Ground-motion simulations of notable earthquakes in the central and eastern United States are limited and typically assume 1D Earth structure. In this study, we use a 3D seismic velocity model to better constrain the depth and focal mechanism of the 5 April 2024, moment magnitude 4.8 Tewksbury earthquake and investigate the spatial variability of earthquake ground motions and the effects of nearby sedimentary basins. We perform earthquake ground-motion simulations up to 0.5 Hz using the 3D spectral-element wave propagation solver SPECFEM3D over a region 280 km wide by 260 km long by 77 km deep. Topography and subsurface geophysical structure are assigned using the U.S. Geological Survey (USGS) National Crustal Model with a minimum shear-wave velocity of 200 m/s. We use earthquake time series from 13 broadband seismic stations in the region that have a uniform azimuthal distribution and epicentral distances ranging from 76 to 131 km to compare with synthetics and explore the effects of 1D versus 3D seismic structure on focal mechanism and depth solutions. Ground-motion intensity metrics are also presented relative to the Next Generation Attenuation-East Project (NGA-East) ground-motion models (GMMs) currently used in seismic hazard assessments for the region. We find that the 3D model, which reveals a wide spatial variability of period-dependent ground motions, yields better predictions of earthquake ground motions relative to the 1D model and the NGA-East ergodic GMM, with a 76% reduction of residual variance in observed ground motions averaged over 3, 5, 7, and 10 s periods. Use of the 3D model to solve for a focal mechanism yields a shallower focal depth at 4 km and a shallower east-dipping focal plane relative to the USGS regional moment tensor and Global Centroid Moment Tensor. Our study demonstrates that use of 3D seismic velocity models can improve estimates of earthquake focal mechanisms, ground motions, and seismic hazard.

ABSTRACT Estimating seismic hazard using 3D earthquake simulations of moderate-to-large magnitude events is becoming a reality. In this study, we further this endeavor by simulating seismic wavefields for five earthquakes in California, United States, and evaluating their pseudospectral acceleration at periods of 2, 5, and 10 s. We compare results from the recently developed U.S. Geological Survey (USGS) National Crustal Model with three well-established and validated regional community velocity models (CVMs): two CVMs for Southern California (CVMS4.26.M01 and CVMH15.1.0) and the USGS San Francisco Bay region 3D CVM. A minimum shear-wave velocity of 500 m/s is imposed in all four of the velocity models. We use finite-difference calculations to simulate the earthquakes and specify a grid and timestep capable of resolving periods down to 1 s. For our simulations, we find that for each earthquake, the available velocity models produce broadly similar amplitudes and patterns of earthquake ground motions. Use of the 3D velocity models generally perform better than ergodic ground-motion models, and variability in the results between earthquakes may indicate a combination of factors including uncertainty in earthquake magnitude and source parameterization, signal-to-noise ratio in the observed time series, and the lack of fault damage zones, topography, and other features in the computational seismic velocity models. Of particular note, we find that for most cases, averaging the ground motions for all available velocity models outperforms the ground-motion results from any single velocity model. Our results indicate that the 3D models considered in this study can be sufficiently independent and have enough predictive power that their combination could be used to improve estimates of earthquake ground motions.

The thermal structure of the continental crust plays a critical role in understanding its elastic and rheologic properties as well as its dynamic processes. Thermal parameter data sets on continental scales have been used to constrain the crustal thermal structure, including both the direct (e.g. temperature, heat flux and heat conductivity measured at the surface) and indirect (e.g. seismically derived Mohorovi & ccaron;i & cacute; discontinuity (Moho) temperature, geomagnetically derived Curie depth) observations. In this study, we present a new continental scale crustal heat generation model with additional information from seismologically inferred crustal composition. Together with previous direct and indirect thermal parameter data sets in the conterminous United States, we use the new crustal heat generation model to construct a 3-D crustal temperature model under a newly developed Bayesian framework. Specifically, we first derive profiles of crustal heat generation based on an empirical geochemical relationship at 1683 locations where seismologically derived crustal composition information is available. Then for each of these locations, the average heat generation values in the upper, middle and lower crust are combined with other thermal parameters through a Markov Chain Monte-Carlo inversion for a conductive, vertically smooth temperature profile. The results, posterior distributions of temperature profiles, are used to generate a 3-D crustal thermal model with the uncertainties systematically assessed. The new temperature model overall exhibits similar patterns to that from the U.S. Geological Survey National Crustal Model, but also reduces possible biases and the model's dependence on a single thermal parameter.

We present initial findings from the ongoing Community Stress Drop Validation Study to compare spectral stress-drop estimates for earthquakes in the 2019 Ridgecrest, California, sequence. This study uses a unified dataset to independently estimate earthquake source parameters through various methods. Stress drop, which denotes the change in average shear stress along a fault during earthquake rupture, is a critical parameter in earthquake science, impacting ground motion, rupture simulation, and source physics. Spectral stress drop is commonly derived by fitting the amplitude-spectrum shape, but estimates can vary substantially across studies for individual earthquakes. Sponsored jointly by the U.S. Geological Survey and the Statewide (previously, Southern) California Earthquake Center our community study aims to elucidate sources of variability and uncertainty in earthquake spectral stress-drop estimates through quantitative comparison of submitted results from independent analyses. The dataset includes nearly 13,000 earthquakes ranging from M 1 to 7 during a two-week period of the 2019 Ridgecrest sequence, recorded within a 1 degrees radius. In this article, we report on 56 unique submissions received from 20 different groups, detailing spectral corner frequencies (or source durations), moment magnitudes, and estimated spectral stress drops. Methods employed encompass spectral ratio analysis, spectral decomposition and inversion, finite-fault modeling, ground-motion-based approaches, and combined methods. Initial analysis reveals significant scatter across submitted spectral stress drops spanning over six orders of magnitude. However, we can identify between-method trends and offsets within the data to mitigate this variability. Averaging submissions for a prioritized subset of 56 events shows reduced variability of spectral stress drop, indicating overall consistency in recovered spectral stress-drop values.

A three-dimensional (3D) geologic framework has been developed for the conterminous United States (U.S.) as part of the U.S. Geological Survey National Crustal Model to enhance seismic hazard modeling. The geologic framework is created from geologic maps and multiple subsurface geologic unit boundaries including the base of the Miocene, Cenozoic, Phanerozoic, and the Mohorovičić discontinuity. Modifications are made to surficial geologic maps to remove discontinuities across state and country borders. The subsurface distribution of rock type and age is extrapolated from the surface, seeded with subsurface geologic information, and constrained by a map of basement geology. The framework provides the basis for estimates of subsurface seismic velocity and density that is needed to improve estimates of earthquake ground shaking and seismic hazard. The present framework greatly expands and updates a previously published 3D geologic framework of the western part of the U.S. that was itself a first-of-its-kind digital 3D portrayal of the nation.

With the recent successful accounting of basin depth ground-motion adjustments in seismic hazard analyses for select areas of the western United States, we move toward implementing similar adjustments in the Atlantic and Gulf Coastal Plains by constructing a sediment thickness model and evaluating multiple relevant site amplification models for central and eastern United States seismic hazard analyses. We digitize and combine existing sediment thickness data sets into a composite surface that delineates the base of Cretaceous sediments under the Atlantic Coastal Plain and the base of Mesozoic sediments under the Gulf Coastal Plain. Amplification models dependent on sediment thickness, site natural period, and source-to-site path length are compared with data sets of observed ground motions to evaluate the ability of the new models to improve ground motion estimates. We find that the amplification models can account for observed trends in sediment-thickness and period-dependent residuals, but some tuning is required. For example, the model of Chapman and Guo requires a reference V S 30 , the time-averaged shear-wave velocity within 30 m of the Earth’s surface, for non-Coastal Plain sites, which we estimate to be between about 1 and 2 km/s. Along with our sediment thickness model, we estimate a velocity profile for application to the Harmon et al. site-natural-period-based model in order to best match the Chapman and Guo period dependence for a broad range of sediment thicknesses. The Next Generation of Attenuation models for the eastern United States Gulf Coast path-based adjustment models can also account for seismic attenuation in the Coastal Plain sediments and reduce the standard deviation of total residuals. If enacted in the U.S. Geological Survey National Seismic Hazard Model, these amplification models will reduce predicted short-period (<1 s) and increase predicted long-period (>1 s) ground motions in the Coastal Plains appreciably.

The Atlantic and Gulf Coastal Plains (CPs) are characterized by widespread accumulations of low-velocity sediments and sedimentary rock that overlay high-velocity bedrock. Geology and sediment thickness greatly influence seismic wave propagation, but current regional ground motion amplification and seismic hazard models include limited characterization of these site conditions. In this study, a new regional seismic velocity model for the CPs is created by integrating shear wave velocity (V S ) measurements, surface geology, and a sediment thickness model recently developed for the CPs. A reference rock V S of 3000 m/s has been assumed at the bottom of the sedimentary columns, which corresponds to the base of Cretaceous and Mesozoic sediments underlying the Atlantic CP and the Gulf CP, respectively. Measured V S profiles located throughout the CPs are sorted into five geologic groups of varying age, and median V S profiles are developed for each group by combining measured V S values within layer thicknesses defined by an assumed layering ratio. Statistical analyses are also conducted to test the appropriateness of the selected groups. A power law model with geology-informed coefficients is used to extend the median velocity models beyond the depths where measured data were available. The median V S profiles provide reasonable agreement with other generic models applicable for the region, but they also incorporate new information that enables more advanced characterizations of site response at regional scales and their effective incorporation into seismic hazard models and building codes. The proposed median velocity profiles can be assigned within a grid-based model of the CPs according to the spatial distribution of geologic units at the surface.

On 5 April 2024, 10:23 a.m. local time, a moment magnitude 4.8 earthquake struck Tewksbury Township, New Jersey, about 65 km west of New York City. Millions of people from Virginia to Maine and beyond felt the ground shaking, resulting in the largest number (>180,000) of U.S. Geological Survey (USGS) “Did You Feel It?” reports of any earthquake. A team deployed by the Geotechnical Extreme Events Reconnaissance Association and the National Institute of Standards and Technology documented structural and nonstructural damage, including substantial damage to a historic masonry building in Lebanon, New Jersey. The USGS National Earthquake Information Center reported a focal depth of about 5 km, consistent with a lack of signal in Interferometric Synthetic Aperture Radar data. The focal mechanism solution is strike slip with a substantial thrust component. Neither mechanism’s nodal plane is parallel to the primary northeast trend of geologic discontinuities and mapped faults in the region, including the Ramapo fault. However, many of the relocated aftershocks, for which locations were augmented by temporary seismic deployments, form a cluster that parallels the general northeast trend of the faults. The aftershocks lie near the Tewksbury fault, north of the Ramapo fault.

The US National Seismic Hazard Model (NSHM) was updated in 2023 for all 50 states using new science on seismicity, fault ruptures, ground motions, and probabilistic techniques to produce a standard of practice for public policy and other engineering applications (defined for return periods greater than ∼475 or less than ∼10,000 years). Changes in 2023 time-independent seismic hazard (both increases and decreases compared to previous NSHMs) are substantial because the new model considers more data and updated earthquake rupture forecasts and ground-motion components. In developing the 2023 model, we tried to apply best available or applicable science based on advice of co-authors, more than 50 reviewers, and hundreds of hazard scientists and end-users, who attended public workshops and provided technical inputs. The hazard assessment incorporates new catalogs, declustering algorithms, gridded seismicity models, magnitude-scaling equations, fault-based structural and deformation models, multi-fault earthquake rupture forecast models, semi-empirical and simulation-based ground-motion models, and site amplification models conditioned on shear-wave velocities of the upper 30 m of soil and deeper sedimentary basin structures. Seismic hazard calculations yield hazard curves at hundreds of thousands of sites, ground-motion maps, uniform-hazard response spectra, and disaggregations developed for pseudo-spectral accelerations at 21 oscillator periods and two peak parameters, Modified Mercalli Intensity, and 8 site classes required by building codes and other public policy applications. Tests show the new model is consistent with past ShakeMap intensity observations. Sensitivity and uncertainty assessments ensure resulting ground motions are compatible with known hazard information and highlight the range and causes of variability in ground motions. We produce several impact products including building seismic design criteria, intensity maps, planning scenarios, and engineering risk assessments showing the potential physical and social impacts. These applications provide a basis for assessing, planning, and mitigating the effects of future earthquakes.

We update the ground-motion characterization for the 2023 National Seismic Hazard Model (NSHM) for the conterminous United States. The update includes the use of new ground-motion models (GMMs) in the Cascadia subduction zone; an adjustment to the central and eastern United States (CEUS) GMMs to reduce misfits with observed data; an updated boundary for the application of GMMs for shallow, crustal earthquakes in active tectonic regions (i.e. western United States (WUS)) and stable continental regions (i.e. CEUS); and the use of improved models for the site response of deep sedimentary basins in the WUS and CEUS. Site response updates include basin models for the California Great Valley and for the Portland and Tualatin basins, Oregon, as well as long-period basin effects from three-dimensional simulations in the Greater Los Angeles region and in the Seattle basin; in the CEUS, we introduce a broadband (0.01- to 10-s period) amplification model for the effects of the passive-margin basins of the Atlantic and Gulf Coastal Plains. In addition, we summarize progress on implementing rupture directivity models into seismic hazard models, although they are not incorporated in the 2023 NSHM. We implement the ground-motion characterization for the 2023 NSHM in the US Geological Survey’s code for probabilistic seismic hazard analysis, nshmp-haz-v2, and present the sensitivity of hazard to these changes. Hazard calculations indicate widespread effects from adjustments to the CEUS GMMs, from the incorporation of Coastal Plain amplification effects, and from the treatment of shallow-basin and out-of-basin sites in the San Francisco Bay Area and Los Angeles region, as well as locally important changes from subduction-zone GMMs, and from updated and new WUS basins.

We assess how well the Next-Generation Attenuation-West 2 (NGA-West2) ground-motion models (GMMs), which are used in the US Geological Survey’s (USGS) National Seismic Hazard Model (NSHM) for crustal faults in the western United States, predict the observed basin response in the Great Valley of California, the Reno basin in Nevada, and Portland and Tualatin basins in Oregon. These GMMs rely on site parameters such as the time-averaged shear-wave velocity ( VS) in the upper 30 m of Earth’s crust ( VS30) and depths to 1.0 and 2.5 km/s shear-wave isosurfaces ( Z1.0 and Z2.5) to capture basin effects and were developed using observations and simulations primarily from the Los Angeles region in southern California. Using ground-motion records from mostly small-to-moderate earthquakes and mixed-effects regression analysis, we find that the GMMs perform well with our local basin-depth models for the California Great Valley. With our local basin-depth models for Reno, the GMMs do not perform as well for this relatively shallow basin and exhibit little sensitivity to the basin parameters used in the NGA-West2 GMMs. We also find good performance for the local Z1.0 model across the Portland region, whereas the local Z2.5 model provides little predictive power except at sites in the deepest part of the Tualatin basin. Additional work could improve the performance of the site and basin terms in the NGA-West2 GMMs for regions with geologic structure different than the deep basins in southern California and the Great Valley. In addition, we find significant discrepancies among the GMMs in how the uncertainty in the ground motion varies with basin depth and pseudospectral period. Our results can help guide seismic hazard analyses on whether to include these local basin-depth models.

We present a model of the lower seismogenic depth of earthquakes in the western United States (WUS) estimated using the hypocentral depths of events M > 1, a crustal temperature model, and historical earthquake rupture depth models. Locations of earth-quakes are from the Advanced National Seismic System Comprehensive Earthquake Catalog from 1980 to 2021 supplemented with seismicity in southern California for event hypocenters that were relocated by Hauksson et al. (2012) to obtain higher precision and better resolution in the model. We calculated the average depth of the deepest 10% of the merged catalog using an adaptive radius of 50 km or more. Along the San Andreas fault, the deepest seismogenic depths are located at 23 km around the Cholame segment, whereas the shallowest depths are located at about 10 km along the Rodgers Creek and Maacama faults. For the WUS outside California, the depth generally varies between 10 and 25 km with an average around 14 km but could extend to 35 km along Cascadia subduction zone. We find good agreement between the small-magnitude depths and rupture depths derived from coseismic slip of large earthquakes across the region. Our estimates are generally deeper than the previous seismogenic depths determined for the Uniform California Earthquake Rupture Forecast, Version 3 model based on work by Petersen et al. (1996) who used seismicity cross sections along major fault zones in California. Our new seismogenic depth distribution correlates closely with crustal temper-ature derived from WUS heat flow (Blackwell et al., 2011). This correlation allowed us to develop a map of the brittle-ductile transition that we use to replace seismogenic depths in the model east of the Intermountain West Seismic Belt where the seismicity rate is low. This updated depth model is useful for recalibrating the lower geologic fault rupture depths, and constraining deformation and seismicity source models in updates of the U.S. Geological Survey National Seismic Hazard Model.

First posted July 6, 2022 For additional information, contact: Director, Geologic Hazards Science CenterU.S. Geological SurveyP.O. Box 25046, Mail Stop 966Denver, CO 80225 In early October of 2020, the U.S. Geological Survey (USGS) held a virtual workshop to discuss Gulf and Atlantic Coastal Plains site-response models. Earthquake researchers came together to assess (1) research related to proposed Coastal Plains amplification models and (2) USGS plans for implementing these models. Presentations spanned a broad range of topics from Atlantic and Gulf Coastal Plains geophysical properties including seismic velocity and attenuation, to ground motion amplification models and their impacts on seismic hazard. Interspersed with these presentations were discussions regarding the definition and extent of the Atlantic and Gulf Coastal Plains, potential complexities of wave propagation in the Atlantic and Gulf Coastal Plains, and problems that need to be overcome to implement various proposed site-response models. Based on feedback from this workshop, the USGS working group on Coastal Plain Amplification is considering applying published models that depend on sediment thickness. The working group is also exploring potential application of models that depend on the length of path traversed across the Coastal Plain, including the Gulf Coastal Plain ground-motion model adjustments from the Next Generation Attenuation Relationships for the Eastern United States.

Seismic attenuation is generally greater in the western United States (WUS) than the central and eastern United States (CEUS), but the nature of this transition or location of this boundary is poorly constrained. We conduct crustal seismic (Lg) attenuation tomography across a region that stretches from the CEUS across the Rocky Mountains to the Basin and Range using a total of 115,870 amplitude measurements from 106 earthquakes recorded on 544 stations across five frequency bands spanning 0.5–16 Hz. Similar to previous studies, we find higher attenuation in the WUS ( Q 0 ∼ 190) than the nominally CEUS ( Q 0 ∼ 250) and comparatively high attenuation on the Gulf Coast ( Q 0 ∼ 175). Our models defy simple east versus west regionalization, however. Heterogeneity within the Rocky Mountain region—low attenuation in the Colorado Plateau interior and Wyoming Craton ( Q 0 ∼ 230) compared to high attenuation in the southern Rockies ( Q 0 ∼ 110)—exceeds the gross differences between the CEUS and western United States. These province‐scale patterns are readily interpreted in terms of intrinsic attenuation. The boundary between the Colorado Plateau and Basin and Range hosts the highest attenuation imaged in the study area ( Q 0 ∼ 90), consistent with localized scattering across contrasting crustal structure. Focused high attenuation in the southern Rockies may represent the effects of represent in situ partial crustal melt. Within the CEUS, second‐order bands of comparatively high attenuation align with the Proterozoic Yavapai‐Mazatzal suture zone and Midcontinent Rift. This complex attenuation structure defies broad regionalization and suggests a need for path‐specific models near these boundaries and for critical infrastructure.

Ground-motion analysis of more than 3000 records from 59 earthquakes, including records from the March 2020 Mw 5.7 Magna earthquake sequence, was carried out to investigate site response and basin amplification in the Wasatch Front, Utah. We compare ground motions with the Bayless and Abrahamson (2019; hereafter, BA18) ground-motion model (GMM) for Fourier amplitude spectra, which was developed on crustal earthquake records from California and other tectonically active regions. The Wasatch Front records show a significantly different near-source rate of distance attenuation than the BA18 model, which we attribute to differences in (apparent) geometric attenuation. Near-source residuals show a period dependence of this effect, with greater attenuation at shorter periods (T<0.5  s) and a correlation between period and the distance over which the discrepancy manifests (∼20–50  km). We adjusted the recorded ground motions for these regional path effects and solved for station site terms using linear mixed-effects regressions, with groupings for events and stations. We analyzed basin amplification by comparing the site terms with the basin geometry and basin depths from two seismic-velocity models for the region. Sites over the deeper parts of the sedimentary basins are amplified by factors of 3–10, relative to sites with thin sedimentary cover, with greater amplification at longer periods (T≳1  s). Average ground-motion variability increases with period, and long-period variability exhibits a slight increase at the basin edges. These results indicate regional seismic wave propagation effects requiring further study, and potentially a regionalized GMM, as well as highlight basin amplification complexities that may be incorporated into seismic hazard assessments.

The 2018 US Geological Survey National Seismic Hazard Model (NSHM) incorporates new data and updated science to improve the underlying earthquake and ground motion forecasts for the conterminous United States. The NSHM considers many new data and component input models: (1) new earthquakes between 2013 and 2017 and updated earthquake magnitudes for some earlier earthquakes; (2) two updated smoothed seismicity models to forecast earthquake rates; (3) two suites of new central and eastern US (CEUS) ground motion models (GMMs) to translate ground shaking for various earthquake sizes and source-to-site distances considered in the model; (4) two CEUS GMMs for aleatory variability; (5) two CEUS site-effect models that modify ground shaking based on alternative shallow site conditions; (6) more advanced western US (WUS) lithologic and structural information to assess basin site effects for selected urban regions; and (7) a more comprehensive range of outputs (22 periods and 8 site classes) than in previous versions of the NSHMs. Each of these new datasets and models produces changes in the probabilistic ground shaking levels that are spatially and statistically analyzed. Recent earthquakes or changes to some older earthquake magnitudes and locations mostly result in probabilistic ground shaking levels that are similar to previous models, but local changes can reach up to +80% and −60% compared to the 2014 model. Newly developed CEUS models for GMMs, aleatory variability, and site effects cause overall changes up to ±64%. The addition of the WUS basin amplifications causes changes of up to +60% at longer periods for sites overlying deep soft soils. Across the conterminous United States, the hazard changes in the model are mainly caused by new GMMs in the CEUS, by sedimentary basin effects for long periods (≥1 s) in the WUS, and by seismicity changes for short (0.2 s) and long (1 s) periods for both areas.

A decade of study into the Virginia earthquake that damaged D.C. and reverberated up and down the Atlantic coast in 2011 has shed light on rare, but risk-laden, seismicity in eastern North America.

First posted July 31, 2020 For additional information, contact: Director, Geologic Hazards Science CenterU.S. Geological SurveyBox 25046, MS-966Denver, CO 80225-0046 The U.S. Geological Survey National Crustal Model (NCM) is being developed to include spatially varying estimates of site response in seismic hazard assessments. Primary outputs of the NCM are continuous velocity and density profiles from the Earth’s surface to the mantle transition zone at 410-kilometer (km) depth for each location on a 1-km grid across the conterminous United States. Datasets used to produce the NCM may have a resolution of better than 1 km near the Earth’s surface in some regions, but, with increasing depth, NCM resolution decreases to tens to hundreds of kilometers in the mantle. Basic subsurface information is provided by the NCM geologic framework, thermal model, and petrologic and mineral physics database. In this report, the velocities and densities that can be extracted from the NCM are calibrated through the development of a porosity model based on Biot-Gassmann theory and more than 2,000 compressional- and (or) shear-wave velocity profiles less than 10 km deep from across the conterminous United States and southwestern Canada.Sediment and rock porosities are derived from shear-wave velocity and are found to depend on effective pressure, rock type, and age (for sedimentary and extrusive volcanic deposits). Porosity-effective pressure functions are then estimated for each rock type (and age for sedimentary and extrusive volcanic deposits). Unconsolidated sediments are found to have higher porosities than consolidated units, which have higher porosities than unweathered igneous units; young sedimentary units (for example, Quaternary age units) tend to have higher porosities than older sedimentary units (for example, pre-Cenozoic age units); porosity decreases with increasing effective pressure; and porosities can decrease quickly through the weathered layer of intrusive rocks.Comparing two Los Angeles area velocity models and the U.S. Geological Survey Bay Area velocity model with the NCM, the NCM does a better job on average of reproducing observed shear-wave velocities below 1 km per second because it has less bias and uncertainty. Approaching and above 1 km per second, the NCM tends to underpredict observed shear-wave velocity. Whereas several factors could contribute to this, the primary factor is probably bias in the NCM geologic framework. For example, the NCM will predict lower velocities in places where the depth to bedrock and basement appear shallower in the measured velocity profiles than specified in the NCM geologic framework. With regard to observed compressional-wave velocity and density, the NCM has significantly less bias than California models for the former, especially below 2 km per second, and all models tend to overpredict density for densities less than about 2,200 kilograms per cubic meter.