography in our test models; the fine grid geometry, with its greater denser of shots and receivers, provides the best results

  • the fine grid geometry recovered the most accurate image over the largest depth range; the triangle geometry is inferior to the other geometries that have a more uniform distribution of shots and receivers and which therefore sample a larger depth range

  • inversion of off-line data as well as in-line data for a network in which the line and shot spacing are similar does not provide significantly better results than inversion of the in-line data alone

  • for the scale of velocity anomalies and reflector topography we have tested, a 3D experiment, with the possible exception of the fine grid geometry, cannot be justified