Estimating yields from magnitudes possible vs probable
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Estimating Yields from Magnitudes Possible vs. Probable. Wayne N. Edwards Canadian Hazards Information Service, Natural Resources Canada. Magnitude – Yield potpourri.

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Estimating Yields from Magnitudes Possible vs. Probable

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Estimating yields from magnitudes possible vs probable

Estimating Yields from MagnitudesPossible vs. Probable

Wayne N. Edwards

Canadian Hazards Information Service, Natural Resources Canada


Magnitude yield potpourri

Magnitude – Yield potpourri

  • Many studies of empirical & theoretical relationships between seismic magnitudes and yield have been undertaken to seek a means of estimating any arbitrary test’s energy using multiple magnitude estimators.

  • Teleseismic Body wave magnitude: mb

    • mb = 3.79 + 0.85*log(Y) Aki et al. (1974) NTS - Rhyolite/Tuff

    • mb = 3.94 + 0.81*log(Y)Murphy (1981) NTS - Rhyolite/Tuff

    • mb = 5.06 + 0.509*log(Y) (>80 kt) Sykes & Cifuentes (1984)Amchitka Island

    • mb = 4.9206 + 0.5597*log(Y)Sykes & Wiggins (1986)Novaya Zemlya

    • mb = 4.262 + 0.973*log(Y) (5.3 < Y < 120 kt) Nuttli (1986)Amchitka Island

    • mb = 4.425 + 0.832*log(Y)Sykes (1996)STS - Salt

    • mb = 4.45 + 0.75*log(Y) Murphy (1996) STS – Granite

  • Surface wave magnitude: MS

    • Ms = 1.20 + 1.33*log(Y) (> 100 kt)Basham & Horner (1973) NTS – Rhyolite/Tuff

    • Ms = 2.14 + 0.84*log(Y) (< 100 kt)Basham & Horner (1973) NTS – Rhyolite/Tuff

    • Ms = 2.05 + 1.00*log(Y)Marshall & Basham (1972)

    • Ms = 2.16 + 0.95*log(Y)Sykes & Cifuentes (1984)Amchitka Island

    • Ms = 2.05+1.00*log(Y)Marshall et al. (1979)

    • Ms = 2.16 + 0.97*log(Y)Sykes & Wiggins (1986)Novaya Zemlya


Magnitude yield potpourri cont d

Magnitude – Yield potpourri cont’d

  • Regional body waves mb(Lg)

  • Developed by Nuttli (1973) to enable direct comparison of western & eastern earthquakes by accounting for anelastic attenuation in the North American crust using Lg phases. Adopted by Nuttli and others to investigate regional magnitude (thus yield) differences between NTS and STS explosions.

  • Regional (~1000 km) Body wave magnitude: mb(Lg)

    • Amplitude correct observations to 10 km and correct for anelastic attenuation via parameter γ

    • A(10 km) = A(Δ)(Δ /10)1/3[sin(Δ/111.1)/sin(10/111.1)]1/2 exp ( γ(Δ- 10) )where γ = πf / ( UQ ) with phase velocity, U, and quality factor Q.

    • After amplitude correction:mb_Lg = 5.0 + log( A(10km)/110 )

    • NOTE: Large geologic variations over a region requires station-dependent attenuation!

  • Using multiple stations around North America Nuttli (1986a) obtained:

    • mb_Lg = 4.307 + 0.765*log(Y) NTS – water saturated events (i.e. well coupled)

    • mb_Lg = 3.965 + 0.833*log(Y)NTS – unsaturated (dry events)

  • Applying the same methodology to STS explosions Nuttli (1986b) measured the discrepancy between NTS & STS magnitudes of 0.35 m.u. (low for NTS).

  • Chun et al., (2009) began to determine attenuation (γ) for NKTS stopping just short of a yield estimation.


What complicates estimation of yield from magnitude

What complicates Estimation of Yield from magnitude?

  • Geological setting of the test

    • Rock-type: Vp/Vs/ρ/porosity/water-content etc.

    • Earth structure  Q, t*, γ

  • Decoupling (DL)

    • Artificial cavity or circumstances of burial around device?

    • Poor coupling  lots of porosity, dry … etc.

    • DL = Wtrue/Wobs, were full decoupling is ~DF = 70 (Sykes 1996)

  • Depth of burial (DOB)

    • Requirement of containment  Z ≈ 122W1/3

    • Was it over-buried?

    • How is amplitude/period effected  magnitude

  • Natural scatter among tests in same region (calibration)


What complicates estimating yield

What complicates estimating yield?

  • Only a few underground test sites are well understood & “calibrated”. (NTS, STS)

    • Calibrations require independent knowledge of yields, emplacement conditions, geology etc.

    • Numerous known tests are to build reliable empirical relationships

  • Lacking details, new test sites are characterized by general comparison to calibrated sites.

    • Is this site NTS-like? STS-like?

    • Granite? Tuff? Rhyolite? Salt? Alluvium? Limestone?

    • Portability of relationships to new test site in question?


Possible vs probable

Possible vs. probable?

Range of possible yield estimates

(Wi)

Process to determine magnitude of the event : mb, Ms, mb(Lg)

Decoupling (DL)

Expected Velocity Model(s) (Geology)

Depth of Burial

(A,τ)

  • We can qualitatively estimate what is possible …

  • Providing lists of possible scenarios …

  • Can we narrow these estimates into what is probable?

    • Geological conditions – range of uncertainty, type(s), attenuation, etc.

    • Emplacement conditions – likelihood of possible depths?

    • Tamped/Decoupled – likelihood of cavity excavation/stability/desire?


Variable rock earth properties

Range of possible yield estimates

(Wi)

Variable Rock/Earth Properties

Process to determine magnitude of the event : mb, Ms, mb(Lg)

Decoupling (DL)

Expected Velocity Model(s) (Geology)

Depth of Burial

(A,τ)

(Reynolds, 1997)

1

t*/Q/γ

Rel, Rc, etc…

P1

0

Rock/Earth property


Depth of burial

Depth of Burial

Range of possible yield estimates

(Wi)

Process to determine magnitude of the event : mb, Ms, mb(Lg)

Decoupling (DL)

Expected Velocity Model(s) (Geology)

Depth of Burial

(A,τ)

  • Standard practices for explosion containment require a depth deep enough such that the explosion cavity, Rc, or any chimney formed afterward does not reach the surface.

  • Rc Depends upon rock-type (previous slide)

  • Containment depth scales with yield (W⅓)

  • Glasstone & Dolan (1977) : depth > 300 feet/kt ⅓ to contain chimney, but may still leak radioactivity if close to surface so …

  • Determined by material strength above cavity

  • NTS: Scaled Depth = 400 feet/kt ⅓ or 122 m/kt ⅓

Z


Decoupling

Decoupling

Range of possible yield estimates

(Wi)

Process to determine magnitude of the event : mb, Ms, mb(Lg)

Decoupling (DL)

Expected Velocity Model(s) (Geology)

Depth of Burial

(A,τ)

Still large uncertainty in the feasibility of decoupling a nuclear explosion.

Requirement of excavating a cavity large enough to extend to the elastic radius of even a small explosion is daunting in any material.

Large uncertainties remain in Rel for explosion in specific media.

Several scenarios, only limited have been attempted (only in salt).

Probability of decoupling ≈ Pdecouple(z(W), E, μ,ρ)

Rc

Rel

Elastic radius

Cavity radius

Rc = 16.3 W0.29 (E0.62ρ-0.24μ-0.67) z-0.11

(Mueller & Murphy 1971)


Final estimates of yield

Final Estimates of Yield

Pgeology × Pattenuation × Pburial × Pdecoupling

Empirical/Theoretical magnitude/yield relations

Probability grid of possible yields

Rock Type X (Vp±,Vs±,ρ±)

Decoupling

Final goal is to provide a realistic range of estimates, based on current/best knowledge, as to what Yields are PROBABLE with a quantifiable measure of certainty.

likely

Depth of Burial

Probability (%)

unlikely


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