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Local small-scale heterogeneities, like geological inhomogeneities, surface topographies and cavities are known to affect seismic wavefield gradients. This effect is in fact measurable with current instruments. For example, the agreement between data and synthetics computed in a tomographic model is often not as good for rotation as it is for displacement. Here, we use the theory of homogenization to explain why small-scale heterogeneities strongly affect wavefield gradients, but not the wavefield itself. We show that at any receiver measuring wavefield gradient, small-scale heterogeneities cause the wavefield gradient to couple with strain through a coupling tensor J. Furthermore, we show that this J is (1) independent of source, (2) independent of time, but (3) only dependent on the receiver location. Consequently, we can invert for J based on an effective model for which synthetics fit displacement data reasonably well. Once inverted, J can be used to correct rotations at that receiver for other sources. Results of the correction are shown for synthetic rotational receivers and for the ring laser located in Wettzell, Germany. We find that compared to synthetics, the synthetics corrected through J are a better fit to the rotation data. Although results here are derived for rotations, they can be extended to receivers measuring any wavefield gradient. [ABSTRACT FROM AUTHOR]

Small-scale structures, like geological inhomogeneities, surface topographies and cavities areknown to affect gradients of displacement. These effects are in fact measurable with currentinstruments. For example, the agreement between data and synthetics computed in atomographic model is often not as good for rotation as it is for displacement. Using thetheory of homogenization, we explain why small-scale structures strongly affect thegradients of displacement, but not displacement itself. We show that at any receivermeasuring gradient of displacement, small-scale structures couple the gradient ofdisplacement with strain through a coupling tensor χ. Furthermore, we show that this χ is(1) independent of source, (2) independent of time, but (3) only dependent on thereceiver location. χ is the solution of the ’cell equation’ from the homogenizationtheory and it can be computed if the geology is known, which is usually not thecase. Nevertheless, we can invert for χ based on a tomographic model that fitsdisplacement data reasonably well. Once inverted, χ can be used to correct andpredict the effect of small-scale structures at that particular receiver. Results ofthe correction and prediction are shown for synthetic rotational receivers beforemoving on to the ring laser located in Wettzell, Germany. We find that χ leadsto a better fit between the computed and rotation data. Although results here arederived for rotations, they can be extended to receivers measuring any wavefieldgradient. [ABSTRACT FROM AUTHOR]