Applications of seismic spatial wavefield gradient and rotation data in exploration seismology Cedric Schmelzbach, Cédéric Van Renterghem, David Sollberger, Mauro Häusler, Johan Robertsson Institute of Geophysics, ETH Zurich, Switzerland (
[email protected])
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Introduction
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Motivation Addressing long-standing problems like coherent-noise suppression, relaxing sampling requirements and wavefield separation
Observations and interpretation 1. Near-vertical P-wave only on vz – no divergence 2. S-wave on vx and vz gives rise to downgoing PD-wave (S-to-P conversion) observable on divergence . D 3. P -, S- and Rayleigh-waves observable on wy . D 4. P - and Rayleigh-wave energy on wx: subsurface topography and/or heterogeneity
Strain and rotations •
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Dense displacement (or velocity) measurements with small multicomponent sensor groups (spacing wavelength) Finite-difference approximation to estimate displacement gradient tensor Displacement gradient tensor associated with volumetric (principal) strain and shear (deviatoric) strain Strain-induced rotation and divergence of the displacement field at the free-surface (a: P-wave velocity, b: S-wave velocity):
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Acquisition • Spatially compact receiver groups of five 3C geophones (Fig. 1) • Spatial gradients estimated with finite-difference technique • Seismic source: sledgehammer • Fig. 1: particle velocity, rotation rate around the horizontal axes and approximated divergence
Proposed solution Seismic spatial wavefield gradient and rotation data as additional measurements [1]: (1) Inherent link between rotation and S-waves and surface waves (2) Gradient estimate for wave-equation based processing (3) Extending the set of seismic observables
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Gradient-data field example
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Outlook Significant advances in the application of gradient and rotation data in seismic exploration can be expected in the following fields [1]: (1) Full elastic wavefield decomposition [3] (2) S-wave and converted wave imaging (3) Velocity model building, single-station dispersions curve analysis and tomography without traveltimes (4) Wavefield reconstruction (5) Anisotropic medium characterization (6) Seismic monitoring (7) Seismic source arrays, source-side gradients, and rotational sources (8) Vector infidelity corrections (sensor tilt) Gradient and rotation data open-up new opportunities for single-station processing particularly relevant for limited-access sites like boreholes, ocean bottom, or for planetary seismology.
Fig. 1. Field-data example of high-resolution multi-component geophone recordings (top; only central geophone of group shown), rotation rates and divergence derived from the sensor groups (bottom). Top right: Sketch of acquisition geometry and wavefield interaction at the free-surface.
Gradient-based wavefield separation 6
Gradient-data application example in wave-equation based processing [2]: • Separation of P-/S-wave and upgoing/downgoing wavefield at the free-surface • Wavefield-separation filters resulting from a Taylor expansions contain spatial wavefield gradients:
References 1.
Rotation around x:
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Rotation around y:
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Divergence:
Partners
Schmelzbach, C., S. Donner, H. Igel, D. Sollberger, T. Taufiqurrahman, F. Bernauer, M. Häusler, C. Van Renterghem, J. Wassermann, and J.O.A. Robertsson (2017), Advances in 6-C seismology: applications of combined translational and rotational motion measurements in global and exploration seismology, Geophysics, submitted. Van Renterghem, C., C. Schmelzbach, D. Sollberger and J.O.A. Robertsson (2017), Spatial wavefield gradient-based seismic wavefield separation, GJI, doi:10.1093/gji/ggx499
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Fig. 2: synthetic and field-data data example demonstrating isolation of upgoing S-waves
Fig. 2. Synthetic-data (left) and field-data (right) example of applying the gradientbased wavefield separation to horizontal-component recordings to isolate S-waves. Note that the filter is not designed to remove the Rayleigh waves marked with R.
Sollberger, D., S.A. Greenhalgh, C. Schmelzbach, C. Van Renterghem, J.O.A. Robertsson (2017), 6-C polarisation analysis using point measurements of translational and rotational ground-motion: Theory and applications, GJI, submitted.
