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Ambient Near-Coastal Seismic Noise and Temporal Monitoring NSF/EAR-0838247 2009/10/01-2011/09/30

Robert W. Clayton, Caltech Sharon Kedar, JPL

Cathleen Jones, JPL Frank Webb, JPL

Nick Graham, SIO & Hydrology Research Center Michael Longuet-Higgins, SIO

Summary

We propose to use the locations of secondary ocean microseisms noise to improve the temporal resolution of changes in crustal velocity, and to map the locations of coastal reflections of primary ocean waves. The proposed microseisms source location technique is based on an algorithm developed for real-time earthquake locations and is suitable for areas like Southern California where multiple simultaneous sources are located within a few hundred km offshore and where there is a well distributed seismic array on land. The use of source locations overcomes a problem with standard correlation methods that require a random distribution of sources to achieve precise measurements, which translates to long correlation times and hence a reduced temporal resolution. Using a set of source locations, a shorter synthetic seismogram can be used in the correlation. The coastal reflection points will be determined by forming an adjoint problem with the hypothesized reflection source and an incident primary wavefield determined from high-resolution Wave Action Models (WAM’s).

The source locations procedure is demonstrated with both a synthetic and real data examples. The results show that there are often many source points active at any given time. To confirm these locations, we plan to use two independent approaches: (1) Synthetic Aperture Radar (SAR) measurements of the intensity of wave-wave interactions at the source regions – a necessary condition for microseisms generation. A new airborne system that will be flown in June 2008 over the offshore S. California to look for opposing ocean wavefields which are indicative of the source points. (2) A comparison between the amplitudes of the observed micoseisms and estimated amplitudes calculated using the source locations and the theory of ocean microseisms [Longuet-Higgins, 1950]. Similar technique was successfully used to verify locations of microseisms in the North Atlantic Ocean.

The importance of the research is both fundamental and practical. The nature of the coastal reflections is currently poorly understood. This research will provide the opportunity to develop a model for this process and to ultimately to generate a description of the complete wave-field that can be incorporated into the next generation of Wave Action Models. Microseisms provide a means to continuously monitor the Rayleigh wave speed across the Los Angeles basins as a potential proxy for stress changes. The use of sources in this procedure increases the temporal resolutions and removes the problem of systematic bias due to the assumption of random source locations.

Broader Impacts: This research bridges three communities: radar interferometry, oceanography and seismology and hence has the potential to spur research in all these areas. Determining the mechanisms for coastal reflections will significantly enhance the community wave action models. The application to southern California can be extended to several other areas including northern California, Cascadia, and Japan. The procedure established by this research could become part of the standard seismic monitoring

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of Southern California. The research will be the PhD thesis of a graduate student and will potentially involve undergraduates at no cost.

1. Introduction Correlation of ambient seismic noise is now widely used to determine earth structure [c.f. Courtland, 2008]. The reason for this is the relative ease of determining the Green’s functions along station to station paths compared to the complexity that an earthquake source introduces, and because of the ability to do this in absence of earthquake sources. The technique has been applied to both short and long-range surveys in many parts of the world.

Recently, correlation methods are being applied to the problem of monitoring temporal variations in the subsurface [Stehly et al., 2006; Brenguier et al., 2008]. For this application the technique would appear almost ideal because the source is omnipresent compared to earthquakes. However, the need to look at correlations for relatively short time windows can lead to a violation of the underlying assumption of the technique. That is that the sources need to be distributed randomly off (either) end of the station-station path [Sneider, 2004]. If this assumption is not met, the technique estimate can be biased by a favored projection of the Green’s function. This will lead to an incorrect travel time estimate and consequently an incorrect velocity estimate. An example of this is shown in Fig 1, where one month averages of the correlation are shown through an entire year. There is a clear amplitude variation in the correlations, and a more subtle travel time variation. When this variation is translated to a velocity, the errors are approximately 3%. Averaging with the acausal Green’s function does not help in this case because it is almost zero.

Figure 1. Example of the problem with non-random source distribution. As the storm pattern changes from the northwest (Gulf of Alaska) in the winter to the southwest (Southern Ocean) in the summer, the correlations change both in amplitude and in timing. The panel on the right shows the measure travel time changes and a function of month.

There exists an ongoing debate about the characteristics and location of secondary (i.e. double frequency) ocean microseism [Longuet-Higgins, 1950]. Stehly et al [2006] used global

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triangulation to locate the source region in the Southern Ocean. In a study of North Atlantic microseism, Kedar et al [2008] located a persistent source during fall and winter months south of Greenland, by modeling the observed microseismic amplitudes using wave directional spectra from Wave Action Models (WAM’s) and bathymetry effects, according to Longuet Higgins’ “Theory of the Origin of Microseisms” [Longuet-Higgins, 1950]. On the west coast of North America, the generation region appears to be near the coast itself [Rhie and Romanowicz, 2005; Tanimoto et al, 2006; Bromirski and Dunnabier, 2002], and the source of the opposing waves is suspected to be coastal reflections. Coastal reflections have rarely been directly observed [Elgar et al. [1994]. Their physics, which depends on multiple variables such as beach slope, wave heights and the state of the tide is highly complex, and is therefore poorly understood.

In this proposal, we couple two ideas to look for the reflection points of the primary waves, and to use the located source points of the secondary microseisms to improve the temporal resolution of ambient noise monitoring. The new ideas in this proposal is the concept of accurately locating the locations of the microseism sources, using this to map the loci of ocean wave reflection points, and the removal of the bias in standard ambient noise correlation. As an application of the latter we propose to monitor Rayleigh wave velocities across the Los Angeles Basin as proxy of stress changes.

2. Locating Secondary Microseism Source Points According to the theory of Longuet-Higgins (L-H) [1950], secondary microseisms are generated where opposing primary waves interact non-linearly to produce an acoustic wave that is efficiently coupled to the seafloor, at double the frequency of the primary wave. Unlike traveling surface gravity waves, whose dynamic pressure oscillations decay exponentially with depth, microseisms do not attenuate with depth. As a result of the combined effect of lack of attenuation, the efficient coupling to the seafloor, and the relatively large areas of interaction of opposing waves on the ocean surface, seismic energy of secondary microseisms is typically 1-2 orders of magnitude larger than the energy input from the primary ocean waves which generate them. The source areas of secondary microseisms at any given time, are those ocean patches where opposing wave-wave interaction occurs.

From a seismic point of view these sources can be viewed as distributed point sources, and hence can, in principle, be located in time and space. The problem of locating the origin points of the secondary microseism points is similar to the problem of locating earthquake sources with a seismic network. The main differences are that there are likely to be several (if not many) concurrent sources at any given time, and because the secondary microseism band is quite narrow (5-8 seconds), phase is the important quantity, rather than time. For earthquake location, multiple simultaneous sources present a problem with associating arrivals with the correct earthquake. The process is non-linear and is particularly sensitive to errors when the sources are close together.

Several researchers have used methods based on triangulation [Cessaro, 1994; Schulte-Pelkum et al, 2004; Stehly et al, 2006]. With this procedure the predominant direction of the secondary energy is determined as the peak of a stack of microseism energy as function of azimuth. With the direction vectors from two or more arrays, the source region is determined by triangulation. A variation of this is to use a vector and a distance determined by the amplitude of the energy

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[Chevrot et al., 2007]. These methods, provide only approximate source locations, and do not resolve the problem of distinguishing between a number of simultaneous sources.

We have developed a location method that is suitable for the situation where the anticipated source region is in the near offshore (within ~400 km) and where there is a well-distributed onshore seismic network, as is the situation in areas such as Southern California and Japan. The procedure is an adaptation of a time-time earthquake location method proposed by Baker et al. [2005]. A similar algorithm was also developed by Kawakatsu [1998].

Figure 2. Synthetic Examples of Locating Microseism Sources. The left panel shows a typical synthetic seismogram at one station for the case of 5 sources distributed as shown by the stars in the center panel. The station locations are also shown in this panel. The right panel shows show the result of locating the source. The results show an accurate location but the amplitude has been affected by the inhomogeneous distribution of stations as discussed in the text. The grid in the center panel is symbolic; the actual solution grid is much finer.

The method is based on a mesh of potential source locations. For each time window and each potential source location we generate synthetic Rayleigh-wave seismograms for every station in the seismic array. These are then cross-correlated with the real data that is filtered to the microseism band. The zero-lag of the cross-correlation is then composited at the mesh point. When a sweep of the mesh is completed, the result is an estimate of the source locations and strengths of the secondary microseism energy. Mathematically, the image of the locations (m) is formed by

( ) (0)s dsr

m x C= ∑

where ( ) ( , ) ( , , )sd r s rC d x t s x x tτ τ= +∫ is the cross-correlation between the data, d, and the synthetics, s,.

In Figure 2, we show some synthetic examples to show the potential of the method. In each case the artificial data was created by computing simple synthetic seismograms due to a spatially distributed set of sources. The location algorithm was then applied to these data with the results shown. In most cases the sources are well located and distinctly resolved. The current version of the algorithm does not account for the amplitude decay of the waves, and the non-uniform distribution of the array.

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Figure 3. Examples of Secondary Microseism Location. The locations of the apparent source points of the secondary microseisms are shown for two different time epochs. The color scale is in arbitrary units and shows the correlation strength. Each represents correlations over one hour. The left shows the situation when many sources are active simultaneously and right panel shows the case where it is dominated by a single source point.

The method does not make an assumption about the number of sources and hence can image arbitrarily complicated source patterns. In Figure 3, we show two examples of locations at two different epochs. One has many sources active at once, while the other appears to only have a single source. We have also tested the robustness of the procedure to sources that are off the presumed mesh. In this case the sources are not artificially mapped onto the mesh, and make no more contribution than the background noise. We have also tested the procedure’s robustness with respect to interfering signals such as primary microseism energy, and this also does not appear to be a problem.

In the current implementation, the procedure performs the correlations in the frequency domain with an integration over the narrow band of secondary microseism periods (5-8 sec). The data are rotated into vertical and radial coordinates, and only these components are used in the cross-correlations because we are focusing on Rayleigh waves. Part of proposed work is to enhance the algorithm with the following:

• Add a mode filter to the data so that only retrograde motion is included in the cross-correlations.

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• Calibrate the response of the network by systematically computing a test response for each point of the mesh, and use it to form a gain parameter to remove the effect of a heterogeneous station distribution and the distance decay of amplitudes.

• Position the sources in an absolute sense requires that the variations in the group velocity of the 6-sec Rayleigh waves be determined. We have determined through synthetic tests that the image itself is robust up velocity errors of 10%. We plan to use a tomographic technique to refine the velocity model of this purpose in much the same manner as iterative location and model studies are done with earthquake data (e.g. Hauksson, [2000]).

3. Confirmation of Source Locations

3.1 Confirmation of Source Locations by Radar Imaging

One way of confirming the source locations is by analysis of the intensity of wave-wave interactions in these areas [Longuet-Higgins, 1950; Kedar et al., 2008]. Strong source areas should, according to the L-H theory, be composed of ocean regions with opposing wave energies of overlapping frequency content. Using Synthetic Aperture Radar (SAR) we can measure the multidirectional wave spectra over a large section of the ocean containing the source area in question, and so obtain a measurement of the success of the location algorithm in characterizing and in locating the microseismic source.

SAR images of the ocean surface can be used to derive directional ocean wave spectra through a nonlinear transformation that relates the SAR image spectrum and the ocean wave spectrum. The formalism for this transformation was first developed by Hasselmann and Hasselmann [1991], and further enhanced in 1995 when Engen and Johnson [1995] proposed using the image cross spectrum to extract the ocean wave spectrum. The cross spectra is the cross correlation of two images of the same location taken at slightly different times. The advantages of the cross-spectrum technique are two-fold: (1) the direction of the ocean wave spectrum is determined correctly (no 180° ambiguity), and (2) the contribution from speckle noise is virtually eliminated.

One limitation of SAR-derived ocean spectra is the relative insensitivity of the instrument to ocean waves traveling perpendicular to the imaging plane. While satellites are limited to one viewing angle, an airborne platform, such as the one used in this study, can collect data along different flight paths over the same area in a relatively short period of time (~1 hour). In addition, some radar antennas can be electronically scanned to different squint angles. UAVSAR is a new airborne radar platform that has been developed for repeat pass interferometry. In addition to having precision flight tracking (within 5 meters of the desired track), this instrument actively controls the antenna squint angle to compensate for changes in the aircraft yaw induced by wind variation during flight. This provides control of the scene viewing angle to ± 0.2°, with up to ±20° steering capability. Of even greater use for our application, UAVSAR has a multi-squint mode in which it can collect data at three different viewing angles on the same pass, increasing access to components of the ocean wave spectra in the along-track direction.

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Figure 4. UAVSAR radar swaths for data collected near the Channel Islands, Southern California. The left panel shows the swaths to be collected to the west of Santa Rosa Island. They are oriented for maximum sensitivity to the northwest swell and the line south of the island is oriented for maximum sensitivity to swell generated by storms in the southern hemisphere. The right panel shows the UAVSAR flight path and radar swaths for data collected around buoy 46069 to the south of Santa Rosa Island. Similar swaths were collected around buoy 46053 and 46063, which are also shown on the map.

Coastal reflections are largest from the areas with the steepest slopes. Parts of the Channel Islands off the coast of southern California have near-vertical cliff faces. In June 2008 we will have obtained L-band SAR data from the UAVSAR instrument collected over the ocean both north and south of Santa Rosa Island (see figure 4). These lines will be collected at three different squint angles, 0° and ±15°. We propose to analyze this data for opposing wave components reflected from the coastal cliffs of the islands and to correlate the predicted microseisms from the measured ocean wave spectrum with seismic data.

To date the fidelity of ocean wave spectra derived from SAR imagery has not been sufficient to reliably extract the smaller components, which include those from coastal reflection. To increase the accuracy, it would be useful to have “ground truth” co-located with the imagery area to refine and validate the model used to extract the ocean wave spectra. For this purpose, we collected UAVSAR data over the ocean at the location of three different buoys around the Channel Islands. Directional buoys are reliable tools for obtaining the dominant direction of the waves, and will be used for ground truthing of that component of the SAR-derived wave field. (The reflected waves, whose energy is typically lower than 5% of the incoming waves’ energy [Elgar et al., 1994], are usually “invisible” to the buoys.) The data will be collected in multi-squint mode and in several passes over each buoy to allow us to recover the full wave spectra. Figure 4 shows the location of the three buoys and the image swaths collected around buoy

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46069. Similar swaths will be collected around buoys 46063 and 46053. In addition to truth data, these swaths provide extra ocean coverage near the Channel Islands.

3.2 Confirmation of Source Locations Using Amplitude Predictions The theory of the origin of microseisms [Longuet-Higgins, 1950] has shown that the ocean surface wave–wave interaction can, under suitable conditions, cause pressure oscillations at double the frequency of the ocean waves, resulting in seismic wave generation at the ocean floor. Recently [Kedar et al., 2008] have demonstrated that with the knowledge of the ocean wave-field, the theory can successfully predict the observed seismic amplitudes in space and time (Figure 5).

Figure 5: Quantitative comparison of measured and modeled ground displacements (from Kedar et al. [2008]). A comparison between modelled vertical ground displacements using the model (red lines) and data of ground amplitudes (black lines) performed over the autumn and winter of 2003–2004, at the sites around the eastern Atlantic Ocean (BORG, Iceland; DRLN, Newfoundland; SCHQ, Quebec; HRV, Massachusetts; BBSR, Bermuda; DWPF, Florida). The seismic station names and the corresponding correlation coefficients are indicated. (Note: The references to Figures 5 and 7 refer to those figures in Kedar et al. [2008] and are not discussed here.)

In order to generate a complete model of the observed microseismic amplitudes, the theory requires full knowledge of the multi-directional ocean wave-field (which was derived from a deep-ocean Wave Action Models (WAM) in the case studied by Kedar et al. [2008]). Since in general, the dominant source of microseisms in Southern California is coastal reflections [Tanimoto et al., 2006; Schulte-Pelkum et al., 2003], which are not included in WAM’s, an alternative approach will be used here. Using the location and amplitude information, calibrated

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for the effects of the uneven station distribution as described above, the observed seismograms will be described as a sum of downward vertical forces (i.e Lamb’s pulses [Lamb, 1904]) from the entire grid, weighted by the amplitudes of the source obtained by the location algorithm. Using the notations of Richards [1979] and Kanamori and Given [1983] the vertical displacement at station i due to a vertical force applied at source element j is:

Uij (t,rij ) = I3(t,rij )∗ s(t)∗G(t)

where I3 is the vertical displacement due to a single vertical single force [Richards, 1979], s(t) is the source time function and G(t) is the instrument response. Superposing the contributions of all ocean floor area elements aj the total displacement is:

Ui(t) = a jj=1

n

∑ Uij

A

where A is the total ocean floor generation area considered.

Since these modeled displacements are based on time-averaged locations, the comparison will be done with time averaged observation time series with the same time average intervals used in the location procedure.

4. Mapping Coastal Reflections It has been shown that coastal reflection is the dominant cause of double-frequency microseisms in Southern California [Rhie and Romanowicz, 2005; Tanimoto, 2006; Bromirski and Dunnabier, 2002]. However, due to the complexities of the interaction of the incoming swell with the coastline, the process has never been characterized. Due to the same complexities coastal reflections are not included in WAM’s, which treat the coasts as absorbing boundaries. In this study a new algorithm that is related to migration in exploration geophysics and to adjoint methods in waveform tomography, and a high-resolution WAM description of the incident wave field, will be used to map and characterize coastal reflections. There is an assumption that the reflection points will be near the shore and that the high amplitude points will be associated with the greatest bathemetry slopes. Conforming this assumption will provide an additional check on the location of the source points.

4.1 Mapping the ocean-wave reflection loci The objective of this procedure is to determine where the coastal reflections are occurring and obtain some idea of the strength of the reflection coefficients. This information can then be used to better understand the physics of coastal reflections and to ultimately (though not as part of this study) incorporate them into the next generation of WAMs.

The microseism source points shown in Figure 3 are, according to the L-H theory, locations in time and space where the primary incident waves and the coastal reflected waves are opposing and coincident. With knowledge of the incident field it is possible to construct an imaging algorithm to map the loci of points that are generating the coastal reflections. This algorithm is conceptually rather simple: Considering the geometry shown in Figure 6 ocean waves are back-propagated from a secondary source point (using the imploding or adjoint Green’s function

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[Tape et al, 2007]), and the intersection of this field with the incident field at a particular time will mark the spatial location of the coastal reflector. Applying this procedure to all secondary source points that are active at a particular time, a composite map of coastal reflectors will be generated. The result can be averaged over time as variations in the incident wave will cause different parts of the coast reflect to be imaged.

Figure 6. Schematic of Imaging Coastal Reflection. The point S is the located source point of secondary microseisms. The red semi-circles are back-propagation of the coastal reflected wave at successive times. The green lines represent the primary wave motion as modeled by the wave action model (WAM). The point where the red and green are coincident in time and space is the coast reflection point (R). By taking the composite of many source points, the locus of reflection points can be mapped out.

The procedure we are proposing is similar to the migration of seismic reflection data. In this case the incident wave is the primary ocean waves, and the scattered or reflected wave is the coastal reflection. The points where we know that the reflected wave is present are the source points of the secondary microseisms. We can image the reflection points by backtracking the ocean waves from the source points and multiplying it by the incident ocean wavefield (as determined from the WAMs), and the places where they are coincident in time and space are the reflection points, and the strength is proportional to the reflection strength.

In practice, the entire map of the secondary sources would be processed at once by treating each point as a potential source with an amplitude equal to the amplitude on the map. This makes the assumption that all the factors in the L-H theory such as the angle between the opposing fields, the area of overlap of opposing fields and the depth dependence of the response are approximately the same for each point. The image is then formed by multiplying this field by the incident field determined by the wave action models (WAMs).

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4.2. High-Resolution Wave Action Models (WAMs) A key component of the previous section is estimating the primary wave field. This is typically done with WAM’s, but for the application here we will need a model with a significantly higher spatial and temporal resolution than publicly available WAM’s. This requires more that just decreasing the mesh size – higher resolution data must also be incorporated.

Figure 7. Wave Action Model. Significant wave height (m) and direction from a rough day along the Southern California coast as simulated by the SCB 0.05 degree resolution implementation of Wavewatch III (v. 2.22).

An existing operational high resolution (~5 km) regional wave model implementation for Southern California Bight (SCB) will be modified for this purpose. A prototype of this implementation was developed to provide operational high resolution wave forecasts for the region (Figure 7). The wave model [Wavewatch III, v. 2.22, Tolman, 2005] uses lateral boundary conditions from a medium-scale (25 km) resolution implementation of Wavewatch III [Tolman, 1998; 1999] run operationally by the National Oceanographic and Atmospheric Administration (NOAA) National Centers for Environmental Prediction (NCEP) Marine Modeling and Analysis Branch (MMAB). Wind data for driving the high resolution wave model come from the 12-km resolution WRF regional atmospheric model, also run operationally by NOAA NCEP. The SCB wave model will be run every 6 hours out to a lead time of 6-hours (longer lead forecasts are not necessary for this study). Corresponding microseism source locations will be determined. The model will produce fields of significant wave height, dominant direction and frequency, and time series of these variables for particular locations (e.g., at wave

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buoy locations). The model will be modified from the existing implementation to provide fields of frequency dependent standing wave cross-term (as was done on larger scales in Kedar et al. [2008]) for the proposed microseism generation study. Directional wave spectra will also be produced at a subset of selected times and locations.

The domain of the regional wave model includes (approximately) the region from 30.7°-35.7°N (Punta Colonet to Pt. Piedras Blancas) and from the mainland out to 122°W (about 80 nm west of Pt. Conception). The spatial resolution is 0.05° latitude-longitude. At this resolution, the islands in the SCB are resolved, though crudely. The model uses realistic bathymetry. The model uses 5° direction bins and 25 frequency bins covering the range from about 2.5-27 second periods.

Wind forcing for the regional model come from the 12-km resolution version of the NOAA NCEP WRF model (denoted here as “WRF-12”; WRF-12 is a follow-on to the 12 km resolution ETA model). The WRF-12 domain covers much of the eastern Pacific and North America, but wind data for the regional model domain only will be used for this regional modeling application. WRF-12 is run every 6 hours.

Lateral boundary conditions (directional wave spectra) for the regional wave model will come from the NOAA NCEP MMAB “North Pacific Hurricane (NPH) wave model. The NPH covers the North Pacific from the mainland out to 170°W, and from the equator to the Alaskan coast at a resolution of 15 minutes latitude and longitude. The NPH model generally uses winds from the NCEP Global Forecast System (GFS) model and specially prepared wind data for eastern Pacific tropical cyclones during hurricane season. The NPH model is nested within the 1° latitude-longitude NCEP global wave model and thus contains information concerning waves generated outside its domain (e.g. waves from the western North Pacific and S. Hemisphere winter cyclones). The global and NPH models are run operationally by NCEP every 6 hours.

5. Applications to Temporal Stress Monitoring

5.1 Monitoring time-dependent crustal changes using source locations We propose to utilize the procedure developed here to provide and test a method for monitoring the temporal variations in the Raleigh wave speed across the Los Angeles Basin and other basins in the S. California region. The procedure would consist of using the entire seismic network to locate the microseism sources in the off-shore regions as described in previous sections. These will be done in time intervals that are short enough to capture an adequate map of the sources before they move too far, and long enough to provide statistically meaningful cross-correlations for the locations, which, based on initial tests, is somewhere between 1 to a few hours. We will then use these sources to construct synthetic seismograms for a suite of key stations that lie on the opposite of the basin of interest. Constructing the synthetics is straightforward – the Green’s functions for the 6-second Rayleigh waves are simply integrated over the map of the source locations (the quantity m in the above equation. The synthetics will be then cross-correlated with the data from the same stations, and the shift in the peak in the correlation defined above will comprise the key measurement, which will track velocity changes as a function of time. This

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procedure implicitly uses the microseismic noise recorded at all the stations to determine the temporal variations along a particular path because of the source location step. This is in contrast to standard correlations between pairs of stations, which make the implicit assumption that the source is spatially and temporally random. This should provide a significant increase in the precision of the measurement, and make it much less sensitive to non-uniform distributions of secondary sources.

A test of the method described here is its ability to detect the known annual cycles due to the seasonal recharging and drawdown of the aquifers [Bawden, 2001]. The 6-sec Rayleigh waves sample the crust to a depth of 10-15 km, and are highly sensitive to changes in the top several kilometers (Figure 8). This is also ideal for monitoring changes in the velocity in the Los Angeles Basin, which is about 9 km deep.

Figure 8. Kernels and velocity sensitivity of 5-6 sec Rayleigh waves. In the left panel the sensitivity kernels as afunction of depth are shown (solid line – Vs, short dashed line – Vp, dashed line – density). The right panel shows the expected changes in phase velocity due to a layer with a 1% reduced velocity with the labeled thicknesses. Adapted from a JPL/Caltech technical report.

Once successful, we will focus our attention on the potential detection of tectonically induced velocity changes. Changes in the compressive stress across the basin [Bawden, 2001] will tend to squeeze the water out of the aquifers, and hence change the seismic velocities. It is this change we ultimately hope to monitor. The monitoring of the velocity changes must be on short enough time scale to avoid aliasing by the man-made changes. We believe that by using the actual sources of the microseisms we can monitor changes at intervals of a few hours.

5.2 Sensitivity analysis The quality of the estimated correlations scale as inverse square root of time in the presence of random noise [Sneider, 2004]. This means that a reasonable correlation function can be obtained with a little as one hour of data. However, as pointed out above, the real problem is bias in the noise source location, and to remove this effect by correlation requires that the data window encompass at least a complete cycle of the process that is causing the bias. If the problem is a systematic shift in the source locations due to a seasonal change in the prevailing ocean wave

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pattern, then the correlations will need to be up to a year long to confidently remove this effect. We suspect this is the problem with the example shown in Figure1, and probably is a significant factor for correlations in Southern California, As part of this project we will study the details of what is causing the bias.

The procedure described the proposal should be largely independent of the source bias problem. A weak dependence might still exist because of a sampling issue with sources moving to a preferred geographic location on a seasonal basis, but this is a second-order effect. Whether such a pattern and effect exist will be investigated under this proposal. With no source bias the necessary correlation lengths are determined by the amount of data needed to produce a reliable correlation in the presence of noise. We will investigate the correlation issues by running the analysis for the seven years of data we have for the broadband array and look for variations that appear to correlate with seasonal phenomena (wave height indices, El Nino cycles, etc).

8. Research Team The expertise and contribution to the project are listed below:

Dr. Robert Clayton a professor at Caltech specializing in seismology, and will provide overall coordination for the project. He and a graduate student will work on the algorithms to locate the microseisms, to map the coastal reflections, and to measure velocity changes across Los Angeles basins.

Dr. Sharon Kedar, is a research scientist at JPL specializing in seismology, will work on modeling the seismic amplitudes using the source locations and the L-H theory.

Dr. Nicholas Graham is a research meteorologist with the Scripps Institution of Oceanography and the Hydrology Research Center and specializes in computational oceanography, will develop the high-resolution WAMs to look at coastal reflections. He has a lot of experience with the development of WAMs.

Dr. Cathleen Jones is a research scientist at JPL specializing in synthetic aperature radar (SAR) imaging, will process SAR images to correlate with WAM and seismic locations.

Dr. Michael Longuet-Higgins, is an emeritus professor at Scripps At UCSD, Institute for Non-Linear Science. He will provide general consultation to the project. His participation is without charge to the project. He developed the basic theory on the generation of secondary ocean microseisms.

Dr. Frank Webb is a research scientist at JPL specializing in GPS and remote-sensing,, will conduct the sensitivity analysis of the temporal monitoring proposed here.

9. Work Plan

Year 1: • Enhance and extend the location method as described in the text and test robustness and

resolution. (Clayton and student) • Analyze SAR data for opposing wavefields and compare to sources predicted from

seismic and WAMs.(Jones and Kedar) • Compute WAMs for the time period of SAR observations and other keys times to start

comparison to seismically estimate sources. (Graham and Kedar) Year 2:

• Produce maps of coast reflection points from seismic images and WAMs, and compare to models of the reflection process. (Clayton, student, and Graham)

• Start the process of monitoring velocity changes across the Los Angeles Basin and do this for the past 8 years that the seismic network has been recording continuous broadband data. Compare the results to the annual ground cycle. (Clayton, student, Kedar, Webb)

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10. Broader Impact Activities The research contained in this proposal requires the expertise of three communities that have not traditionally worked together. They are seismology, oceanography, and space-based observations. If successful, it should promote a closer integration of the works of these disciplines. The P.I.s of this proposal held a special session at the Fall 2004 AGU on the topic of the use of microseisms in geophysics and it was widely attended. The publication Kedar and Webb (2005) reports on the discussion of that conference. The results of this study will be reported in the journals of each of the three disciplines. A recent publication by this project team [Kedar et al., 2008] has provided a first quantitative confirmation of the L-H theory. Education Aspects of the Proposal: This proposal will fund the Ph.D. research of a graduate student at Caltech. As is out standard practice, we will attempt to involve an undergraduate in the research either through the SURF (Summer Undergraduate Research Foundation) or MURF (Minority Undergraduate Research Foundation) programs at Caltech. These are fully funded programs and do not require additional resources from the project (other than supervision). The P.I. has had 3 SURF students and 1 MURF students in the last 5 years. References Baker , T., R. Granat, and R. Clayton, (2005), Real-time Earthquake Location Using Kirchhoff

Reconstruction, Bull. Seism. Soc. Am., 95: 699 - 707. Bawden, G., W. Thatcher, R. Stein, K. Hutnet, and G. Peltzer, (2001), Tectonic contraction across Los

Angeles after removal of groundwater pumping effects, Nature, 412, pp.812-815, doi:10.1038/35090558.

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