Correcting wavefield gradients for the effects of local small-scale heterogeneities

Abstract

Summary 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.

An introduction to the two-scale homogenization method for seismology

“…Note that correction is needed not just for point-measured wavefield gradient measurements but also for array-derived wavefield gradient measurements. The full study on this topic can be found in Singh et al (2020).…”

Seismological Processing of Six Degree-of-Freedom Ground-Motion Data

“…Since rotational data are gradient measurements, they are mainly sensitive to small-scale heterogeneity (i.e., large values are measured where the wavefield changes rapidly in space) [79]. This local sensitivity can help to better constrain the near-receiver structure.…”

Strain to ground motion conversion of distributed acoustic sensing data for earthquake magnitude and stress drop determination

“…In recent years, the implementation of distributed acoustic sensing (DAS) for seismological purposes is rapidly expanding, for both on-land (e.g., Zhan, 2020;Fang et al, 2020;Jousset et al, 2018;Yu et al, 2019;Ajo-Franklin et al, 2019;Walter et al, 2020) and ocean-bottom (e.g., Sladen et al, 2019;Lior et al, 2021;Lindsey et al, 2019;Williams et al, 2019;Spica et al, 2020) applications. However, the use of DAS for several fundamental seismological tasks is yet to be fully established.…”

“…Spatial and slowness resolutions exhibit a tradeoff since increasing the segment length will increase the slowness resolution and decrease the spatial resolution. Coherency lengths are expected to be small for DAS strain (rate) records since they may be dominated by scattered waves (e.g., Lior et al, 2021) and are extremely sensitive to local media heterogeneities (e.g., van den Ende and Ampuero, 2020; Singh et al, 2019) and fiber coupling (e.g., Sladen et al, 2019;Lior et al, 2021). Thus, in the current application, short cable segments are used, as further described.…”