Velocity and Density Models Incorporating elocity and Density Models Incorporating 

the Cascadia Subduction Zone for 3D the Cascadia Subduction Zone for 3D 

Earthquake Ground Motion Simulations Earthquake Ground Motion Simulations 

Open-File Report 2007-1348 Open-File Report 2007-1348 

U.S. Department of the Interior U.S. Department of the Interior 

U.S. Geological Survey U.S. Geological Survey 
Earthquake Hazards Ground Motion Investigations 

Velocity and Density Models Incorporating the 

Cascadia Subduction Zone for 3D Earthquake 

Ground Motion Simulations 

Version 1.3 

By W.J. Stephenson 

Open-File Report 2007–1348 

U.S. Department of the Interior 

U.S. Geological Survey 
U.S. Department of the Interior 

DIRK KEMPTHORNE, Secretary 

U.S. Geological Survey 

Mark D. Myers, Director 

U.S. Geological Survey, Reston, Virginia 2007 

For product and ordering information: 

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Telephone: 1-888-ASK-USGS 

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not imply endorsement by the U.S. Government. 

Although this report is in the public domain, permission must be secured from the 

individual copyright owners to reproduce any copyrighted material contained within 

this report. 

Suggested citation: 

Stephenson, W.J., 2007, Velocity and density models incorporating the Cascadia 

subduction zone for 3D earthquake ground motion simulations, Version 1.3: U.S. 

Geological Survey, Earthquake Hazards Ground Motion Investigations, Open-File 

Report 2007–1348, 24 p. 

ii 
iii 

Contents 

Introduction ........................................................................................................................................................... 1

The Primary Geology-Based Model Units and Their Velocity-Density Properties................................... 5

Continental Sedimentary Basins..................................................................................................................... 7

Continental Crust ............................................................................................................................................... 9

Continental Mantle ............................................................................................................................................ 9

Oceanic Sediments ......................................................................................................................................... 10

Oceanic Crust................................................................................................................................................... 10

Oceanic Mantle................................................................................................................................................ 11

Discussion and Summary ................................................................................................................................. 11

Acknowledgments.............................................................................................................................................. 18 

References Cited ................................................................................................................................................ 18

Figures 

1. Region of velocity and density models described in this report............................................................. 2

2. Contour map of Cascadia subduction slab................................................................................................. 4 

3. Model volume sliced both east-west and north-south through urbanized sedimentary 

basins ................................................................................................................................................................ 6 

4. East-west slices through Vs model............................................................................................................ 12 

5. Vs model slices in depth .............................................................................................................................. 13 

6. Vp model slices in depth .............................................................................................................................. 15 

7. Vp/Vs model slices in depth ........................................................................................................................ 16 

8. Rho model slices in depth............................................................................................................................ 17 
Velocity and Density Models Incorporating the Cascadia 

Subduction Zone for 3D Earthquake Ground Motion 

Simulations 

By W.J. Stephenson 

Introduction 

In support of earthquake hazards and ground motion studies in the Pacific 

Northwest, three-dimensional P- and S-wave velocity (3D Vp and Vs) and density (3D 

rho) models incorporating the Cascadia subduction zone have been developed for the 

region encompassed from about 40.2°N to 50°N latitude, and from about -122°W to 

-129°W longitude (fig. 1). The model volume includes elevations from 0 km to 60 km 

(elevation is opposite of depth in model coordinates). Stephenson and Frankel (2003) 

presented preliminary ground motion simulations valid up to 0.1 Hz using an earlier 

version of these models. The version of the model volume described here includes more 

structural and geophysical detail, particularly in the Puget Lowland as required for 

scenario earthquake simulations in the development of the Seattle Urban Hazards Maps 

(Frankel and others, 2007). Olsen and others (in press) used the model volume discussed 

here to perform a Cascadia simulation up to 0.5 Hz using a Sumatra-Andaman Islands 

rupture history. As research from the EarthScope Program (http://www.earthscope.org) 

is published, a wealth of important detail can be added to these model volumes, 

particularly to depths of the upper-mantle. However, at the time of development for this 

model version, no EarthScope-specific results were incorporated. This report is intended 

to be a reference for colleagues and associates who have used or are planning to use this 

preliminary model in their research. To this end, it is intended that these models will be 

1 
considered a beginning template for a community velocity model of the Cascadia region 

as more data and results become available. 

2 
Figure 1. Region of velocity and density models described in this report. Base image is 

from GoogleEarth®, showing the urban centers of Portland, Oreg., Seattle, Wash., and 

Vancouver, British Columbia. Red polygon is approximate boundary of velocity and 

density property volumes that include the Cascadia subduction zone. Latitude and 

longitude coordinates at corners of red polygon are, clockwise from upper left, 50°N, 

-129°W; 50°N, -122°W; 40.2°N, -122°W; and 40.2°N, -129°W. Projection is geographic 

WGS 84. 

The Cascadia subduction zone stretches for over 1,000 km, from the Mendocino 

triple junction off the northern California coast northward to Vancouver Island, Canada 

(fig. 2). The primary reasons for developing these model volumes are (1) for simulating 

strong ground motions in the urbanized sedimentary basins of western Washington and 

Oregon and (2) for simulating Tsunami effects from a great (M 8–9) Cascadia subduction 

zone earthquake. As such, these are geophysical property models constrained by firstorder geologic boundaries only. No effort has been made to represent detailed geologic 

terranes in the model volume unless they were deemed important for ground motion 

variability in urbanized regions. Thus, unique terranes within the continental crust, such 

as Siletz or Wrangellia, are not treated as unique units within the model; however, these 

units are essentially represented de facto through the use of passive- and active-source 

tomographic imaging results. 

The velocity and density models were developed primarily with EarthVision®

software on the Solaris operating system. Matlab®

 was also used as part of the 

development of the density model and for performing quality-control of the model 

volumes output in Institute of Electrical and Electronics Engineers, Incorporated (IEEE) 

3 
binary format from EarthVision®

. While a wealth of published information for the 

Cascadia region has been incorporated in the development of these models, significant 

smoothing during extrapolation and interpolation in portions of the model were required 

to create the model interfaces and geophysical property volumes. Because there are 

many areas within the model where published data are sparse or of low resolution, there 

is significant uncertainty and therefore subjectivity involved in building model horizons 

and in populating the model volumes. 

Figure 2. Contour map of Cascadia subduction slab showing estimated locked (red) and 

transitional (green) zones (Flück and others, 1997; McCrory and others, 2005). Contours 

in kilometers below sea-level. Figure is modified from Olsen and others (in press). 

4 
The model volume incorporates bathymetry (data of etopo5; Wessel and Smith, 

1991) but does not incorporate topography. Topography was not included in the current 

version of the model volume because the initial objective in developing these models was 

for use in 3D finite-difference ground motion calculations with modeling codes that do 

not allow grid points for terrain. This omission of topography in the current model 

volume can be easily rectified in future versions using EarthVision®

. 

The Primary Geology-Based Model Units and Their VelocityDensity Properties 

The backbone of the property volumes is the geologic model consisting of 

autonomous units representing simplified geologic volumes. For the purposes of this 

model, six units were defined. As shown in figure 3, these are (1) continental 

sedimentary basins, (2) continental crust, (3) continental mantle, (4) oceanic sediments, 

(5) oceanic crust, and (6) oceanic mantle. In addition to the Cascadia megathrust, the 

Seattle fault was incorporated into these models because of its use as a seismogenic 

source in the Seattle Urban Hazards Maps (Frankel and others, 2006). The modeling 

demands for the smaller-scale Seattle maps also drove the more detailed, complex overall 

appearance of the Puget Lowland region in the current velocity and density models. The 

Seattle fault delimits the southern edge of the Seattle basin and thrusts crystalline crust 

over basin sediments, creating a sharp lateral velocity-density contrast. Its surface trace 

was extracted from Blakely and others (2002) and projected to a depth of about 20 km 

assuming a 45° south dip. This dip angle is essentially a median value based on the range 

of dips published from seismic reflection surveys (Pratt and others, 1997; Johnson and 

others, 1999; ten Brink and others, 2002; Calvert and others, 2003). Additional crustal 

faults may be incorporated into the model as need and additional information arise. 

5 
Because much of the velocity information published in the literature is P-wave 

velocity (Vp), this property was first derived for each unit in the geologic model, then 

relationships between Vp and both S-wave velocity (Vs) and density (rho) were used to 

derive these latter properties on a geologic unit-by-unit basis. First, Vp was defined for 

each unit based on available published results. Then Vp was converted to Vs using the 

empirical relation with depth of Brocher (2005), except for Quaternary and Tertiary 

sedimentary basin units. Property Vs for these units is defined in a later section, entitled 

“Continental Sedimentary Basins.” 

Figure 3. Model volume sliced through urbanized sedimentary basins overlying 

Cascadia subduction zone (for example, the Seattle and Tacoma basins) of the Puget 

Lowland, western Washington. Cascadia velocity and density models cover 40.2° to 50° 

N. latitude, -121° to -129° W. longitude, and 0- to -60-km elevation. Bathymetry is 

6 
included while topography above mean sea level (0 m) is excluded. Model projected into 

Universal Transverse Mercator Zone 10 North (UTM) coordinates for display. Sliced 

view shows the seven basic geology-based model units and their relationships at depth. 

Cascadia subduction fault surface is inferred along top of oceanic crust model unit. 

Seattle fault is shown by red line within the Puget Lowland basins; fault dip within model 

volume is 45° south. 

As noted earlier, rho values for all model units were calculated directly from the 

empirical relationship with Vp derived by Brocher (2005), which is approximately the 

deterministic form of the Nafe-Drake law. This empirical equation is: 

rho = 1.6612*Vp - 0.4721*Vp2 + 0.0671*Vp3 - 0.0043*Vp4 + 0.000106*Vp5

where Vp is in km/s and rho is in g/cm3. After this calculation, the minimum and 

maximum nonwater densities were then constrained to be 2.0 g/cm3

 and 3.5 g/cm3, 

respectively. Ocean water was set to 1.028 g/cm3. 

Continental Sedimentary Basins 

 Sedimentary basin deposits are further subdivided into Quaternary and Tertiary 

geologic units. The thickness of Quaternary deposits through the southern Puget 

Lowland was compiled by Jones (1996) and Johnson and others (1999), and was 

originally used by Frankel and Stephenson (2000) then later by Pitarka and others (2004) 

for 3D ground motion modeling of the Seattle basin. For the Quaternary thickness 

through eastern Juan de Fuca Strait, the data of Mosher and Johnson (2000) were 

incorporated to create the Quaternary-Tertiary interface throughout the Puget Lowland. 

7 
Quaternary Vp varied one-dimensionally with a range of 1,500, 1,905, and 1,980 m/s at 

0, 200, and 1,000 m depth, respectively. These values were derived from land surface 

measurements and high-resolution marine seismic surveys (for example, Williams and 

others, 1999; Calvert and others, 2003). The Quaternary unit Vs is derived from Vs30 

and Vp30 measurements at the surface to constrain Vp/Vs to approximately 2.5, while 

Vp/Vs at 1 km was constrained to approximately 2.2. The minimum Vs in the 

Quaternary unit, and also in all nonwater regions of the model volume, was constrained 

to 600 m/s. For water regions, Vs was set to 0. 

The base of the Tertiary sediments within the Puget Lowland is inferred to be at 

the 4,500-m/s velocity contour, based on oil-industry borehole data (Brocher and Ruebel, 

1998). This contour surface was extracted from the Seismic Hazards Investigations in the 

Puget Sound (SHIPS) and earthquake data 3D P-wave tomography of Ramachandran and 

others (2004, 2006), which incorporate the same or similar data from many previous 

tomography studies in the lowland (for example, Stanley and others, 1999; Brocher and 

others, 2001; Van Wagoner and others, 2002). The Willammette Valley basin deposits 

(Portland area) are derived from well data intersecting crystalline rocks under (generally) 

Tertiary deposits (Yeats and others, 1996; Gannett and others, 1998). Quaternary 

deposits are generally less than 30 m in thickness and are currently not included in the 

model region for these basin deposits. Future consideration of simulations requiring grid 

spacing less than 100 m should include a thin Quaternary layer. Additionally, recent 

gravity modeling has suggested that a significant thickness of lower-density sediment 

may exist in the Tualatin basin west of Portland below what is interpreted in this model 

as the base of basin sediments (about 12-km depth versus about 0.5-km depth in current 

model; McPhee and others, 2007). 

8 
 The Vp of the Tertiary subunit in the Puget Lowland basins is defined by 

tomography results from SHIPS and local earthquake data as calculated by 

Ramachandran and others (2004, 2006). The Vp within the Willammette Valley basin 

deposits assumes a similar velocity-depth structure to that of the Puget Lowland. A 

constant Vp/Vs conversion factor of 2 was imposed on the Tertiary subunit to obtain Vs. 

Rho was derived from Vp using the empirical relationship of Brocher (2005). 

Continental Crust 

 Topography is not included in this current model. The surface of the continental 

crust below Mean Sea Level was controlled by the smoothed continental shoreline as 

well as numerous published active and passive source results along the continental 

margin (for example, Trehu and others, 1994; Clowes and others, 1997; Flueh and others, 

1998; Fuis, 1998; Gulick and others 1998; Fleming and Trehu, 1999; Parsons and others, 

1999; Stanley and Villasenor, 2000; Bostock and others, 2002; and Ramachandran and 

others, 2004). This unit’s Vp is derived from the above-mentioned studies and, most 

prominently, from the 3D tomography model of Ramachandran and others (2004, 2006) 

through the Puget Lowland. Properties Vs and rho were derived from Vp using the 

empirical relationship of Brocher (2005). 

Continental Mantle 

The top of continental mantle is derived from data of Chulick and Mooney 

(2002). These data were edited and smoothed to create the surface of this unit. The 

tomography of Stanley and others (1999) from the Puget Lowland area was used to 

constrain upper mantle Vp, extrapolating a generalized Vp-depth structure throughout the 

9 
unit. Rho and Vs were derived from Vp using the empirical relationship of Brocher 

(2005). 

Oceanic Sediments 

The oceanic sediment unit represents accreted and sedimentary deposits overlying 

the top of the continental crustal unit and underlying the eastern portion of the 

bathymetric surface. Parameter Vp is derived from results of Parsons and others (1999) 

and numerous active-source marine seismic surveys (for example,). Parameter Vp varies 

primarily as a function of depth. Parameters Vs and rho were derived from Vp using the 

empirical relationship of Brocher (2005). Preliminary ground motion studies suggest this 

unit will be subject to more intense shaking during a Cascadia megathrust event than 

other units of similar distance from the fault rupture (Olsen and other, in press). 

Oceanic Crust 

 The top of the oceanic crustal unit is defined in the subsurface based on the results 

of Flück and others (1997) and McCrory and others (2005). These data are merged with 

bathymetric data west of the oceanic sediment terminus to create the oceanic crust 

surface. The top of oceanic crust in the subsurface is also defined to be the top of the 

Cascadia megathrust (subducting slab). Based on available marine seismic-reflection 

profiling (for example, Fuis, 1998) and studies worldwide (for example, Turcotte and 

Shubert, 1982), the thickness of the oceanic crust was set to 5 km. This thickness is most 

likely on the low end of realistic values. Average values derived from marine seismic 

surveys were extrapolated to obtain Vp (for example, Trehu and others, 1994; Flueh and 

others, 1998; Fuis, 1998; Gulick and others 1998; Fleming and Trehu, 1999; and 

Ramachandran and others, 2004, 2006) and extrapolated smoothly to 60 km depth. Rho 

10 
and Vs were derived from Vp using the empirical relationship of Brocher (2005). As the 

oceanic crust subducts into the mantle, the crust at depth is less dense and slower than the 

surrounding mantle to the bottom of the model at 60 km depth. 

Oceanic Mantle 

The ocean mantle is the only unit in the model underlying oceanic crust. The top 

surface is derived by down-projecting the top of the oceanic crust 5 km and smoothing 

the resulting surface. This unit has the poorest-resolved Vp, Vs, and rho parameters 

because of limited published results. Parameter Vp was set to vary from 7,900 m/s to 

8,300 m/s between about 10 km and 60 km depth, respectively. Parameters Vs and rho 

were derived from Vp using the empirical relationship of Brocher (2005). 

Discussion and Summary 

 The first two sets of incremental property slices discussed here are from the Vs 

model volume because of this property’s importance for earthquake ground motion 

characterization. In figure 4, east-west slices spaced every 200 km through the model 

reveal the subducting slab and areas of the model with higher apparent resolution in 

western Washington due in large part to P-wave tomography results using SHIPS data 

(for example, Brocher and others, 2001; Ramachandran and others, 2004, 2006). 

Elevation slices from the Vs property volume from -4 to -44 km, every 10 km, are shown 

in figure 5. Velocities for Vs range from 600 m/s to 4,830 m/s. The -4 km elevation slice 

shows the oceanic sediment as the arc-shaped light-blue-colored band of approximately 

2,000 m/s. Small light-blue patches in the northeast quadrant of this slice are lowvelocity sediments within basins of the Puget Lowland. Subducting oceanic crust is 

11 
clearly visible in the depth slices -14 km to -44 km. At elevations below -14 km, oceanic 

mantle Vs is consistently higher than continental units at the same elevation. 

Figure 4. East-west slices through Vs model every 200 km. Velocities are scaled from 

400 to 5,000 m/s. Water velocity is set to 0 m/s. 

12 
Figure 5. Vs model slices at 10-km elevation intervals, beginning at -4 km elevation. 

Velocity scale is same as in figure 4. 

13 
Property Vp slices, corresponding in elevation to the Vs slices in figure 5, are 

shown in figure 6. Velocities range from 1,290 m/s to 8,470 m/s in the Vp model. The 

Vp/Vs elevation slices, shown in figure 7, reveal that nominal ratios in the deeper crust 

and mantle range between 1.71 and 1.76. The mean Vp/Vs between -15 km and -60 km 

elevation is approximately 1.733, consistent with a Poisson solid value of 1.732 g/cm3 for 

non-ocean-water regions. Property Vp/Vs varies most markedly at elevations above -2 

km, where the ratio goes as high as 2.5 in urban sedimentary basins in the upper few 

hundred meters. Property rho elevation slices, again corresponding to those displayed for 

Vs in figure 5, are shown in figure 8. These values for rock units range from 2.0 g/ cm3

in Quaternary basin sediments up to 3.46 g/ cm3 for ocean mantle at great depth. 

The model volume in the immediate vicinity of Seattle, including most of the 

Puget Lowland, has been validated with ground motion simulations of the 2001 Nisqually 

earthquake as well as other weak-motion events (Frankel and others, 2006, 2007). The 

Vs, Vp, and rho model volumes were implemented in these ground motion simulations, 

and these results were incorporated into the U.S. Geological Survey Urban Hazards Maps 

for Seattle. The Seattle urban hazard model volume was a subset of the greater Cascadia 

velocity-density model volume. These finite difference simulations with these velocitydensity models have been qualitatively accurate at matching waveform data to 1 Hz. 

14 
Figure 6. Vp model slices at 10-km elevation intervals, beginning at -4 km elevation 

(same elevations as slices shown in figure 5). 

15 
Figure 7. Vp/Vs model slices at 10-km elevation intervals, beginning at -4 km elevation 

(same elevations as slices shown in figure 5). 

16 
Figure 8. Rho model slices at 10-km elevation intervals, beginning at -4 km elevation 

(same elevations as slices in figure 5). 

17 
The 3D velocity and density property models described in this paper were 

developed in FY2005 and FY2006 for use in strong ground motion simulations of Seattle 

fault, Cascadia megathrust, and other earthquake events of interest. These models were 

derived primarily using published geophysical data in addition to borehole and other 

geological constraints. The model volume as developed in EarthVision®

 is designed to be 

flexible and can be modified to add further complexity as new published information 

becomes available or as scientific focus is redirected to new challenges in the Cascadia 

region. This flexibility allows model grid, or node, spacing to be customized from the 

EarthVision®

 model for a user’s specific purpose. At present, the model can be obtained 

from the author (wstephens@usgs.gov) in raw IEEE binary format. 

Acknowledgments 

I thank Art Frankel for his patience and advice through the various permutations of this 

model volume’s development. I also thank Jack Odum and Robert Williams for their 

reviews, which greatly improved this manuscript. Discussions with Kim Olsen, Todd 

Wagner, and Paul Vincent helped prompt me to formally complete this documentation. 

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18 
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