Seismic Gradiometry using Ambient Seismic Noise in an Anisotropic Earth

Abstract

We introduce a wavefield gradiometry technique to estimate both isotropic and anisotropic local medium characteristics from short recordings of seismic signals by inverting a wave equation. The method exploits the information in the spatial gradients of a seismic wavefield that are calculated using dense deployments of seismic arrays. The application of the method uses the surface wave energy in the ambient seismic field. To estimate isotropic and anisotropic medium properties we invert an elliptically anisotropic wave equation. The spatial derivatives of the recorded wavefield are evaluated by calculating finite di↵erences over nearby recordings, which introduces a systematic anisotropic error. A two step approach corrects this error: finite di↵erence stencils are first calibrated, then the output of the wave-equation inversion is corrected using the linearized impulse response to the inverted velocity anomaly. We test the procedure on ambient seismic noise recorded in a large and dense ocean bottom cable array installed over Ekofisk field. The estimated azimuthal anisotropy forms a circular geometry around the production-induced subsidence bowl. This conforms with results from studies employing controlled sources, and with 2 S.A.L. de Ridder and A. Curtis interferometry correlating long records of seismic noise. Yet in this example, the results where obtained using only a few minutes of ambient seismic noise.

Seismic Attenuation From Ambient Noise Across the North Sea Ekofisk Permanent Array

“…Their results fitted well with their seismically derived compaction map (which does not show the center of the array due to there being a seismically obscured area in the center of the array). The ringed structure of the velocity and Q at the Ekofisk array can also be observed in surface wave group velocity tomography (de Ridder et al, ; de Ridder & Biondi, ), surface wave phase velocity tomography (de Ridder & Biondi, ; de Ridder & Curtis, ), and compressional and shear wave velocity (Kazinnik et al, ) estimates at the site.…”

“…Subsidence will likely cause fracturing of the rock, which may cause a reduction in Q. Surprisingly, the Q values seem to show little relation to the large-scale subsidence (even though the group and phase velocities and also their anisotropy are clearly related to subsidence (see Figure 7 and also Barkved et al, 2005;de Ridder et al, 2015;de Ridder & Curtis, 2017). There is a suggestion of a relation in the north of the 1 Hz plot, but nowhere else.…”

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

“…De Ridder and Biondi [48] demonstrated that such methods, which are closely related to the wave gradiometry technique, can be successfully applied to short recordings of ambient seismic noise to image the local velocity structure without the need to compute cross-correlations of long noise records. De Ridder and Curtis [49] extended the method to also yield anisotropic wavefield parameters.…”

Seismic Azimuthal Anisotropy for the Southeastern Tibetan Plateau Extracted by Wave Gradiometry Analysis

“…De Ridder and Curtis (2017) deduced a second‐order anisotropic elliptic equation of high‐frequency noise surface wave energy based on information on wave gradients and then estimated the azimuthal anisotropy of the shallow surface of the Ekofisk. The second‐order spatial gradient can generally reduce truncation errors, but it works best for a rectangular array.…”