Shear-Wave Splitting Indicates Non-Linear Dynamic Deformation in the Crust and Upper Mantle

Abstract

We demonstrate that non-linear dynamic deformation exists throughout the crust and upper mantle of the Earth. Stress-aligned shear-wave splitting, seismic birefringence, is widely observed in the Earth’s upper crust, lower-crust, and uppermost ∼400 km of the mantle. Attributed to the effects of pervasive distributions of stress-aligned fluid-saturated microcracks in the crust (and controversially intergranular films of hydrated melt in the mantle), the degree splitting indicates that ‘microcracks’ are so closely spaced that they verge on failure in fracturing and earthquakes if there is any disturbance. Phenomena that verge on failure are critical systems with non-linear dynamics that impose a range of new properties on conventional sub-critical geophysics that we suggest is a New Geophysics. Consequently, shear-wave splitting provides directly interpretable information about the progress of non-linear dynamic deformation in the deep otherwise-inaccessible interior of the microcracked Earth. Possibly uniquely for non-linear dynamic phenomena, observation of shear-wave splitting allows the progress towards singularities to be monitored in deep in situ rock, so that earthquakes and volcanic eruptions can be predicted (we prefer stress-forecast). The response to other processes, such as hydraulic fracking, can be monitored, and in some cases calculated and effects predicted. Here, we review shear-wave splitting and demonstrate the prevalence of non-linear dynamic deformation of the New Geophysics in the crust and uppermost ∼400 km of the mantle.

Preamble

Schopenhauer 1788–1860: ‘All truth passes through three stages: ridicule; violent-opposition; self-evident’.

Appendices

Appendix 1: Ray-Path Geometry for Observing Undisturbed Shear Waves and SWS at the Shear-Wave Window at a Horizontal Free-Surface, and Identification of Band-1 and Band-2 Directions in Distributions of Parallel Vertical Fluid-Saturated Microcracks

Figure 5 shows ray-path geometry for observing undisturbed waveforms of SV-waves and SWS in stress-aligned fluid-saturated microcracks in the effective shear-wave window at a horizontal free-surface. (The wave-forms of SH-waves are preserved for all angles of incidence at a horizontal free-surface.) ABSCD is the crack-plane through distributions of parallel-vertical microcracks, and S is the recorder on a horizontal free-surface. The exact shear-wave window in an isotropic half-space is ray paths within the solid angle subtending sin⁻¹(Vs/Vp) ≈ 35° marking the critical angle for Vp reflection (Booth and Crampin 1985). The effective shear-wave window is ray paths within the solid angle AGFED-to-S and similar ray paths reflected in the crack-plane. However, near-surface low-velocity layers in the Earth bend rays upwards so that the effective shear-wave window may often be taken as straight-line ray paths out to 45° as in Fig.5.

Fig. 5

Ray-path geometry for observing undisturbed waveforms of shear-waves and SWS in stress-aligned fluid-saturated microcracks in the shear-wave window at a horizontal free-surface (after Crampin and Gao 2013)

Band-1 directions to the free-surface, where time-delays are sensitive to crack aspect-ratio (Crampin 1999; Crampin and Gao 2016), are within the solid angle EFGH-to-S subtending 15–45° to the crack plane within the effective shear-wave window. Band-2 directions to the free-surface, where time-delays are dominated by crack-density (Crampin 1999), are within the solid angle ADEHG-to-S to the crack plane. Both Band-1 and Band-2 directions include equivalent solid-angle directions reflected in the far side of the imaged crack plane (After Crampin and Gao 2013).

Appendix 2: Monitoring NLD Deformation to Stress-Forecast Impending Earthquakes

The effects of changing stress on in situ rocks can be monitored by SWS imaging NLD changes in microcrack geometry (Crampin 1999; Crampin and Peacock 2008; Crampin and Gao 2016). Observations of SWS indicate that increases of stress in the Earth (typically originate from magma generation and subduction, and interactions at the margins of tectonic plates) can be monitored by measuring changes in SWS. Initially, such NLD stress-accumulation is widespread throughout tectonic plates and the stress-field does not initially identify the fault-planes where the stress will eventually be released by slippage in earthquakes. The accumulating stress modifies crack aspect ratios throughout the stressed rock-mass, until the microcrack geometry approaches levels of fracture-criticality (Crampin 1999). Only then does the stress-field concentrate on envelopes of weakness surrounding the impending fault-planes, and stress-relaxation occurs as microcracks coalesce onto the impending fault break in NLD deformation (Gao and Crampin 2004; Wu et al. 2006; Crampin and Peacock 2008; Crampin and Gao 2013; Crampin et al. 2013).

The Earth is highly heterogeneous and stress accumulates irregularly. If stress accumulates over a small rock volume, the increase will be rapid but the eventual earthquake will be small. If stress accumulates over a larger volume, the increase will be slower but the eventual earthquake will be larger. Consequently, durations of the changes and the magnitudes possess self-similarity, so that monitoring NLD changes in the surrounding rock mass allows the time, magnitude, and in some cases fault break, of the impending earthquake to be stress-forecast. Note that we refer to this phenomenon as earthquake stress-forecasting, rather than earthquake forecasting or earthquake prediction, to emphasize the different methodology.

New Geophysics demonstrates that stress-accumulation before earthquakes can be recognized by increasing average SWS time-delays in Band-1 directions in the shear-wave window (Fig.5), and corresponding decreases in average SWS time-delays for stress-relaxation (Crampin 1999; Crampin and Peacock 2008; Crampin and Gao 2013, 2016). NLD stress-accumulation was first positively identified in changes in SWS before a M 5 earthquake in Iceland with similar changes in SWS to those before a M 5.1 earthquake 6 months earlier (Fig.6). A stress-forecast was emailed (10th Nov., 1998) to the Iceland Meteorological Office (IMO) ‘… an event could occur any time between now (M ≥ 5) and the end of February (M ≥ 6)’ on a specified fault with continuing seismic activity. Three days later (13th Nov., 1998), a M = 5 earthquake occurred on the identified fault (Crampin et al. 1999, 2004a, 2008). We claim this as the first successful scientifically stress-forecast/predicted earthquake, as opposed to less-specific probabilistic estimates. Similar characteristic variations are seen retrospectively before 16 earthquakes elsewhere (Crampin and Gao 2015).

Fig. 6

Variations with time of SWS time-delays normalized to ms/km in Band-1 directions (middle diagram) and Band-2 directions (Top diagram) for 5 years at station BJA in SW Iceland showing, in Band-1, least-squares increases before larger earthquakes within 20 km of BJA in lower diagram. The curves in the time-delays in the top and middle diagrams are nine-point moving averages. The red line (Oct. 1996–Nov. 1998) marks a least-squares average of 2 ms/km/year relaxation interpreted as the Mid-Atlantic Ridge responds to the large Gjàlp, Vatnajökull eruption of Oct. 1996. The vertical red bar in Nov. 1998 marks the time of the successfully stress-forecast M 5 (Crampin et al. 1999, 2008). (Modified after Volti and Crampin 2003b)

Later, it was recognized that the observed stress-accumulation stops abruptly before the impending earthquake occurs. There is stress-relaxation, average time-delays decrease, and the earthquake occurs at a comparatively low value of implied stress (Gao and Crampin 2004). Figure 7 shows stress-accumulation and stress-relaxation, before six earthquakes (and two laboratory experiments) ranging in magnitude from M 6 to M 1.7, in a normalized format convenient for displaying such characteristic changes. The successfully stress-forecast earthquake is Fig.7c. All six earthquakes show similar behaviour despite orders of magnitude differences in released energy and durations of stress-accumulation ranging from 6 years to a few hours.

Fig. 7

Examples of stress-accumulation and stress-relaxation in field and in laboratory. Shear-wave time delays normalized to ms/km and plotted against time before six earthquakes ranging in magnitude from M _S  = 6 to M = 1.7 and two laboratory experiments. More complete information is in Gao and Crampin (2004)

Logarithms of the durations of both the stress-accumulations and the stress-relaxations are both linear (self-similar) with the impending magnitudes (Crampin et al. 1999, 2008; Gao and Crampin 2004; Crampin and Peacock 2008). Stress-relaxation is interpreted as microcracks coalescing onto the impending fault-plane (Gao and Crampin 2004; Wu et al. 2006). Characteristic patterns of stress-accumulation increases and stress-relaxation (crack-coalescent) decreases have been recognized retrospectively before (currently) 15 earthquakes ranging from a M 1.7 swarm event in Iceland (Crampin et al. 2008) to the M 9.2, 2004, Sumatra-Andaman Earthquake (SAE), where changes in SWS were recognized in Iceland at the width of the Eurasian Plate (∼10,500 km) from Indonesia (Crampin and Gao 2012). Before SAE, ten stress-forecasts were emailed to IMO (13th Sept., 2002 to 18th Feb., 2005) updated every few months, warning of an impending large earthquake (Crampin and Gao 2012). At that time the full NLD sensitivity of SWS had not been recognized, and a M ≈ 7 earthquake in Iceland was stress-forecast. It was only in retrospect that it was recognized that the stress-forecasts were for the SAE (Crampin and Gao 2012).

Stress-forecasting is possible whenever SWS can be routinely monitored. Swarms of small earthquakes are generally far too scarce and irregular for routine monitoring of SWS. Only in Iceland where two transform faults of the Mid-Atlantic Ridge uniquely run onshore in SW Iceland and North-Central Iceland and provide the persistent low-level seismicity necessary for reliable routine stress-forecasting (Volti and Crampin 2003a, b).

Note that New Geophysics implies that earthquakes cannot be predicted by monitoring effects at the source. Earthquakes are singularities which lead to deterministic chaos; thus, although the source effects may on occasions be modelled explicitly, they are essentially unrepeatable as they are likely to depend critically on otherwise negligible (butterfly effect) details of initial conditions. The only mechanism for stress-forecasting/prediction is using SWS to monitor stress-accumulation and stress-relaxation in the rock surrounding the impending earthquake (or volcanic eruption) by the conventional effects of changing stress on microcrack geometry in rocks surrounding the impending source (Crampin 1999; Crampin et al. 2008). The source of the shear-waves may either be the irregular and unreliable swarms of small earthquakes, or controlled-source Stress-Monitoring Sites (SMSs) (Crampin and Gao 2016). SMSs provide a mechanism for routinely monitoring stress accumulating before impending earthquakes and volcanic eruptions so that the earthquake or eruption can be stress-forecast.

Appendix 3: Monitoring NLD Deformation to Stress-Forecast Impending Volcanic Eruptions

Monitoring SWS before impending volcanic eruptions shows similar characteristic NLD deformation behaviour as that seen before earthquakes and can be similarly interpreted as stress-accumulation and stress-relaxation before the event.

Figure 8 compares stress-accumulation and stress-relaxation, in the normalized format of Fig.7, before (a) the 2010 ash-cloud (flank) eruption of Eyjafjallajökull Volcano in SW Iceland (Liu et al. 1997) with (b) the successfully stress-forecast earthquake in Fig.7c 90 km to the west (Gao and Crampin 2004). Both events show stress-accumulation increases, of 7 months and 4 months, respectively, and stress-relaxation decreases, of ∼40 days and four days, respectively. Considering the very different geophysical processes involved, the NLD behaviour of the variations of SWS time-delays seems remarkably similar and supports the existence of New Geophysics in the reservoir rock.

Fig. 8

Comparison of the behaviour of shear-wave splitting before (a) a volcanic eruption and before (b) an earthquake. The eruption is the ash cloud eruption of Vatnajökull, Iceland, March 2010 and the earthquake is in SW Iceland in Fig.7c. Both show similar stress-accumulation increases and brief stress-relaxation (crack coalescence) decreases before both eruption and earthquake occurs

Appendix 4: Monitoring Fluid Injection (Aka Hydraulic Fracking)

Angerer et al. (2002) use APE to model the response of a cracked carbonate reservoir to critically high-pressure and low-pressure CO₂ injections (hydraulic fracking). Figure 9 shows seismograms of a multi-component 4-D (time-lapse 3-D) 3C reflection survey in Vacuum Field, New Mexico, in 1995, by the Reservoir Characterization Project (RCP), Colorado School of Mines (Roche et al. 1997).

Fig. 9

(a) Pre-injection waveforms of a multi-component nearly vertical ray reflection survey near the centre of Vacuum Field, New Mexico, carbonate reservoir (Angerer et al. 2002). S1-, S2-, and P-waves are reflection sections with mutually orthogonal polarizations, where the horizontals S1, and S2, have been rotated into the split shear-wave polarizations parallel and perpendicular to the direction of maximum horizontal stress, respectively. Left-hand (LH) five traces are observed waveforms at adjacent recorders 17 m apart, and the right-hand (RH) three traces are synthetic seismograms modelled by APE to match the shear-wave and SWS arrivals. Top and bottom of injection zone for shear waves are marked by arrows with time-delays in ms/km. (b) Post-injection waveforms two-weeks after a high-pressure CO₂-injection (hydraulic fracking). Again, the LH traces are observations and RH traces are synthetic seismograms modelled by APE with the structure from (a) and an injection pressure of 6.4 MPa (after Angerer et al. 2002)

The record sections headed S1 and S2 are in the same orthogonal azimuthal directions. In (a) the pre-CO₂ injection: the arrowed arrivals at the top and bottom of the target zone are at 176 ms for S1 and 178 ms S2 so that S1 is the faster shear wave. In (b) the post-CO₂ injection, the target zone is at 204 ms for the S1-direction and 184 ms for S2. This means that the high-pore fluid pressure injection is critically high and has induced a 90°-flip in the orientation of the faster split shear-wave arrivals for both observed and calculated seismograms for shear waves travelling through the injection zone. Such 90°-flips have since been observed elsewhere in high-pressure reservoirs and near seismically active fault-planes where critically high pore-fluid pressures are encountered on all seismically active fault-planes (Crampin et al. 2002, 2004b).

The 90°-flip was not expected, and the match of observations with APE is strong confirmation of the validity of APE and New Geophysics in crustal rock.