Attenuation tomography. Modelling regional love waves: Imperial Valley to Pasadena

Abstract to Part I

The inverse problem of seismic wave attenuation is solved by an iterative back-projection method. The seismic wave quality factor, Q, can be estimated approximately by inverting the S-to-P amplitude ratios. Effects of various uncertain ties in the method are tested and the attenuation tomography is shown to be useful in solving for the spatial variations in attenuation structure and in estimating the effective seismic quality factor of attenuating anomalies.

Back-projection attenuation tomography is applied to two cases in southern California: Imperial Valley and the Coso-Indian Wells region. In the Coso-Indian Wells region, a highly attenuating body (S-wave quality factor (Q_β ≈ 30) coincides with a slow P-wave anomaly mapped by Walck and Clayton (1987). This coincidence suggests the presence of a magmatic or hydrothermal body 3 to 5 km deep in the Indian Wells region. In the Imperial Valley, slow P-wave travel-time anomalies and highly attenuating S-wave anomalies were found in the Brawley seismic zone at a depth of 8 to 12 km. The effective S-wave quality factor is very low (Q_β ≈ 20) and the P-wave velocity is 10% slower than the surrounding areas. These results suggest either magmatic or hydrothermal intrusions, or fractures at depth, possibly related to active shear in the Brawley seismic zone.

No-block inversion is a generalized tomographic method utilizing the continuous form of an inverse problem. The inverse problem of attenuation can be posed in a continuous form , and the no-block inversion technique is applied to the same data set used in the back-projection tomography. A relatively small data set with little redundancy enables us to apply both techniques to a similar degree of resolution. The results obtained by the two methods are very similar. By applying the two methods to the same data set, formal errors and resolution can be directly computed for the final model, and the objectivity of the final result can be enhanced.

Both methods of attenuation tomography are applied to a data set of local earthquakes in Kilauea, Hawaii, to solve for the attenuation structure under Kilauea and the East Rift Zone. The shallow Kilauea magma chamber, East Rift Zone and the Mauna Loa magma chamber are delineated as attenuating anomalies. Detailed inversion reveals shallow secondary magma reservoirs at Mauna Ulu and Puu Oo, the present sites of volcanic eruptions. The Hilina Fault zone is highly attenuating, dominating the attenuating anomalies at shallow depths. The magma conduit system along the summit and the East Rift Zone of Kilauea shows up as a continuous supply channel extending down to a depth of approximately 6 km. The Southwest Rift Zone, on the other hand, is not delineated by attenuating anomalies, except at a depth of 8-12 km, where an attenuating anomaly is imaged west of Puu Kou. The Ylauna Loa chamber is seated at a deeper level (about 6-10 km) than the Kilauea magma chamber. Resolution in the Mauna Loa area is not as good as in the Kilauea area, and there is a trade-off between the depth extent of the magma chamber imaged under Mauna Loa and the error that is due to poor ray coverage. Kilauea magma chamber, on the other hand, is well resolved, according to a resolution test done at the location of the magma chamber.

Abstract to Part II

Long period seismograms recorded at Pasadena of earthquakes occurring along a profile to Imperial Valley are studied in terms of source phenomena (e.g., source mechanisms and depths) versus path effects. Some of the events have known source parameters, determined by teleseismic or near-field studies, and are used as master events in a forward modeling exercise to derive the Green's functions (SH displacements at Pasadena that are due to a pure strike-slip or dip-slip mechanism) that describe the propagation effects along the profile. Both timing and waveforms of records are matched by synthetics calculated from 2-dimensional velocity models. The best 2-dimensional section begins at Imperial Valley with a thin crust containing the basin structure and thickens towards Pasadena. The detailed nature of the transition zone at the base of the crust controls the early arriving shorter periods (strong motions), while the edge of the basin controls the scattered longer period surface waves. From the waveform characteristics alone, shallow events in the basin are easily distinguished from deep events, and the amount of strike-slip versus dip-slip motion is also easily determined. Those events rupturing the sediments, such as the 1979 Imperial Valley earthquake, can be recognized easily by a late-arriving scattered Love wave that has been delayed by the very slow path across the shallow valley structure.

Steady capillary-gravity waves on deep water

The properties of capillary-gravity waves of permanent form on deep water are studied. Two different formulations to the problem are given. The theory of simple bifurcation is reviewed. For small amplitude waves a formal perturbation series is used. The Wilton ripple phenomenon is reexamined and shown to be associated with a bifurcation in which a wave of permanent form can double its period. It is shown further that Wilton's ripples are a special case of a more general phenomenon in which bifurcation into subharmonics and factorial higher harmonics can occur. Numerical procedures for the calculation of waves of finite amplitude are developed. Bifurcation and limit lines are calculated. Pure and combination waves are continued to maximum amplitude. It is found that the height is limited in all cases by the surface enclosing one or more bubbles. Results for the shape of gravity waves are obtained by solving an integra-differential equation. It is found that the family of solutions giving the waveheight or equivalent parameter has bifurcation points. Two bifurcation points and the branches emanating from them are found specifically, corresponding to a doubling and tripling of the wavelength. Solutions on the new branches are calculated.

Sea-level rise in Hawaii: Implications for future shoreline locations and Hawaii coastal management

Management of coastal development in Hawaii is based on the location of the certified shoreline, which is representative of the upper limit of marine inundation within the last several years. Though the certified shoreline location is significantly more variable than long-term erosion indicators, its migration will still follow the coastline's general trend. The long-term migration of Hawaii’s coasts will be significantly controlled by rising sea level. However, land use decisions adjacent to the shoreline and the shape and nature of the nearshore environment are also important controls to coastal migration. Though each of the islands has experienced local sea-level rise over the course of the last century, there are still locations across the islands of Kauai, Oahu, and Maui, which show long- term accretion or anomalously high erosion rates relative to their regions. As a result, engineering rules of thumb such as the Brunn rule do not always predict coastal migration and beach profile equilibrium in Hawaii. With coastlines facing all points of the compass rose, anthropogenic alteration of the coasts, complex coastal environments such as coral reefs, and the limited capacity to predict coastal change, Hawaii will require a more robust suite of proactive coastal management policies to weather future changes to its coastline. Continuing to use the current certified shoreline, adopting more stringent coastal setback rules similar to Kauai County, adding realistic sea-level rise components for all types of coastal planning, and developing regional beach management plans are some of the recommended adaptation strategies for Hawaii. (PDF contains 4 pages)

Reforming state-level coastal management and development policies: strategic retreat as an innovative, proactive and equitable coastal environmental management strategy

Atlantic and Gulf Coast shorelines include some of the most unique and biologically rich ecosystems in the United States that provide immeasurable aesthetic, habitat and economic benefits. Natural coastal ecosystems, however, are under increasing threat from rampant and irresponsible growth and development. Once a boon to local economies, complex natural forces – enhanced by global climate change and sea level rise - are now considered hazards and eroding the very foundation upon which coastal development is based. For nearly a century, beach restoration and erosion control structures have been used to artificially stabilize shorelines in an effort to protect structures and infrastructure. Beach restoration, the import and emplacement of sand on an eroding beach, is expensive, unpredictable, inefficient and may result in long-term environmental impacts. The detrimental environmental impacts of erosion control structures such as sea walls, groins, bulkheads and revetments include sediment deficits, accelerated erosion and beach loss. These and other traditional responses to coastal erosion and storm impacts- along with archaic federal and state policies, subsidies and development incentives - are costly, encourage risky development, artificially increase property values of high-risk or environmentally sensitive properties, reduce the post-storm resilience of shorelines, damage coastal ecosystems and are becoming increasingly unsustainable. Although communities, coastal managers and property owners face increasingly complex and difficult challenges, there is an emerging public, social and political awareness that, without meaningful policy reforms, coastal ecosystems and economies are in jeopardy. Strategic retreat is a sustainable, interdisciplinary management strategy that supports the proactive, planned removal of vulnerable coastal development; reduces risk; increases shoreline resiliency and ensures long term protection of coastal systems. Public policies and management strategies that can overcome common economic misperceptions and promote the removal of vulnerable development will provide state and local policy makers and coastal managers with an effective management tool that concomitantly addresses the economic, environmental, legal and political issues along developed shorelines. (PDF contains 4 pages)

Building a sustainable community of coastal leaders to deal with sea level rise and inundation

Sea level rise and inundation were stated to be the highest priorities in the community-developed Ocean Research Priorities Plan and Implementation Strategy in 2005. Although they remain stated priorities, very few resources have been allocated towards this challenge. Inundation poses a substantial risk to many coastal communities, and the risk is projected to increase because of continued development, changes in the frequency and intensity of inundation events, and acceleration in the rate of sea-level rise along our vulnerable shorelines. (PDF contains 4 pages) There is an increasing urgency for federal and state governments to focus on the local and regional levels and consistently provide the information, tools, and methods necessary for adaptation. Calls for action at all levels acknowledge that a viable response must engage federal, state and local expertise, perspectives, and resources in a coordinated and collaborative effort. A workshop held in December 2000 on coastal inundation and sea level rise proposes a shared framework that can help guide where investments should be made to enable states and local governments to assess impacts and initiate adaptation strategies over the next decade.

Two mechanisms for population inversion via two-colour coherent excitation in three-level systems

We analyse the physical origin of population inversion via continuous wave two-colour coherent excitation in three-level systems by dressing the inverted transition. Two different mechanisms are identified as being responsible for the population inversion. For V-configured systems and cascade (E) configured systems with inversion on the lower transition, the responsible mechanism is the selective trapping of dressed states, and the population inversion approaches the ideal value of 1. For Lambda-configured systems and Xi-configured systems with inversion on the upper transition, population inversion is based on the selective excitation of dressed states, with the population inversion tending towards 0.5. As the essential difference between these two mechanisms, the selective trapping of dressed states occurs in systems with strong decay into dressed states while the selective excitation appears in systems with strong decay out of dressed states.

Stormsmart coasts in action: Two case studies of local level climate change adaptation

Coastal communities throughout the United States have dealt with the devastating effects of storms for centuries, however today’s threats are greater due to three factors. First, the population along the coastline has grown, and is projected to increase.i Additionally, past land use management decisions in the coastal zone have rarely led to the greatest protection from threats. Finally, climate change is predicted to affect coastal areas by accelerating current sea level rise rates and possibly increasing storm intensity.ii These factors compounded together mean that coastal communities are facing a very dangerous situation that threatens economies and human life. (PDF contains 4 pages)

Improving reporting of uncertainties in sea level rise assessments

Sea level rise (SLR) assessments are commonly used to identify the extent that coastal populations are at risk to flooding. However, the data and assumptions used to develop these assessments contain numerous sources and types of uncertainty, which limit confidence in the accuracy of modeled results. This study illustrates how the intersection of uncertainty in digital elevation models (DEMs) and SLR lead to a wide range of modeled outcomes. SLR assessments are then reviewed to identify the extent that uncertainty is documented in peer-reviewed articles. The paper concludes by discussing priorities needed to further understand SLR impacts. (PDF contains 4 pages)

Liquid silicate equation of state : using shock waves to understand the properties of the deep Earth

The equations of state (EOS) of several geologically important silicate liquids have been constrained via preheated shock wave techniques. Results on molten Fe₂SiO₄ (fayalite), Mg₂SiO₄ (forsterite), CaFeSi₂O₆ (hedenbergite), an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆ (anorthite-hedenbergite), and an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆-CaMgSi₂O₆(anorthite-hedenbergite-diopside) are presented. This work represents the first ever direct EOS measurements of an iron-bearing liquid or of a forsterite liquid at pressures relevant to the deep Earth (> 135 GPa). Additionally, revised EOS for molten CaMgSi₂O₆ (diopside), CaAl₂Si₂O₈ (anorthite), and MgSiO₃ (enstatite), which were previously determined by shock wave methods, are also presented.

The liquid EOS are incorporated into a model, which employs linear mixing of volumes to determine the density of compositionally intermediate liquids in the CaO-MgO-Al₂O₃-SiO₂-FeO major element space. Liquid volumes are calculated for temperature and pressure conditions that are currently present at the core-mantle boundary or that may have occurred during differentiation of a fully molten mantle magma ocean.

The most significant implications of our results include: (1) a magma ocean of either chondrite or peridotite composition is less dense than its first crystallizing solid, which is not conducive to the formation of a basal mantle magma ocean, (2) the ambient mantle cannot produce a partial melt and an equilibrium residue sufficiently dense to form an ultralow velocity zone mush, and (3) due to the compositional dependence of Fe2+ coordination, there is a threshold of Fe concentration (molar X_Fe ≤ 0.06) permitted in a liquid for which its density can still be approximated by linear mixing of end-member volumes.

Neural routing circuits for forming invariant representations of visual objects

This thesis presents a biologically plausible model of an attentional mechanism for forming position- and scale-invariant representations of objects in the visual world. The model relies on a set of control neurons to dynamically modify the synaptic strengths of intra-cortical connections so that information from a windowed region of primary visual cortex (Vl) is selectively routed to higher cortical areas. Local spatial relationships (i.e., topography) within the attentional window are preserved as information is routed through the cortex, thus enabling attended objects to be represented in higher cortical areas within an object-centered reference frame that is position and scale invariant. The representation in V1 is modeled as a multiscale stack of sample nodes with progressively lower resolution at higher eccentricities. Large changes in the size of the attentional window are accomplished by switching between different levels of the multiscale stack, while positional shifts and small changes in scale are accomplished by translating and rescaling the window within a single level of the stack. The control signals for setting the position and size of the attentional window are hypothesized to originate from neurons in the pulvinar and in the deep layers of visual cortex. The dynamics of these control neurons are governed by simple differential equations that can be realized by neurobiologically plausible circuits. In pre-attentive mode, the control neurons receive their input from a low-level "saliency map" representing potentially interesting regions of a scene. During the pattern recognition phase, control neurons are driven by the interaction between top-down (memory) and bottom-up (retinal input) sources. The model respects key neurophysiological, neuroanatomical, and psychophysical data relating to attention, and it makes a variety of experimentally testable predictions.