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Roger D. Borcherdt

Publications and source records attributed to Roger D. Borcherdt.

At least 19 recordsLinked to original sources
USGS2024

Seismic tomography 2023

Seismic tomography is the most abundant source of information about the internal structure of the Earth at scales ranging from a few meters to thousands of kilometers. It constrains the properties of active volcanoes, earthquake fault zones, deep reservoirs and storage sites, glaciers and ice sheets, or the entire globe. It contributes to outstanding societal problems related to natural hazards, resource exploration, underground storage, and many more. The recent advances in seismic tomography are being translated to nondestructive testing, medical ultrasound, and helioseismology. Nearly 50 yr after its first successful applications, this article offers a snapshot of modern seismic tomography. Focused on major challenges and particularly promising research directions, it is intended to guide both Earth science professionals and early‐career scientists. The individual contributions by the coauthors provide diverse perspectives on topics that may at first seem disconnected but are closely tied together by a few coherent threads: multiparameter inversion for properties related to dynamic processes, data quality, and geographic coverage, uncertainty quantification that is useful for geologic interpretation, new formulations of tomographic inverse problems that address concrete geologic questions more directly, and the presentation and quantitative comparison of tomographic models. It remains to be seen which of these problems will be considered solved, solved to some extent, or practically unsolvable over the next decade.

Bulletin of the Seismological Society of America↗
USGS2024

Preliminary implications of viscoelastic ray theory for anelastic seismic tomography models

The recent developments in general viscoelastic ray theory provide a rigorous mathematical framework for anelastic seismic tomography. They provide closed‐form solutions of forward ray‐tracing and simple inverse problems for anelastic horizontal and spherical layered media with material gradients. They provide ray‐tracing computation algorithms valid for all angles of incidence that account for changes in wave speed, attenuation, and trajectory of anelastic P and S body waves induced by anelastic boundaries. They account for theoretical predictions that seismic waves refract as inhomogeneous waves across anelastic boundaries for all angles of incidence, which in turn accounts for energy carried by plane waves along seismic boundaries at head wave critical angles and wide‐angle refracted (WAR) ray paths that are not predicted by elastic models. Exact viscoelastic ray‐tracing numerical results for various models provide examples that illustrate the effects of anelastic boundaries on the travel times and amplitudes of seismic waves. They show the effects are strongly dependent on angle of incidence. For near‐critical and wide angles of incidence the anelastic effects on travel times and amplitudes can be large and are not explained by elastic ray theory, but the effects on travel times can be relatively small and difficult to distinguish from those for elastic media for pre‐near‐critical angles of incidence. The results for some models indicate that reflected anelastic WAR waves may be observable at the surface and possibly account for some prominent seismic arrivals not explained by elasticity. These preliminary results suggest that the application of exact viscoelastic ray‐tracing computation algorithms to exploration and teleseismic data sets can reveal new insights regarding the properties and distribution of anelastic materials in the Earth.

Bulletin of the Seismological Society of America↗
USGS2024

Wave propagation in layered soil deposits

Recent advances in the general theory of viscoelastic waves and rays in layered media provide a rigorous mathematical framework for site-specific, soil-response models used for earthquake resistant design. The advances provide general closed-form anelastic solutions for the classic problems of the response of a stack of soil layers to S and P waves, ray theory for reflected and refracted waves, Rayleigh- and Love-Type surface waves, and head waves. These general solutions valid for anelastic media regardless of the amount of material damping yield new insights regarding the characteristics of seismic waves and their ray paths that are not provided by conventional models. They provide corresponding numerical ground-response models and ray-tracing computation algorithms that account for changes in velocity and attenuation of anelastic waves associated with changes in inhomogeneity of the waves induced by anelastic soil and soil-rock boundaries. These anelastic effects manifest themselves as variations in amplitude response, amplitude attenuation, raypath location, and travel time as observed at the Earth’s surface. Implications of these anelastic effects for soil-response models used for earthquake resistant design are provided herein.

Conference Paper↗
USGS2015

Simulation of acceleration field of the Lushan earthquake (Ms7.0, April 20, 2013, China)

The acceleration field of the Lushan earthquake (Ms7.0, April 20, 2013, China) is simulated using a new modified version of the stochastic finite-fault method (EXSIM) based on a dynamic corner frequency approach. To incorporate the effect of heterogeneous slip distribution on the variation of source spectrum, we adopt an empirical source spectral model and derive the corresponding dynamic parameters, which vary with the cumulative seismic moment of the ruptured area. The new modified method is validated by: 1) comparison of the simulation results with those obtained from the EXSIM method using near-fault ground motion data of the 1994 Northridge earthquake; 2) comparison of simulated PGA contour map inferred from synthetic time histories at 315 grid locations with the observed PGA shakemap for the 2013 Lushan earthquake; 3) comparison of simulated PGA with those predicted by ground-motion prediction equations (GMPEs); and 4) comparison of simulated time histories with observed acceleration records at six strong motion stations during the mainshock of the Lushan earthquake, in which local site response is considered in the simulation. These comparisons confirm the validity of the new simulation procedure for purposes of regional strong ground motion estimation. Limitations of the procedure in modeling the phasing of different arrivals in the seismic signal and near-surface response of geologic deposits are discussed.

Lushan↗
USGS2015

NGA-West 2 GMPE average site coefficients for use in earthquake-resistant design

Site coefficients corresponding to those in tables 11.4–1 and 11.4–2 of Minimum Design Loads for Buildings and Other Structures published by the American Society of Civil Engineers (Standard ASCE/SEI 7-10) are derived from four of the Next Generation Attenuation West2 (NGA-W2) Ground-Motion Prediction Equations (GMPEs). The resulting coefficients are compared with those derived by other researchers and those derived from the NGA-West1 database. The derivation of the NGA-W2 average site coefficients provides a simple procedure to update site coefficients with each update in the Maximum Considered Earthquake Response MCER maps. The simple procedure yields average site coefficients consistent with those derived for site-specific design purposes. The NGA-W2 GMPEs provide simple scale factors to reduce conservatism in current simplified design procedures.

Open-File Report↗
USGS2014

Implications of next generation attenuation ground motion prediction equations for site coefficients used in earthquake resistant design

Proposals are developed to update Tables 11.4-1 and 11.4-2 of Minimum Design Loads for Buildings and Other Structures published as American Society of Civil Engineers Structural Engineering Institute standard 7-10 (ASCE/SEI 7–10). The updates are mean next generation attenuation (NGA) site coefficients inferred directly from the four NGA ground motion prediction equations used to derive the maximum considered earthquake response maps adopted in ASCE/SEI 7–10. Proposals include the recommendation to use straight-line interpolation to infer site coefficients at intermediate values of (average shear velocity to 30-m depth). The NGA coefficients are shown to agree well with adopted site coefficients at low levels of input motion (0.1 g) and those observed from the Loma Prieta earthquake. For higher levels of input motion, the majority of the adopted values are within the 95% epistemic-uncertainty limits implied by the NGA estimates with the exceptions being the mid-period site coefficient, F v , for site class D and the short-period coefficient, F a , for site class C, both of which are slightly less than the corresponding 95% limit. The NGA data base shows that the median value of 913 m/s for site class B is more typical than 760 m/s as a value to characterize firm to hard rock sites as the uniform ground condition for future maximum considered earthquake response ground motion estimates. Future updates of NGA ground motion prediction equations can be incorporated easily into future adjustments of adopted site coefficients using procedures presented herein. Published 2014. This article is a U.S. Government work and is in the public domain in the USA. Earthquake Engineering & Structural Dynamics published by John Wiley & Sons Ltd.

Earthquake Engineering and Structural Dynamics↗
USGS2012

Energy and plane waves in linear viscoelastic media

The mathematical framework for describing plane waves in elastic and linear anelastic media is presented. Theoretical results suggest that the nature of plane waves in anelastic materials is distinctly different from the nature of plane waves in elastic materials. In elastic media the only type of inhomogeneous plane wave ( P or S ) that can propagate is one for which planes of constant phase are perpendicular to planes of constant amplitude. However, in anelastic media this is the only type of inhomogeneous wave that cannot propagate. For an inhomogeneous P or S plane wave the particle motion is elliptical, the velocity is less than that of a corresponding homogeneous wave, the maximum attenuation is greater than that of a corresponding homogeneous wave, and the direction of maximum energy flow is not the direction of phase propagation. Expressions for the energy flux, energy densities, dissipated energy, stored energy, and Q −1 are derived from an explicit energy conservation relation, valid for an arbitrary steady state viscoelastic radiation field. Each energy expression is valid for homogeneous or inhomogeneous P or S plane waves in elastic or linear anelastic media.

Journal of Geophysical Research↗
USGS2012

Short-period strain (0.1–105 s): Near-source strain field for an earthquake (ML 3.2) near San Juan Bautista, California

Measurements of dilational earth strain in the frequency band 25–10 −5 Hz have been made on a deep borehole strainmeter installed near the San Andreas fault. These data are used to determine seismic radiation fields during nuclear explosions, teleseisms, local earthquakes, and ground noise during seismically quiet times. Strains of less than 10 −10 on these instruments can be clearly resolved at short periods (< 10 s) and are recorded with wide dynamic range digital recorders. This permits measurement of the static and dynamic strain variations in the near field of local earthquakes. Noise spectra for earth strain referenced to 1 (strain) 2 /Hz show that strain resolution decreases at about 10 dB per decade of frequency from −150 dB at 10 −4 Hz to −223 dB at 10 Hz. Exact expressions are derived to relate the volumetric strain and displacement field for a homogeneous P wave in a general viscoelastic solid as observed on colocated dilatometers and seismometers. A rare near-field recording of strain and seismic velocity was obtained on May 26, 1984, from an earthquake ( M L 3.2) at a hypocentral distance of 3.2 km near the San Andreas fault at San Juan Bautista, California. While the data indicate no precursory strain release at the 5 × 10 −11 strain level, a coseismic strain release of 1.86 nanostrain was observed. This change in strain is consistent with that calculated from a simple dislocation model of the event. Ground displacement spectra, determined from the downhole strain data and instrument-corrected surface seismic data, suggest that source parameters estimated from surface recordings may be contaminated by amplification effects in near-surface low-velocity materials.

California↗
USGS2012

Influence of welded boundaries in anelastic media on energy flow, and characteristics of P, S-I, and S-II waves: Observational evidence for inhomogeneous body waves in low-loss solids

A general computer code, developed to calculate anelastic reflection-refraction coefficients, energy flow, and the physical characteristics for general P , S -I, and S -II waves, quantitatively describes physical characteristics for wave fields in anelastic media that do not exist in elastic media. Consideration of wave fields incident on boundaries between anelastic media shows that scattered wave fields experience reductions in phase and energy speeds, increases in maximum attenuation and Q −1 , and directions of maximum energy flow distinct from phase propagation. Each of these changes in physical characteristics are shown to vary with angle of incidence. Finite relaxation times for anelastic media result in energy flow due to interaction of superimposed radiation fields and contribute to energy flow across anelastic boundaries for all angles of incidence. Agreement of theoretical and numerical results with laboratory measurements argues for the validity of the theoretical and numerical formulations incorporating inhomogeneous wave fields. The agreement attests to the applicability of the model and helps confirm the existence of inhomogeneous body waves and their associated set of distinct physical characteristics in the earth. The existence of such body waves in layered, low-loss anelastic solids implies the need to reformulate some seismological models of the earth. The exact anelastic formulation for a liquid-solid interface with no low-loss approximations predicts the existence of a range of angles of incidence or an anelastic Rayleigh window, through which significant amounts of energy are transmitted across the boundary. The window accounts for the discrepancy apparent between measured reflection data presented in early textbooks and predictions based on classical elasticity theory. Characteristics of the anelastic Rayleigh window are expected to be evident in certain sets of wide-angle, ocean-bottom reflection data and to be useful in estimating Q −1 for some ocean bottom reflectors.

Journal of Geophysical Research B: Solid Earth↗
USGS2012

Implications of NGA for NEHRP site coefficients

Three proposals are provided to update tables 11.4-1 and 11.4-2 of Minimum Design Loads for Buildings and Other Structures (7-10), by the American Society of Civil Engineers (2010) (ASCE/SEI 7-10), with site coefficients implied directly by NGA (Next Generation Attenuation) ground motion prediction equations (GMPEs). Proposals include a recommendation to use straight-line interpolation to infer site coefficients at intermediate values of ̅v s (average shear velocity). Site coefficients are recommended to ensure consistency with ASCE/SEI 7-10 MCE R (Maximum Considered Earthquake) seismic-design maps and simplified site-specific design spectra procedures requiring site classes with associated tabulated site coefficients and a reference site class with unity site coefficients. Recommended site coefficients are confirmed by independent observations of average site amplification coefficients inferred with respect to an average ground condition consistent with that used for the MCE R maps. The NGA coefficients recommended for consideration are implied directly by the NGA GMPEs and do not require introduction of additional models.

Open-File Report↗
USGS2012

VS30 – A site-characterization parameter for use in building Codes, simplified earthquake resistant design, GMPEs, and ShakeMaps

VS30, defined as the average seismic shear-wave velocity from the surface to a depth of 30 meters, has found wide-spread use as a parameter to characterize site response for simplified earthquake resistant design as implemented in building codes worldwide. VS30 , as initially introduced by the author for the US 1994 NEHRP Building Code, provides unambiguous definitions of site classes and site coefficients for site-dependent response spectra based on correlations derived from extensive borehole logging and comparative ground-motion measurement programs in California. Subsequent use of VS30 for development of strong ground motion prediction equations (GMPEs) and measurement of extensive sets of VS borehole data have confirmed the previous empirical correlations and established correlations of SVS30 with VSZ at other depths. These correlations provide closed form expressions to predict S30 V at a large number of additional sites and further justify S30 V as a parameter to characterize site response for simplified building codes, GMPEs, ShakeMap, and seismic hazard mapping.

Conference Paper↗
USGS2010

Reflection—refraction of general P- and type-I S-waves in elastic and anelastic solids

The reflection and refraction of general (homogeneous or inhomogeneous) plane P and type-I S ( SV ) body waves incident on plane boundaries are considered for general linear viscoelastic solids. Reflection—refraction laws, physical characteristics of the waves, and the nature of critical angles are examined in detail at welded boundaries and a free surface. General visco-elasticity with no low-loss approximations predicts that contrasts in intrinsic absorption at boundaries give rise to inhomogeneous reflected and refracted waves with elliptical particle motions, velocities and maximum attenuations that vary with frequency and angle of incidence, energy propagation at speeds and directions different from phase propagation, phase propagation that in general is parallel to the boundary for at most one angle of incidence, and reflection—transmission coefficients dependent on energy flow due to wave interaction. None of these physical characteristics are predicted for waves incident on boundaries that respond instantaneously.

Geophysical Journal International↗
USGS2008

Viscoelastic love-type surface waves

The general theoretical solution for Love-Type surface waves in viscoelastic media provides theoreticalexpressions for the physical characteristics of the waves in elastic as well as anelastic media with arbitraryamounts of intrinsic damping. The general solution yields dispersion and absorption-coefficient curves for the waves as a function of frequency and theamount of intrinsic damping for any chosen viscoelastic model.Numerical results valid for a variety of viscoelastic models provide quantitative estimates of the physicalcharacteristics of the waves pertinent to models of Earth materials ranging from small amounts of damping in the Earth&rsquo;s crust to moderate and large amounts of damping in soft soils and water-saturated sediments. Numerical results, presented herein, are valid for a wide range of solids and applications.

Conference Paper↗
USGS2005

Integrated surface and borehole strong-motion, soil-response arrays in San Francisco, California: Empirical measurements of low-strain site coefficients at site class E and D soil sites

An integrated set of four borehole arrays and ten surface installations is installed in the city of San Francisco, California to measure the response of soft-soil deposits to strong earthquake ground motions. The borehole arrays extend through thick layers of soft water-saturated soils of Holocene age and older more consolidated soils of Pleistocene age into bedrock at depths up to 90 m. The surface installations are configured in pairs to provide simultaneous comparative surface measurements of soft soils and nearby rock. The rock locations also permit comparative measurements of rock as observed at the surface and in nearby boreholes. The arrays are designed to address a wide variety of scientific and engineering issues, and especially the issue of anelastic and nonlinear soil response at high strain levels as might be recorded during a large regional earthquake. Recordings of ground motions from the largest regional earthquakes which have occurred since the installation of the arrays show marked evidence of amplification as measured on the borehole and surface arrays. Implications of the results for low-strain site coefficients in present U.S. building codes are discussed.

Calfornia↗
USGS2005

Erratum: Empirical evidence for acceleration-dependent amplification factors

Incorrect versions of Figures 5 and 6 containing normalization errors were accidentally published by Borcherdt (2002) . They should be replaced with the figures shown here. The text and tabulated regression values published in Borcherdt (2002) are correct and refer to the figures shown here.

Bulletin of the Seismological Society of America↗