SCEC Award Number 13001 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Nonlinear attenuation in the uppermost few hundred meters and ambient intact rock and regolith as fragile geological features
Name Organization
Norman Sleep Stanford University
Other Participants Dr. Brittany Erickson (Stanford) will participate informally with numerical calculations.
SCEC Priorities 6, 4, 3 SCEC Groups GMP, Geology, EEII
Report Due Date 03/15/2014 Date Report Submitted N/A
Project Abstract
Strong Love waves propagate from the San Andreas Fault into Greater Los Angeles. Three-dimensional numerical calculations from the SCEC community indicate that these waves funnel through Whittier Narrows with high amplitudes. Estimates of their past and future peak ground velocities (PGV) require consideration of the nonlinear attenuation. Our semi-analytical methods aid and extend numerical results. The tendency of the shallow subsurface to self-organize (by low-cycle fatigue) couples past and future behavior. Love waves impose strain (PGV / phase velocity) conditions on the shallow subsurface. Dynamic stress is strain times shear modulus. Frictional failure occurs when dynamic stress exceeds frictional strength. For simplicity in explanation, the water table is at the surface and frictional strength increases linearly with depth; intact exhumed sedimentary rocks extend initially to the surface. Crack damage occurs down the maximum depth where dynamic stress can cause frictional failure. Cracks reduce the shear modulus above this depth, eventually to linearity with depth where the material barely becomes nonlinear (only a few new cracks form) with typical strong shaking. The shear modulus does not go all the way to zero at very shallow depths. Still larger rouge shaking would cause the full damaged depth range to become strongly nonlinear, greatly attenuating the wave. The depth to the water table is important. For example, pumping the water table down to several 100 m depth at Whittier Narrows from its current and pre-industrial shallow depth would nearly double the amplitude of the waves that pass unscathed toward Downtown Los Angeles.
Intellectual Merit Inferring the past and future amplitudes of strong seismic shaking is central to the SECC project. We infer past shaking from strong Love waves (expressed as peak ground velocity) from the shear wave velocity as a function of depth within the sedimentary basins of Greater Los Angeles. Failure, damage, and nonlinear attenuation occur when dynamic stress exceeds frictional strength. Conversely, the persistence of stiff intact rock at shallow depths is a fragile geological feature. Strong waves from San Andreas events funnel through Whittier Narrows. We will be able to infer the past peak amplitude of such waves once the shallow (upper few 100 m) shear wave velocity has been accurately measured in that locality, provided that past Love waves have in fact damaged the rock forming seismic regolith. In any case, future Love waves greater than our calculated past amplitude attenuate nonlinearly; diminished waves then will continue toward Downtown Los Angeles. Deep pumping down of the water table at Whittier Narrows would nearly double the amplitude of waves impinging on Downtown Los Angeles. In general, our results aid in formulating, extending, and understanding nonlinear numerical calculations of strong seismic waves.
Broader Impacts We extended our method to strong shaking by Rayleigh waves. Such shaking has occurred from earthquakes over geological time. Large ~50 km diameter) asteroid impacts caused much stronger shaking on the ancient Earth and the ancient Moon. Observed distal ground damage supports the reality of terrestrial impacts and a basis for evaluating putative more recent extreme waves. The tendency of shallow rock (and cold ice in the outer solar system) to self-organize from repeated damage so that shear modulus increases linearly with depth yields cracked seismic and tidal regolith, a potentially habitable environment for astrobiology. There is also tendency for damaged material to move down slope while shaking occurs. Hence the persistence of topographic relief on the modern Earth is a widespread fragile geological feature.
Exemplary Figure Figure 1: Schematic diagram of the effect of peak ground velocity (PGV) on nonlinear attenuation of Love waves. Peak dynamic stress is proportional to the shear modulus times PGV. Frictional strength (straight dashed line), for simplicity, increases linearly with depth; shaded depths and stresses imply linear behavior. Failure occurs whenever the dynamic stress exceeds the frictional strength. (A) The subsurface has been damaged by numerous strong Love waves. The material self-organizes so that the shear modulus increases linearly with depth between depths S and Z. The modulus cannot go all the way to zero near the surface and past seismic waves have not been strong enough for damage to occur below depth Z. A slight increase in PGV from just below that of typical past strong waves (thin solid line) to above that PGV (thick dotted line) causes the depth of failure to increase from S to Z with sudden onset of nonlinear attenuation. Typically strong waves barely cause failure as shown by the thick dotted line. (B) The shear modulus is constant with depth below a shallow layer. An increase in PGV modestly increases the depth of failure and nonlinear attenuation. Intact rock persists in the absence of damage from strong shaking.Modified from Sleep, N. H., and B. Erickson (2014) Nonlinear attenuation of S-waves and Love waves within ambient rock. Submitted to Geochem. Geophys. Geosyst.