a review of retrospective stress-forecasts of earthquakes and ...gaoyua/44.pdfrocks in the earth’s...

Review

A review of retrospective stress-forecasts of earthquakes and eruptions

Stuart Crampin a,b,⇑, Yuan Gao c, Julian Bukits a

aBritish Geological Survey, Edinburgh EH9 3LA, Scotland, UKb School of GeoSciences, University of Edinburgh, EH9 3FW Scotland, UKc Institute of Earthquake Science, China Earthquake Administration, 100036 Beijing, China

a r t i c l e i n f o

Article history:

Received 1 May 2015Accepted 26 May 2015Available online 5 June 2015

Keywords:

EarthquakesEruptionsRetrospective stress-forecastsShear-wave splittingStress monitoring

a b s t r a c t

Changes in shear-wave splitting (SWS) monitor stress-induced changes to the geometry of thestress-aligned fluid-saturated microcracks pervading almost all sedimentary, igneous, and metamorphicrocks in the Earth’s crust and upper mantle. Changes in SWS implying stress–accumulation and stress–relaxation (suggesting crack-coalescence) before large earthquakes have been observed retrospectivelyin the rock mass surrounding large or larger earthquakes. In one case, the time, magnitude, andfault-plane of a M 5 earthquake in SW Iceland, was successfully stress-forecast 3 days before it occurred.Similar characteristic behaviour of shear-wave splitting has been observed retrospectively before �17other earthquakes and before three volcanic eruptions. These retrospective stress-forecasts have beenpublished in different formats in different journals. For clarification, this paper redraws all observationsof stress–accumulation and stress–relaxation in a consistent normalised format that allows the overallsimilarities in behaviour to be recognised before earthquakes and volcanic eruptions. Such behaviour,inconsistent with conventional sub-critical geophysics, confirms the compliance of the New Geophysicsof a critically microcracked Earth, where the microcracks are so closely-spaced that they verge on failureand hence are critical-systems that impose a range of fundamentally-new properties on conventionalsub-critical geophysics. One of the implications of New Geophysics is that there are similarities in thebehaviour of stress before earthquakes and volcanic eruptions. The normalised formats show such sim-ilarities and include the opportunity to stress-forecast both earthquakes and eruptions.

Ó 2015 Published by Elsevier B.V.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772. Observations of stress–accumulation and stress–relaxation (crack coalescence) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

2.1. Stress–accumulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782.2. Stress–relaxation (tentatively interpreted as crack-coalescence) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812.3. Goodness-of-fit and error bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3. Summary of retrospective stress-forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.1. Retrospective stress-forecasts of earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.2. Retrospective stress-forecasts of volcanic eruptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4. Durations of stress increases and stress decreases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835. Implications for successful (real-time) stress-forecasting of earthquakes and volcanic eruptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.1. Implications for successfully stress-forecasting earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.2. Implications for successful stress-forecasting volcanic eruptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6. Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

http://dx.doi.org/10.1016/j.pepi.2015.05.0080031-9201/Ó 2015 Published by Elsevier B.V.

⇑ Corresponding author at: British Geological Survey, Murchison House, West Mains Road, Edinburgh EH9 3LA, Scotland, UK. Tel.: +44 131 650 0362(O), +44 131 2254771(H).

E-mail addresses: [email protected] (S. Crampin), [email protected] (Y. Gao), [email protected] (J. Bukits).URL: http://www.geos.ed.ac.uk/homes/scrampin/opinion (S. Crampin).

Physics of the Earth and Planetary Interiors 245 (2015) 76–87

Contents lists available at ScienceDirect

Physics of the Earth and Planetary Interiors

journal homepage: www.elsevier .com/locate /pepi

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Appendix A. A brief outline of New Geophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Appendix B. Ray-path geometry for monitoring stress–accumulation and SWS time-delays within the shear-wave window at the free-surface 85References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

1. Introduction

Worldwide observations of shear-wave splitting (SWS) showthat rocks throughout the upper- and lower-crust and upper man-tle are pervaded by distributions of stress-aligned fluid-saturatedtypically-vertically-oriented microcracks (Crampin, 1994; Helbigand Thomsen, 2005; Crampin and Peacock, 2008). [In the upper-most �400 km of the mantle, where SWS is also observed(Savage, 1999), the ‘microcracks’ are arguably intergranular filmsof hydrated melt (Crampin, 2003).] The degree of observedshear-wave velocity anisotropy (SWVA) shows that microcracksare so closely-spaced that they verge on fracturing and the occur-rence of earthquakes (Crampin, 1994; Crampin and Peacock, 2008).Phenomena that verge on failure are critical-systems in a NewPhysics (Davies, 1989) (hence a New Geophysics) which imposes arange of fundamentally-new properties on conventionalsub-critical physics/geophysics with wholly-new implicationsand applications (Davies, 1989). Appendix A is a brief outline ofNew Geophysics (Crampin and Gao, 2013) and Table A1 lists someof these fundamentally-new properties. We shall show that thecriticality of the microcrack geometry and application of theseproperties allows earthquakes and volcanic eruptions to bestress-forecast, where the process is referred to asstress-forecasting, rather than forecasting or predicting earthquakesand eruptions, to emphasise the different methodology.

After 35 years since SWS was first identified in the crust(Crampin et al., 1980) and upper mantle (Ando et al., 1980), thereis still discussion over the cause of SWS in both crust and mantle.Suggestions have included various combinations ofpreferentially-oriented: anisotropic mineral grains; multiple lay-ers; small scale inhomogeneities, joints, cracks, and microcracks;lattice-preferred orientation; shape-preferred orientation; andothers (Svitek et al., 2014; Xie et al., 2015). However, twoover-riding observational constraints restrict possible causes. (1)The preferred orientations of SWS in the upper- and lower-crust,and the upper-most �400 km of the mantle (Savage, 1999), areparallel in the direction of maximum horizontal stress. (2)Changes in SWS have been observed, particularly changes in SWStime-delays (Crampin et al., 1999, 2008; Crampin and Gao, 2013).

(1) The preferred orientations of SWS: anisotropic symmetry sys-tems demonstrate (Chen et al., 1993) that only symmetrysystem with (stress) aligned parallel polarizations withinthe shear-wave window at a horizontal free surface is hexag-onal symmetry (transverse-isotropy) with a horizontal axisof symmetry (HTI) in the direction of minimum stress. Theonly geological phenomenon with such HTI-symmetry arethe pervasive distributions of vertically-oriented microc-racks striking parallel to the direction of the maximumstress (perpendicular to the direction of minimum stress)which is typically horizontal (Crampin, 1994; Crampin andPeacock, 2008). Distributions of parallel vertical thin layersor metamorphic re-crystallisation in slates and schists,may also have TIH-symmetry, but such formations are rareand seldom uniform over tens of kilometres of lateral andvertical extent as observed by SWS.

(2) Changes in SWS: Fluid-saturated stress-aligned microcracksare the only geological phenomenon which responds almostimmediately to small changes of stress (Crampin, 1994,1999).

Consequently, the only common geological phenomenon thatsatisfies the two observational criteria are distributions ofstress-aligned fluid-saturated microcracks (intergranular films ofhydrated melt in the mantle), and the cause of SWS is necessarilystress-aligned fluid-saturated microcracks (Crampin, 1994;Crampin and Peacock, 2005, 2008).

Swarms of small earthquakes are used as the source ofshear-waves. By analysing changes in SWS within theshear-wave window at the surface, we monitor changes in thestress-induced behaviour of microcracks along shear-waveray-paths in the rock mass above the swarm. [The shear-wave win-dow is specified in Appendix B.] These changes typically showstress–accumulation before impending events that may be veryclose: �2 km either side of a flank eruption on Mt Etna, Sicily(Bianco et al., 2006); �2 km from the epicentre in the first success-fully stress-forecast (M 5) earthquake in SW Iceland (Crampinet al., 1999, 2004a, 2008); or very distant, changes in SWS beforethe 2004 Mw 9.2 Sumatra Earthquake were observed in Iceland ata distance of �10,500 km, the width of the Eurasian Plate, fromIndonesia (Crampin and Gao, 2012). Such extreme sensitivity isexpected in critical-systems (Property P8 Sensitivity in Table A1).

Retrospective observations of stress-forecast earthquakes havebeen published in different formats in different journals. For clarifi-cation, this paper re-draws all known observations of stress–accu-mulation and stress–relaxation before the 18 earthquakes listed inTable 1, and before three volcanic eruptions listed in Table 2, wherethe SWS time-delays are plotted in a consistent normalised formatin Figs. 1 and2 so that overall similarities in behaviourmaybe recog-nised. These figures have minimal descriptions and the reader isreferred to the original publications listed in Tables 1 and 2 for com-prehensive discussions. Fig. 1 displays in one diagram the character-istic behaviour before impending earthquakes that showsobservations of SWS can stress-forecast the time, magnitude andin some circumstances location of impending earthquakes. Fig. 2shows similar behaviour before volcanic eruptions.

2. Observations of stress–accumulation and stress–relaxation

(crack coalescence)

Observations of SWS time-delays above swarms of small earth-quakes are subject to a large scatter (sometimes referred to as a‘‘±80%’’ scatter Crampin, 2006). Controlled-source signals in explo-ration seismics do not show such scatter (Li and Crampin, 1991).The scatter is the result of 90°-flips (Angerer et al., 2002) in SWSpolarisations whenever shear-waves penetrate or exit thecritically-high pore-fluid-pressure envelopes surrounding allseismically-active fault-planes (Crampin et al., 2002, 2004b).Such 90°-flips reverse the sign of time-delays, and the combinationof flipped and unflipped polarisations along different but adjacentray-paths accounts for the ±80% scatter seen in all observations ofSWS time-delays above swarms of small earthquakes (Crampinet al., 2004b), including the observations in Figs. 1 and 2.Although the behaviour can be modelled and calculated givenknown initial conditions in controlled-source environments(Angerer et al., 2002), the observed scatter above small earth-quakes cannot generally be exactly matched or eliminated, as thescatter depends critically on miniscule details of the initial condi-tions at depth in the rock mass, which are essentially unknownand unknowable (Crampin et al., 2002, 2004b).

S. Crampin et al. / Physics of the Earth and Planetary Interiors 245 (2015) 76–87 77

2.1. Stress–accumulation

Earthquakes release stress by slippage on fault-planes, whichcan only occur when sufficient strain-energy has accumulated forrelease by the appropriate magnitude earthquake. Apart fromrepetitive bi-diurnal tidal effects, the principal changes of strainand stress in the Earth are caused by interactions at the boundariesof tectonic plates: plate generation and spreading at oceanicridges; and plate subduction at plate margins as plates are thrust

beneath each other. Initially stress–accumulation from interac-tions at plate boundaries is widely distributed and independentof the location, mechanism, and circumstances of the eventualstress-release by impending earthquakes (Crampin and Peacock,2005, 2008; Crampin and Gao, 2013).

Increasing-stress modifies the geometry of the fluid-saturatedstress-aligned microcracks which SWS shows pervade almost allrocks throughout the upper and lower crust (Crampin, 1994,1999; Crampin and Peacock, 2008), and the uppermost �400 km

Table 1

Seismic stations (Fig. 1) where retrospective earthquake stress-forecasts have been observed in order of increasing earthquake magnitude with duration in of stress–accumulationand stress–relaxation. The successful stress-forecast is included as Eq. No. 10.

Eq. No. (Fig. No) Magn* Earthquake identifier; Recording location Year Seismic station Durat of stress-acc (days) Durat of stress-rel (days) Refs.¥

1 MI 1.7 Swarm event; N Iceland 2002 BRE P0055 00,306 [1]2 MI 2.5 Swarm event; N Iceland 2002 BRE P021 00,465 [1]3 MI 3.4 SW Iceland; SW Iceland 1997 BJA 47

o [2]4 M 3.6 Dongfang; Hainan, China 1992 GAC 21 o [3]5 Md 3.8 Enola Swarm; Arkansas, USA 1982 MHC P45 0123 [4]6 MI 3.8 SW Iceland; SW Iceland 1997 BJA 40

o [2]7a ML 4.0 Parkfield; California, USA 1988 [VC] �200

o [5]7b ‘’ ‘’ ‘’ [MM] �305 o [5]8 MI 4.4 SW Iceland; SW Iceland 1997 BJA 83 18 [2]9a MI 4.9 Grímsey Lineament; N Iceland 2002 [FLA] 163

o [6]9b ‘’ ‘’ ‘’ [GRI] 147 24 [6]10aà MI 5.0 SW Iceland; SW Iceland 1998 [BJA] 127 44 [7,8,9]10bà ‘’ ‘’ ‘’ [KRI] 121 o [7]11a MI 5.1 SW Iceland; SW Iceland 1998 [BJA] 117

o [2]11b ‘’ ‘’ ‘’ [SAU] 123 o [2]12§ M 5.3 Shidan; Yunnan, China 1992 BS o 38 [10]13§ M 5.9 ‘’ ‘’ BS 400 o [10]14 Ms 5.9 Xiuyan; Liaoning, China 1999 YK 136

o [14]15$ Ms 6.0 North Palm Springs; CA, USA 1986 KNW 1100 69 [11,12,13]16a§ Ms 6.6

€ SW Iceland; SW Iceland 2000 [BJA] 151 21 [15]16b§ ‘’ ‘’ ‘’ [SAU] 175 38 [15]17£ Mw 7.7 Chi-Chi; Taiwan 1999 CHY 589 131 [16]18a Mw 9.2 Sumatra; Iceland 2004 [BJA] 1260 275 [17]18b ‘’ ‘’ ‘’ [SAU] 1105 442 [17]18c ‘’ ‘’ ‘’ [KRI] o o [17]18d ‘’ ‘’ ‘’ [GRI] 1503 486 [17]18e ‘’ ‘’ ‘’ [FLA] 1281 380 [17]18f ‘’ ‘’ ‘’ [BRE] o o [17]18 g ‘’ ‘’ ‘’ [HED] 1110 547 [17]

* Magnitudes listed as originally reported; many are IMO Station body-wave magnitudes MI. Multiple recording stations for any earthquake in brackets, where earthquake ‘N’ is identified by ‘Na’, ‘Nb’, etc.à Successful real-time stress-forecast Crampin et al. (1999, 2004a, 2008).§ Complicated by three earthquakes (M 5.2, 5.9, 5.3) within 2 months, where stress response cannot be wholly separated.o Absent or unreliable durations.$ Earthquake where changes in SWS time-delays (stress–accumulation) were first recognised Peacock et al. (1988).€ Complicated by three earthquakes (MS 6.6, 5.7, 6.6) within 5 days, where stress response cannot be separated, and durations are for the combined magnitudes.

£ SWS time-delays are time-delays between the top and bottom of a 200 m-deep borehole.¥ References: [1] Gao and Crampin (2004); [2] Volti and Crampin (2003b); [3] Gao et al. (1998); [4] Booth et al. (1990); [5] Liu et al. (1997); [6] Gao and Crampin (2006); [7]Crampin et al. (1999); [8] Crampin et al. (2004a); [9] Crampin et al. (2008); [10] Gao et al. (2004); [11] Peacock et al. (1988); [12] Crampin et al. (1990); [13] Crampin et al.(1991); [14] Tai et al. (2008); [15] Wu et al. (2006); [16] Crampin and Gao (2005); [17] Crampin and Gao (2012).

Table 2

Seismic stations (Fig. 2) where retrospective stress-forecasts of three volcanic eruptions have been observed in chronological order with durations of stress–accumulation andstress–relaxation. Format as in Table 1.

Eq. No. (Fig. No) Earthquake identifier; Recording location Year Seismic station Duration of stress-acc (days) Duration of stress-relax (days) Refs.¥

1a Vatnajökull (Gjálp); SW Iceland 1996 [BJA] 80 o [1]1b* ‘’ ‘’ [BJA] 80 770 [1]1c ‘’ ‘’ [SAU] 120 16 [1]2 Etna flank; Etna, Sicily 2001 [ESP] 130 3 [2]2 ‘’ ‘’ [MNT] 130 1 [2]3à Eyjafjallajökull; SW Iceland 2010 GOD 190 40 [3]

* Stress–relaxation after the Gjálp (Vatnajökull) eruption over 27 months at �2 ms/km/year, interpreted as the response of the Mid-Atlantic Ridge following the release ofstress above the mantle plume beneath the 1996 Gjálp (Vatnajökull) eruption [1]. The stress–accumulation increases, carried on the stress–relaxation decrease, labelled (i) to(v) in Fig. 2 No. 1b are those of Table 1 and Fig. 1 Nos. 6, 8, 3, 11, and 10, with magnitudes MI 3.8, 4.4, 3.4, 5.1, and 5.0, respectively. SWS time-delays are nine-point moving averages in three-event steps [2].à Durations are before the Eyjafjallajökull flank-eruption - see caption to Fig. 7 in Liu et al. (2014).o Absent or unreliable duration.¥ References: [1] Volti and Crampin (2003b); [2] Bianco et al. (2006); [3] Liu et al. (2014).

78 S. Crampin et al. / Physics of the Earth and Planetary Interiors 245 (2015) 76–87

of the mantle (Crampin, 2003). Such stress–accumulation can bemonitored by measuring changes in the average SWS time-delaysin Band-1 directions (Appendix B) Crampin (1999), whenever thereis an appropriate source of shear-waves. The most convenient nat-ural sources of shear-waves are swarms of small earthquakes.Monitoring stress–accumulation above earthquake swarms typi-cally monitors increasing stress originating at plate boundaries(Crampin and Peacock, 2008; Crampin and Gao, 2013). Since the

increase of stress from interactions at plate boundaries is asemi-continuous process, stress–accumulation is thenearly-ubiquitous state of the Earth’s crust, as is demonstratedby intermittent worldwide seismicity.

SWS suggests that increasing horizontal stress is the drivingmechanism for crustal earthquakes (Crampin and Peacock, 2005,2008; Crampin and Gao, 2013). Crampin (1999) shows thatincreasing stress increases the aspect-ratio of vertical microcracks

Fig. 1. Plot of all known variations in SWS implying stress variations before earthquakes. Uniform plots of precursory variations in SWS time-delays (above swarms of smallearthquakes) before larger earthquakes on seismograms from stations listed in Table 1 for retrospective earthquake stress-forecasts in cited papers (specified in Table 1).Plotted in order of increasing magnitude, time-delays are normalised to ms/km, and time-scales are normalised to the same dimensions for each earthquake data set. Headersshow earthquake number, earthquake magnitude, earthquake identification, earthquake location, seismic station code (three or sometimes two letter codes), and year ofearthquake. If earthquake ‘N’ has more than one station showing SWS variations, entries are numbered ‘Na’, ‘Nb’, etc. SWS time-delays for Earthquake No. 1: Left-hand-side,least-squares regression line through stress–accumulation increase before a M 17 swarm event in N Iceland observed at Station BRE Gao and Crampin (2004); Right-hand-side: enlarged time-scale for red-dotted box in LHS with red-dashed least-squares regression line showing abrupt precursory decrease before the impending event.Earthquakes Nos. 2–18g, format as in Earthquake No. 1. There is no red box and the right-hand-side is empty, either when there are no source events for the precursorydecrease immediately before the earthquake (Nos. 3, 6, 10b, 11a, 14), or when there is no abrupt precursory decrease and the stress–accumulation increase continues untilthe impending event occurs (Nos. 4, 7a, 7b, 9b, 11b, 13). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of thisarticle.)


aligned parallel to the direction of the (typically-horizontal) maxi-mum tectonic stress. The seismic effect is to increase the averageSWS time-delay in Band-1 directions in the shear-wave windowat the free-surface (Crampin, 1999). Band-1 directions areshear-wave ray-paths to the free-surface in the shear-wave win-dow (Booth and Crampin, 1985) within the double-leafed solidangle between 15° and 45° to the average crack plane. Thesource-to-recorder geometry is illustrated in Fig. B1 in AppendixB. As shown in Figs. 1 and 2, such stress–accumulation increases

lead to robust observations, that are seen whenever suitableshear-wave source-to-receiver geometry is available before largeor larger earthquakes (Crampin, 1994; Crampin and Peacock,2008; Crampin and Gao, 2013), and before volcanic eruptions(Volti and Crampin, 2003a, 2003b; Bianco et al., 2006; Liu et al.,2014).

The least-squares regression lines for stress–accumulation inthe left-hand diagrams of Figs. 1 and 2, are fitted to the scatterleading up to the time of the impending event. In the normalised

Fig. 1 (continued)

Fig. 2. Variations of SWS before volcanic eruptions in similar format to Fig. 1: variations of SWS time-delays (above swarms of small earthquakes) in uniform normalisedplots of durations of observed stress–accumulation increases and stress–relaxation decreases for three volcanic eruptions specified in Table 2. In diagram 3), theEyjafjallajökull eruption had two phases of unusually long duration: flank-eruption (yellow); and summit-eruption (blue). (For interpretation of the references to colour inthis figure legend, the reader is referred to the web version of this article.)


figures the slopes of these lines are approximately similar, despitethe huge range of earthquake magnitudes from a M 1.7 swarmevent to the 2004 Mw 9.2 Sumatra Earthquake. This result is func-tion of Properties P3 Uniformity, and P7 Universality.

Stress–accumulation before two earthquakes (Table 1,Earthquakes Nos. 10 and 18) was recognised before the earth-quakes occurred. Based on the implied stress–accumulation ofSWS time-delay increases at seismic station BJA (Fig. 1, No. 10a),on 10th November 1998, the University of Edinburgh (UE) emailedIceland Meteorological Office (IMO): ‘‘. . .an event could occur anytime between now (MP 5) and the end of February (MP 6)’’.Three days later, IMO emailed UE: ‘‘. . . there was a magnitude 5earthquake just near to BJA . . . this morning 10 38 GMT’’ (Crampinet al., 1999, 2004a, 2008). This was before stress–relaxationdecreases had been recognised (Gao and Crampin, 2004). The mag-nitude of the stress-forecast earthquake was based on the durationof the stress–accumulation increase (the left-hand diagram inFig. 1, No. 10a), where increasing SWS time-delays indicated thatlevels of fracture-criticality were approaching based on variationsin SWS time-delays before other earthquakes in SW Iceland(Fig. 1, Nos. 3, 6, 8, 11a, 11b) (Crampin et al., 1999, 2004a, 2008).We claim this successful stress-forecast as the first scientificallypredicted earthquake, as opposed to less accurate probabilisticestimates discussed by Kossobokov (2007) and others.

Note that Fig. 1, No. 10a is from Gao and Crampin (2004) whoused a lower-magnitude-limit data-set for IMO earthquakes thanVolti and Crampin (2003a,b). Consequently, although the SWSeffects are compatible with the variations in earthquake (v) inFig. 2, No. 1b, the exact time-delay data in the figures are margin-ally different.

Stress–accumulation was also recognised before the 2004 Mw9.2 Sumatra Earthquake had occurred (Fig. 1, Nos. 18a-to-18g)(Crampin and Gao, 2012). Recognising the possibility of stress–ac-cumulation, a stress-forecast was emailed to IMO on 13thSeptember, 2002. Updated stress-forecasts were emailed to IMOevery two or three months (up to a total of 10 emails) until 22ndDecember, 2004 (listed in Table 1 of Crampin and Gao, 2012).The extreme sensitivity (Property P8) of SWS time-delays in NewGeophysics had not been fully recognised at that time and theimpending earthquake was incorrectly stress-forecast as a large(M �7) earthquake in Iceland, rather than the impending Mw 9.2Sumatra Earthquake in Indonesia at �10,500 km from Iceland(Crampin and Gao, 2012). Consequently, although stress–accumu-lation was recognised before the time of the Sumatra Earthquake,the magnitude and location of the earthquake were notstress-forecast.

There has been speculation on stress–relaxation before the finalrupture of an earthquake for many years, such as thedilatancy-diffusion hypothesis of Scholz et al. (1973), and Mainet al. (1989) discuss the phenomenon in terms of b-value anoma-lies. We suggest that New Geophysics provides the overall physicalbasis of the process (Appendix A).

2.2. Stress–relaxation (tentatively interpreted as crack-coalescence)

Stress–accumulation before an impending earthquake typicallycontinues until the stress-field responds to a weakness at an exist-ing, or more rarely impending, fault plane, and pre-rupture stress–relaxation is observed as small earthquakes progressively concen-trate stress in the surrounding rock mass by microcrack coales-cence around the impending fault. Eventually a large volume ofde-stressed weak rock is surrounded by stressed rock and theimpending earthquake occurs as microcrack geometry reachesthe threshold of fracture-criticality (Crampin, 1994; Gao andCrampin, 2004; Crampin and Peacock, 2008; Crampin and Gao,2013).

Observations of stress–relaxation decreases are less robust thanstress–accumulation increases. Whenever there is sufficient sourcedata (sufficient numbers of small shear-wave-source-swarm earth-quakes immediately before the impending event, which is usuallyat a distance and tectonically unrelated to the swarm events) toshow the effects at a monitoring station, stress–accumulationincreases typically change slope abruptly to stress–relaxationdecreases. These decreases are tentatively interpreted as microc-racks coalescing around the impending fault-plane for earthquakes(Gao and Crampin, 2004), or coalescing around the impendingmagma conduit for volcanic eruptions (Liu et al., 2014).Observing such stress–relaxation decreases requires sufficientshear-wave source events immediately before the impendingevent, and these are not always available so that observations ofstress–relaxation are less robust.

Characteristic stress–accumulation increases in SWStime-delays, before earthquakes, have been recognised on the 28time-delay diagrams before 17 earthquakes listed in Table 1 rang-ing in magnitude from a MI 1.7 swarm-event in North Iceland(Fig. 1, No. 1) (Gao and Crampin, 2004) to the 2004 Mw 9.2Sumatra Earthquake (Fig. 1, Nos. 18a-to-18g) (Crampin and Gao,2012). One earthquake seismogram (Fig. 1, No. 12) shows stress–relaxation but stress–accumulation is hidden by earlier earth-quakes (Fig. 1, No. 13).

Stress–accumulation increases are typically observed at seismicstations whenever there is appropriate source-to-recorder geome-try and impending larger earthquakes. Stress–relaxation(crack-coalescence) decreases are less consistently observed: 16(62%) of the 26 stress–accumulations in Fig. 1 show stress–relax-ation; five (19%) possible stress–relaxations are hidden wherethere are insufficient small source-earthquakes immediatelybefore the impending event to show stress–relaxation; and thereare six earthquakes (23%), where increasing stress–accumulationappears to continue until the impending earthquake occurs.

Stress–relaxation is not well understood. Attributing decreasesto crack-coalescence may be too simplistic: different source nucle-ation processes may modify stress–relaxation; and the inescapablelarge (±80%) scatter in time-delays above small (source) earth-quakes (Crampin et al., 2004b) may disturb SWS time-delays atthe monitoring site sufficiently to hide possible stress–relaxationdecreases before impending larger earthquakes.

All changes in SWS time-delays noted in Table 1 were observedretrospectively apart from the two exceptions discussed inSection 2.1, above. Of the 26 records listed in Table 1, wherestress–accumulation was observed, 16 recorded stress–relaxationdecreases before earthquakes. Note that whenever the appropriatesource-to-receiver geometry above swarms of small earthquakes isavailable, stress–accumulation increases before large or largerearthquakes have always been observed. There are no knownexceptions (Crampin and Peacock, 2008).

Table 2 lists seismograms in Fig. 2 before three volcanic erup-tions where stress–accumulation increases have been observedretrospectively. Stress–accumulation increases, similar to earth-quakes, has been recognised on six seismograms before three vol-canic eruptions, of which five seismograms also show stress–relaxation decreases.

2.3. Goodness-of-fit and error bars

The well-understood ±80% scatter of SWS time-delays (Crampinet al., 2002, 2004b) means that scatter in the data is so large thatthe least-squares regressions lines in Figs. 1 and 2 have irrelevantgoodness-of-fit criteria. The value of the regression lines is justifiedby the uniformity of the diagrams in the Figs. 1 and 2 where, wesuggest, the regression lines in normalised displays show similaroverall behaviour for all earthquakes and eruptions irrespective


of the magnitude of the earthquake or eruption, the quality of therecorded time-delays, and the density and scatter of data points.

Meaningful error bars are difficult to determine invisually-assessed data. Consequently, error bars on SWStime-delay data points in Figs. 1 and 2 are based on earthquakelocation statistics and errors on the normalising individualray-path distances. In many cases these error bars are too smallto be visible. Details are in the individual references listed inTables 1 and 2.

3. Summary of retrospective stress-forecasts

3.1. Retrospective stress-forecasts of earthquakes

Fig. 1 plots in a uniform normalised format all 29 observed vari-ations with time of the durations of SWS time-delay variationsbefore the 18 earthquakes, listed in Table 1. These are observationsof: 16 possible retrospective stress-forecasts of earthquake timesand magnitudes, sometimes at more than one seismic station; withtwo exceptions (Table 1, Earthquakes Nos. 10 and 18) wherestress–accumulation was recognised before the event (Section 2.1).

The durations of the stress–accumulation increases in Fig. 1have been normalised so that the rates of increase can be directlycompared. All seismic stations [except Fig. 1, No. 12, M 5.3 andFig. 1, No. 13, M 5.2 and M 5.9, where stress–accumulation washidden by earlier earthquakes], show uniform (least-squareregression-line) stress–accumulation increases before 17 earth-quakes (two in real time). This is in the presence of the unavoidable±80% scatter in SWS time-delays. These variations can be modelledas stress–accumulation before earthquakes, as expected in theNew Geophysics of a critically-microcracked rock mass (Crampin,1999, 2006; Crampin and Gao, 2013), but are inexplicable in termsof conventional sub-critical geophysics without devising specialcases for each observation.

As discussed above, although stress–accumulation iswell-understood and increases are consistently observed, stress–relaxation decreases are less robustly observed. As noted inSection 2.2, stress–relaxation decreases are present in 62% of thestress–accumulations, 19% are hidden by lack of source earth-quakes, and 23% show increases continuing until the impendingearthquake occurs without indicating stress–relaxation. Stress–re-laxation is not a well understood phenomenon.

3.2. Retrospective stress-forecasts of volcanic eruptions

Using the same normalised formats as in Fig. 1, Fig. 2 plots thedurations of the observed variations of SWS time-delays aboveswarms of small earthquakes before and after three volcanic erup-tions (listed in Table 2) where stress–accumulation and stress–re-laxation in SWS time-delays have been observed retrospectively.Other observations of changes in SWS before and after volcaniceruptions have been reported (Miller and Savage, 2001; Gerstand Savage, 2004; Keats et al., 2011; Johnson and Poland, 2013;amongst others). Unfortunately, these other observations do nothave the consistent source-to-recorder-geometry (within theshear-wave window at the free surface) required for analysis ofthe stress–accumulation and stress–relaxation as in Figs. 1 and 2.Consequently, these other observations of changes in SWS beforeeruptions cannot be easily analysed or interpreted.

Interactions with the topographically irregular free-surface andsub-surface around volcanoes make the behaviour of SWS beforevolcanic eruptions more complicated than before most earth-quakes. Consequently, each of the three examples in Fig. 2,Table 2, has strong individual characteristics. Fig. 2, Nos. 1a and1c are of the 1996 Gjálp eruption beneath the Vatnajökull Ice

Cap �260 km ENE of BJA and SAU in SW Iceland which showedstress–accumulation at Stations BJA and SAU (Volti and Crampin,2003a, 2003b). There were no source events beneath BJA immedi-ately before the eruption so the typical stress–relaxation decreasebefore earthquakes is only visible at SAU (Fig. 2, No. 1c).

Following the 1996 Gjálp, Vatnajökull, eruption, SWStime-delays measured at BJA showed an average decrease of�2 ms/km/year which lasted 2 years (Fig. 2, No. 1b), which is inter-preted as stress–relaxation as the Mid-Atlantic Ridge adjusts to thestress released by the Gjálp fissure eruption above the magmaticplume beneath the Vatnajökull Ice Cap. Variations in SWStime-delays for stress–accumulation before earthquakes is super-imposed on this widespread average decrease: these local varia-tions labelled (i)–(v) in Fig. 2, No. 1b, refer to earthquakes Fig. 1,Nos. 6, 8, 3, 11, and 10, respectively, which vary in magnitude fromM 3.4 to 5.1.

The SWS time-delays above small earthquakes before the 2001flank eruption of Mount Etna, Sicily, showed both stress–accumu-lation and stress–relaxation at two stations ESP and MNT (Fig. 2,Nos. 2 and 2b) (Bianco et al., 2006). Both stations were within�2 km either side of the flank eruption.

Changes in SWS before the 2010 Eyjafjallajökull eruption, SWIceland, were monitored retrospectively at Station GOD, �8 km

Fig. 3. Variations of logarithms (base 10) of duration in days against earthquakemagnitude of SWS time-delays as specified in Table 1 for: (a) stress–accumulationincreases; and (b) stress–relaxation (crack-coalescence) decreases.


east of the flank eruption (Fig. 2, No. 3) (Liu et al., 2014).Eyjafjallajökull was unusual in having two prolonged activephases: a flank eruption lasting �20 days (plotted yellow); and asummit eruption lasting �39 days (plotted blue) (Gudmundssonet al., 2011). The time-delays plotted in Fig. 2, No. 3, are from atight swarm of small events associated with the flank eruption sothe ray paths to GOD are almost identical which may be the reasonthere is less scatter than the ±80% usually observed. SWStime-delay variations within the shear-wave window at GOD(Fig. 2, No. 3) (Liu et al., 2014) before the Eyjafjallajökull eruption,are very similar to variations of SWS at BJA before the 1998 M 5successfully stress-forecast earthquake (discussed in Section 2.1):compare Fig. 1, No. 10a with Fig. 2, No. 3. Eyjafjallajökull is�90 km east of Station BJA, which has recorded stress–accumula-tion before seven earthquakes (Table 1, Nos. 3, 6, 8, 10, 11, 16, 18).

The strong similarities in stress variations before volcanic erup-tions and earthquakes would be a remarkable coincidence in con-ventional sub-critical geophysics, but is directly compatible withmany of the fundamentally-new properties expected of NewGeophysics (listed in Table A1) that are imposed on conventionalsub-critical geophysics. These similarities are strong support forseveral of the properties of the New Geophysics of acritically-microcracked crust and uppermost �400 km of the man-tle (particularly properties: P1 Self-similarity; P3 Uniformity; P7Universality; and P8 Sensitivity; in Table A1). These critical proper-ties are imposed on and may, in some circumstances, dominate thebehaviour of sub-critical conventional geophysics.

4. Durations of stress increases and stress decreases

The association of changes in SWS time-delays and earthquakesis confirmed by the near linearity of logarithms of durations ofboth stress–accumulations increases and stress–relaxationdecreases with earthquake magnitudes in Fig. 3. These are analo-gous to the linearity of the Gutenberg–Richter (1956) relationshipboth in earthquakes and in moonquakes (Crampin and Gao, 2015).Fig. 3 shows plots against magnitude of the log10 durations of: (a)stress–accumulation increases; and (b) stress–relaxation decreasesof all reliable data in Table 1. The scatter is not unexpected as noattempt has been made to use a unified magnitude scale.

In Fig. 3a, the stress–accumulation for larger earthquakesMP 6, say, physically extends into the upper mantle which isexpected to store and release stress in different ways from thecrust, especially in different plate-generation and subductionregimes, which may have different rates of stress generation.This probably accounts for the scatter of the two black ‘OtherMagnitude’ outliers on the right-hand-side of Fig. 3a. TheMS 6 out-lier (Fig. 1, No. 15) is the duration of stress–accumulation beforethe 1986 North Palm Springs Earthquake on the San AndreasFault in California, and the Mw 7.7 outlier (Fig. 1, No. 17) is theduration before the 1999 Chi-Chi Earthquake in Taiwan in thePhilippine Subduction Zone. The two plate boundaries are unlikelyto have similar rates of stress generation, and outliers are notunexpected.

Data for the open circles, in Fig. 3a, are the durations of thestress–accumulation increases before the 2004 Mw 9.2 SumatraEarthquake (Fig. 1, Nos. 18a–18g). The points should be at anunspecified larger duration (indicated by the arrow-head to theright), unspecified because the initial time-delays are hidden bynoisy data and may well extend to before data was available, soa good estimate of duration is not available. Extrapolation of theleast-squares line as plotted (correlation-coefficient 0.70) throughthe remaining data points reaches Mw 9.2 at �10,000 days(�27 years) which may be associated with the worldwide returnperiod of M �9 earthquakes (Crampin and Gao, 2012).

In contrast, in Fig. 3b for stress–relaxation decreases, the dura-tions (open circles) for the Sumatra Earthquake are believed to becorrectly located, which together with the duration of the Mw 7.7Chi-Chi Earthquake (the other ‘Magnitude Outlier’), give an upwardtrend beyond the end of the least-squares line(correlation-coefficient 0.78) through the durations for the smallerearthquakes. The rates of change are thought to be the rates atwhich cracks in fracture networks coalesce. Since fracture net-works for larger earthquakes extend into the hotter more-mobileupper-mantle it is expected that cracks in the mantle will coalescefaster than fracture networks in the cooler crust and will have rel-atively shorter durations leading to the upward trend for magni-tudes above M 7 in Fig. 3b.

The approximate linearity of log10 durations for earthquakesless than about M 7 of both stress–accumulation and stress–relax-ation would not be expected in conventional sub-critical geo-physics and shows property P1 Self-Similarity, which is strongsupport for New Geophysics. Indeed, the well-known linearity ofthe well-established Gutenberg–Richter relationship (Bak andTang, 1989; Main, 1995) is also a demonstration of the criticalityof New Geophysics which cannot be matched in conventionalsub-critical geophysics (Crampin and Gao, 2015). As discussed byCrampin and Gao (2015), it is well known that the linearity ofthe Gutenberg–Richter relationship implies criticality betweenthe numbers and magnitudes of earthquakes. Previously criticalityhas been treated as a somewhat isolated phenomenon not fullyunderstood. New Geophysics provides a physical basis and showsthat the criticality of closely-spaced stress-aligned fluid-saturatedmicrocracks pervades the crust and at least the uppermost�400 km of the mantle, with the properties in Table A1.

5. Implications for successful (real-time) stress-forecasting of

earthquakes and volcanic eruptions

5.1. Implications for successfully stress-forecasting earthquakes

Time-delay variations in the 29 listed SWS time-delay data sets(from 18 earthquakes) in Table 1 plotted in Fig. 1, where: oneearthquake (Fig. 1, No. 10a) was successfully stress-forecast inreal-time; one earthquake (Fig. 1, Nos. 18a–18g) had stress–accu-mulation recognised in real-time, but was not stress-forecast;and one earthquake (Fig. 1, No. 12) had stress–accumulation hid-den by earlier earthquakes. The remaining 15 earthquakes showstress–accumulation increases observed retrospectively. The varia-tions in SWS time-delays show that had time-delays been moni-tored in real time at seismic stations, where stress-forecasts wererecognised retrospectively, the 15 earthquakes had the potentialfor also being successfully stress-forecast in real-time. Successfulreal-time stress-forecasts would have been particularly likely inthose cases where there were sufficient shear-wave source data(sufficient small earthquakes in the swarm at the monitoring site)and the earthquakes were sufficiently large so that stress–relax-ation decreases with durations of several days could also have beenidentified, before the impending events. The time-delays in Fig. 1,Nos. 8, 9a, 15, 16a, 16b, 17, and of course 10a and 18, show thatthe times, magnitudes (and possibly fault-breaks) of these earth-quakes, could have been successfully stress-forecast in real timehad they been monitored before the events.

5.2. Implications for successful stress-forecasting volcanic eruptions

In general, the stress-induced variations of SWS time-delaysbefore eruptions are similar to the variations before earthquakesas expected in the properties in Table A1. In particular, the beha-viour of SWS time-delays before the 2010 flank eruption of


Eyjafjallajökull, SW Iceland at Station GOD (Fig. 2, No. 3) is directlysimilar to the behaviour of SWS before the 1998 successfullystress-forecast earthquake (Fig. 1, No. 10a) at Station BJA, some�90 km to the west of GOD. This correlation is discussed by Liuet al. (2014).

In this example, the stress–relaxation decrease at GOD reachesthe original level of time-delays (5–10 ms/km) at the beginning ofthe stress–accumulation increase as the flank eruption begins(Fig. 2, No. 3). This means that, if SWS had been monitored inreal-time, the time of the flank eruption could have beenstress-forecast to within one or two days. Although, numerousphenomena typically indicate ‘‘unrest’’ before impending erup-tions, ‘‘. . . immediate short-term eruption precursors may be sub-tle and difficult to detect’’ (Sigmundsson et al., 2010).Consequently, the stress–relaxation decrease in the right-hand dia-gram in Fig. 2, No. 3 may well be the most definitive short-termindication of the time of an impending eruption yet suggested(Liu et al., 2014).

6. Discussion

The uniformity of the stress–accumulation increases in SWStime-delays in Fig. 1, and stress–relaxation decreases inwell-over half the time-delay diagrams in Fig. 1, indicates thatthe time, magnitude, and in some cases location of many, perhapsmost, large or larger earthquakes could be stress-forecast, if suit-able sources of shear-waves were available and SWS monitoredbefore the earthquakes occurred. As currently understood, SWSitself gives no direct indication of impending earthquake location.However, if an earthquake is stress-forecast by SWS, other anoma-lous behaviour may lead to fault-break identification, as was thecase for the successfully real-time stress-forecast earthquake(Fig. 1, No. 10a) (Crampin et al., 1999, 2004a, 2008) – indicationof an impending earthquake from records at Station BJA, SWIceland, suggested correctly to co-author Ragnar Stefánsson(IMO) that the impending earthquake would occur on thefault-plane of an earthquake 6 months earlier (Fig. 1, No. 11a)where low-level seismic activity was still ongoing. This realizationallowed the time, magnitude, and fault-plane of the impending M 5earthquake to be correctly stress-forecast (Crampin et al., 1999,2004a, 2008).

Note that although stress–accumulation and stress–relaxationwas identified in Iceland before the 2004 Mw 9.2 SumatraEarthquake (Fig. 1, No. 18) (Crampin and Gao, 2012), similarchanges have not been recognised before the 2011 Mw 9Tohoku-Oki Earthquake, Japan. Unfortunately, financial constraintsmeant there has been no-one available to search the data. Howeverthe effects of the 2004 Mw 9.2 Sumatra Earthquake may be said tobe marginal (Fig. 1, No. 18) and the Tohoku-Oki Earthquake isslightly smaller but slightly (�10%) less distant. Probably morecrucially, half the great-circle path between Iceland andTohoku-Oki is along the convoluted margin between the Eurasiaand Arctic Plates, so that changes in SWS may not be easily trans-mitted towards Iceland instruments.

The problem of predicting an impending volcanic eruptions isdifferent from predicting earthquakes in that the location is typi-cally known (although the particular eruptive vent may not be)but, as with earthquakes, the time and magnitude are not known.The observed variations in SWS before Eyjafjallajökull eruptionwould have allowed the time of the flank eruption to bestress-forecast within one or two days (Fig. 2, No. 3), had SWStime-delays been monitored before the event. Eruptions are com-plicated and there is no agreed measure of the size of an eruptionas there is with the magnitudes of earthquakes.

Note that claims of criticality in the occurrence of earthquakesare not new. Bak and Tang (1989) suggested self-organised critical-ity and Main (1995) linked criticality with earthquake b-values.However, the hypothesis of New Geophysics is the first time thatcriticality replaces conventional sub-critical geophysics.

Note also the preponderance of references to Crampin and col-leagues. This is because changes in SWS can only be interpreted asimplied changes of stress above small earthquakes for the veryspecific source-to-recorder Band-1-and-Band-2 geometry indi-cated in Fig. B1 suggested by Crampin (1999). Only Crampin andcolleagues and Bianco et al. (2006) have used such geometry.SWS is a common crustal phenomenon and there are numerouspapers reporting observations of SWS above small earthquakesby other researchers (from Buchbinder, 1989, to Giannopouloset al., 2015), where some imply changes in SWS, but, without thespecific Band-1 and Band-2 geometry on a comparatively horizon-tal free-surface, the results are merely phenomenological and can-not be interpreted in terms of changes of stress.

7. Conclusions

(1) SWS demonstrates that stress-induced variations to microc-rack geometry before large or larger earthquakes is estab-lished so that the times, magnitudes, and in somecircumstances fault-planes, of large earthquakes can bestress-forecast if suitable source-to-receiver monitoringgeometry is available.

(2) Stress-induced variations before earthquakes and volcaniceruptions are similar so that the onset of eruptions can alsobe stress-forecast. If SWS had been monitored, the time ofthe onset of the 2010 disruptive ash-cloud eruption ofEyjafjallajökull volcano in Iceland could have beenstress-forecast to within one or two days.

(3) The New Geophysics of a critical-system of stress-alignedfluid-saturated microcracks in the Earth is established withimportant applications and implications both to earthquakeand volcanic eruption stress-forecasting (Crampin, 2004;Crampin and Gao, 2013) and to hydrocarbon seismics(Crampin, 2006).

Acknowledgements

The authors thank: Sheila Peacock and Francesca Bianco fornumerous discussions about shear-wave splitting which greatlyimproved the ms#. We also thank Brian Baptie, David Booth, andthe late Russ Evans, for valuable comments on the ms#. YuanGao was partially supported by the National Natural ScienceFoundation of China, Project 41174042. We thank the Director ofScience and Technology of the British Geological Survey (NERC)for approval to publish the paper.

Appendix A. A brief outline of New Geophysics

Stress-aligned shear-wave splitting (SWS) (illustrated schemat-ically in Fig. A1) is observed worldwide in the shear-wave window(Appendix B) above small earthquakes (Crampin, 1994; Crampinand Peacock, 2008) and in record sections in seismic exploration(Helbig and Thomsen, 2005). SWS shows that most rocks through-out the Earth’s crust (and uppermost �400 km of the mantle,Savage, 1999) are pervaded by stress-aligned fluid-saturatedmicrocracks (Crampin, 1994; Crampin and Peacock, 2008) [inter-granular films of hydrated melt in the upper mantle, Crampin,2003].


Fig. A2 shows that the degree of observed SWS (the percentageof shear-wave velocity anisotropy, SWVA), �1.5% to �4.5%, meansthat the microcracks in the Earth are so closely-spaced they vergeon failure at fracture criticality leading to fracturing and earth-quakes (Crampin, 1994). Phenomena that verge on failure in thisway are a New Physics (Davies, 1989) (hence a New Geophysics,Crampin, 1999, 2006) of critical-systems that imposes a range offundamentally-new properties on conventional sub-critical phy-sics (and geophysics, Crampin and Gao, 2013). Table A1 lists someof these fundamentally-new properties. The references in Crampinand Gao (2013) demonstrate that these properties have beenobserved many times over thousands-to-millions ofsource-to-receiver ray paths [only property P6 Controllability hasnot been tested]. We suggest this provides irrefutable prove thatNew Geophysics is valid proposition.

These properties answer several conundrums (Crampin et al.,2013; Crampin and Gao, 2013). In particular, the well-establishedGutenberg–Richter (1956) relationship demonstrates that someaspects of earthquakes are controlled by non-linear elasticity.The properties of New Geophysics explain how conventionalsub-critical purely-elastic geophysics can satisfy tens of thousandsof theoretical, analytical, and observational investigations of earth-quakes and seismic-wave propagation in the Earth, despiteGutenberg–Richter demonstrating that non-linear elasticityapplies to fundamental aspects of geophysical behaviour(Crampin and Gao, 2015).

Note that one cannot understand the new properties in Table A1from experience based solely on conventional sub-critical

geophysics. A paradigm shift in understanding is required(Crampin and Gao, 2013, 2015).

Appendix B. Ray-path geometry for monitoring stress–

accumulation and SWS time-delays within the shear-wave

window at the free-surface

Shear-waves have strong interactions at the free-surface (Boothand Crampin, 1985). In an isotropic half-space with a horizontalfree-surface, SH-waves have complete internal reflection at a hor-izontal free-surface at all incidence angles. In an isotropichalf-space with a horizontal free-surface, SV-waves have completeinternal reflection only for incidence angles less than the criticalangle for P-wave reflections, sinÿ1(b/a), which is �35° for aPoisson’s ratio of 025, where a and b are the P- and S-wave veloc-ities, respectively. Since an arbitrary shear-wave has componentsof both SV- and SH-motion, this critical angle defines the radiusof the shear-wave window for observing undisturbedshear-waves and SWS at a free-surface. For larger angles of inci-dence, P-waves are generated, and the amplitude andwave-forms of shear-waves observed at a free-surface are severelydistorted (Evans, 1984). Since SWS, in an anisotropic half-space, istypically a mixture of SH- and SV-motion, the waveforms,

Fig. A1. Schematic illustration of shear-wave splitting in the distributions of stress-aligned fluid-saturated microcracks throughout the Earth’s crust.

Fig. A2. Schematic (dimensionless) illustration of the observed percentages of shear-wave velocity-anisotropy (SWVA) interpreted as uniform distributions of equal-sizedparallel penny-shaped cracks, where e is crack density, and a is crack radius per unit cube. Fracture criticality is at the percolation threshold of e = 0.055 for stress-alignedmicrocracks, where the cracks are so closely-spaced they verge on fracturing if there is any disturbance Crampin (1994) and Crampin and Zatsepin (1997).

Table A1

Properties of the New Geophysics of critically-microcracked Earth [1].

Property Effects

P1) Self-similarity: Logarithmic plots of many properties are linear [1,2]P2) Monitorability: Behaviour can be monitored with shear-wave

splitting [1,3]P3) Uniformity: Statistical behaviour is more like other critical-

systems than it is to the underlying sub-criticalgeophysics [1,3]

P4) Calculability: Behaviour is more uniform than sub-criticalgeophysics, and can be modelled or calculated withthe equations of Anisotropic Poro-Elasticity (APE)[1,3,4,5,6,7]

P5) Predictability: If impending changes can be quantified, behaviourcan be calculated (Item 4, above) and predicted [1,7]

P6) Controllability: If conditions can be monitored (Item 2), calculated(Items 4), and modified by injection pressures, say(Item 5), then in principle the behaviour of the in siturock mass can be controlled by feedback (optimisingflow-directions by fluid-injection, say, inhydrocarbon production)

P7) Universality: Effects pervade all available space: upper- and lower-crust, upper mantle [1,8,9]

P8) Sensitivity: Butterfly’s-wing-effect sensitivity to minisculedifferences in initial conditions [5,8,9,10]

[1] Crampin and Gao (2013); [2] Gutenberg and Richter (1956); [3] Crampin andZatsepin (1997); [4] Crampin (1999); [5] Crampin et al. (2002); [6] Crampin et al.(2004b); [7] Angerer et al. (2002); [8] Volti and Crampin (2003b); [9] Crampin andGao (2012); [10] Lorenz (1972).


polarisations, and SWS time-delays are uninterpretable outside theshear-wave window (Booth and Crampin, 1985).

The geometry of SWS in stress-aligned vertical microcracksimposes further restrictions on observations of SWS at afree-surface. Fig. B1, Appendix B, is the ray-path geometry forobserving undisturbed waveforms of shear-waves and SWS instress-aligned fluid-saturated microcracks at a horizontalfree-surface. ABSCD is a crack-plane in a half-space with a uniformdistribution of parallel-vertical microcracks, where S is athree-component recorder on the horizontal free-surface. Band-1directions to the free-surface, where SWS time-delays are sensitiveto crack aspect-ratio (Crampin, 1999), are within the solid angleEFGH-to-S subtending 15° to 45° to the crack plane within theeffective shear-wave window. Band-2 directions to thefree-surface, where time-delays are dominated by crack-density(Crampin, 1999), are within the solid angle ADEHG-to-S to thecrack plane. Both Band-1 and Band-2 directions include equivalentsolid-angle directions reflected in the far side of the imaged crackplane.

Note that the effects of the shear-wave window for observa-tions of SWS (as well as isotropic observations of shear waves),are determined by the topography within about a wavelength ofthe recorder. Consequently, irregular surface topography placessevere constraints on measuring SWS time-delays and polarisa-tions on recorders in mountainous localities. SWS may beobserved, but will be impossible to interpret realistically unlessthe criteria in Fig. B1, can be met. Several of the 17 common falla-cies about SWS listed by Crampin and Peacock (2008) are the resultof neglecting the effects of the free-surface on observations andmeasurements of SWS.

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Fig. B1. The ray-path geometry for observing undisturbed waveforms of shear-waves and SWS measurements in stress-aligned fluid-saturated microcracks at ahorizontal free-surface in an isotropic half-space (after Crampin and Gao, 2013).


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