Use of Geophysics for Levee Investigation

Levee State-of-the-Practice Symposium

April 22, 2016

Horacio Ferriz

California State University Stanislaus

With the collaboration of

Koichi Hayashi, Geometrics

Resham Sandhu, CSU East Bay

Ashley Loogman, Fremont Gold

Use of Geophysics for Levee Investigation

Why geophysics?

Types of levees

Fauchard, C., Mériaux, P., 2007

Anatomy of a levee

Airborne electromagnetic induction

Galvanic electric resistivity

Capacitively coupled resistivity

Traditional electromagnetic induction

Ground penetrating radar

Spontaneous potential

Seismic refraction

Multi-channel analysis of surface waves (R- and L-wave

surveys)

What has been tried?

Airborne electromagnetic induction

(Hickey, 2012)

Galvanic electric resistivity

Electromagnetic induction

Slingram E-34

Fauchard, C., Mériaux, P., 2007, Geophysical and geotechnical methods for

diagnosing flood protection dikes: Editions Quae, ISBN 978-27592-00313, 128 pp.

The Sacramento-San Joaquin estuary

Capacitively-coupled resistivity

Dipole-dipole CC resistivity surveys

Multi-channel analysis of surface waves

Schematic of the process of

multi-channel analysis of R-

surface waves (reproduced with

permission from Park Seismic

webpage

www.parkseismic.com).

Sherman Island – A case study

Sandhu, 2017

Hayashi et al, 2013

Areas of future research

The Levee Project

The Levee Project is a collaborative

educational project between CSU

Stanislaus, Merced College, and

Delta College. Its goal is to have

students from the different

institutions meet, work collaborative

in the data acquisition, and develop

interest in graduating from college

with a STEM degree. Our

“graduates” have used the data to

prepare posters (AEG, GSA, WRPI,

COAST, NASA, and JPL) and to

apply for graduate school. Besides,

there is nothing like a sunny day in

the estuary!Resistivity mapping

Questions? hferriz@csustan.edu

Capacitively-coupled resistivity is a technique that arose from pioneering work in the US

and Russia [Kuras et al. (2006) provide a good historical perspective]. The technique

was further developed and popularized by Geometrics, through their OhmMapper

instrument, which exploits the capacitor properties of shielded coaxial cables. The

method relies on one transmitter and several receivers that are dragged behind a person

or vehicle. In our case we used one transmitter and five receivers.

The method is comparable to the dipole-dipole method of resistivity surveying, where a

current is injected using two current electrodes separated by a distance a, and the drop

in the voltage of the potential field is measured by a different pair of potential electrodes,

also separated by a distance a, which are placed at varying distances na from the

current electrodes (where n is a number that varies from 0.5, 1.0, 1.5, 2.0, …). The

known current and the voltage drop are used to calculate the resistance of the ground in

ohms, and using a suitable geometric factor, to calculate the resistivity of the ground in

ohms·m. In the case of the Geometrics OhmMapper, the “electrodes” are the woven

metallic shields of coaxial cables on both sides of the transmitter, the geometric function

is a complicated expression (Geometrics, 2009), and the voltage “electrodes” are the

shields of coaxial cables on both sides of each receiver.

CAPACITIVELY-COUPLED RESISTIVITY

OHM-MAPPER - THE DEVIL IS IN THE DETAILS

When the transmitter applies a current to the current “electrodes” one of them develops

a positive charge and the other develops a negative charge. The current cannot flow

through the ground because of the cable insulation. Instead, each cable behaves like a

capacitor, where one plate is the woven metallic shield of the coaxial cable and the other

is the ground. The cable with the negative charge repels electrons in the ground, while

the cable with the positive charge attracts electrons, thus creating an electrical current in

the ground and the instantaneous development of a potential field. At the same time all

this is happening, the transmitter sends a radio signal to each of the potential receivers,

imprinting on them the timing and intensity of the current. Just like in the case of the

current “electrodes”, the potential “electrodes” measure the negative and positive

charges induced in their capacitors to calculate the voltage drop and the corresponding

apparent resistivity. The calculated value is an apparent resistivity in that a very simple

assumption is made about the attribution of the resistivity value in the subsurface; the

assumption is that it is the resistivity of a point at depth located at 45º down from the

center of the current and potential electrodes, a point that we will call “attribution node”

Since there are five receivers, separated from each other by distance a, each electric

pulse of the transmitter generates 5 data points at different depths. The array is dragged

along the ground at a slow speed (say 3.6 km/hr or 60 m/min, or 1 m/sec) and a new

pulse is delivered every 0.5 sec, so apparent resistivities are gathered every half meter

(the precise number is determined by GPS), so in a very short time a dense swath of

five data points at different depths can be acquired over a distance of several hundreds

of meters. Our survey lines had typical lengths or 500 to 1,000 m.

To increase the depth of data collection, the initial distance between the transmitter and

the first receiver (which must be of the magnitude na) can be increased by changing the

spacing to a different value of na. In our case, we used a values of 2.5 m, and n values

of 1, 2, 2.5, and 3.

The last step is to invert the data (Loke, 2013; Loke et al., 2013). We used a least-

squares inversion with a “fast” Jacobian matrix (Loke et al., 2013) implemented by the

program RES2DINV (Loke, 2004). In layman terms, a model of the resistivity distribution

with depth is “guessed”, the apparent resistivity values such model would create at each

of the attribution nodes is calculated, and is then compared with the field value for the

same attribution nodes. The values would of course be different, so the initial “guess” is

refined, with the purpose of minimizing the square of the difference between the field

attributed values and the model calculated values. After several iterations a best fit is

achieved, and the resulting model is presented as the best possible model of resistivity

distributions in a tomogram form (as we know such solutions are not unique, and it is

good practice to produce two or three models by changing the inversion parameters).

Multichannel analysis of surface waves is a technique popularized by Park et al. (1999)

and Miller et al. (2000) for the estimation of seismic velocities at shallow depths. Very

readable explanations of the technique can be found in Park et al. (2007) and the

website www.MASWA.com As explained by Park et al. (2007), the multichannel analysis

of surface waves (MASW) method uses surface waves in the lower frequencies (e.g., 4-

100 Hz), which propagate through a depth of several tens meters, to estimate shear-

wave velocity (Vs) variations with depth. Shear-wave velocity is directly proportional to

the square root of the shear modulus μ and inversely proportional to the square root of

the bulk density ρ [Vs = SQRT(μ/ρ)], which in turn are linked to the stiffness and

compaction of the soil materials.

The method was developed for use with Raleigh waves (R-waves), but in our case we

used Love waves (L-waves) generated by hitting the end of a heavy railroad tie with a 10

lb sledge hammer (our selection was based on the pure shear nature of L-waves. Lane

(2009) compared the phase velocity spectra of repeat surveys using R- and L-waves on

the flood plain of the Tennessee River, where a few meters of soil cover limestone

bedrock, and found that at this particular site the records from the Love wave data

analysis produced a superior phase velocity spectrum in comparison to the spectrum

obtained from Rayleigh wave data.

MULTI-CHANNEL ANALYSIS OF SEISMIC

SURFACE WAVES

For every location, or set, we stacked three “blows” of the hammer to cancel random

noise and enhance the signal, collected the data using 10 horizontal field geophones

with a natural frequency of 4.5 Hz, with a distance of 2.5 m between the source and the

first geophone, and a constant separation of 2.5 m between geophones. For the sake of

ease of data acquisition the geophones were mounted on heavy docking stations on a

landstreamer, both manufactured by Geo Stuff, and the array was advanced by pulling it

with a truck at 5 m intervals. The records of every five sets were gathered by using the

common-depth point technique of seismic reflection.

The sampling depth of a particular frequency component of surface waves is in direct

proportion to its wavelength, so the measured surface wave velocity is both frequency-

and depth-dependent. In other words, the surface waves disperse themselves at

different depths as a function of their wavelengths/frequencies. The multichannel

analysis of surface waves method uses this dispersion property of surface waves for the

purpose of Vs profiling in 1D (depth) under each midpoint of the array. Since the array is

being dragged along and every five sets are gathered, each gather (every 5 m)

generates a 1D velocity profile. By contouring the 1D profiles along the entire length of

the survey line (typically 500 to 1,000 m), a 2D tomogram of shear wave velocities is

created.

To facilitate identification and picking of the surface wave dispersion curve, a wavefield

transform is applied to the seismic record to convert data from the offset-time dimension

(x-t) to the frequency-wavenumber (f-k), frequency-slowness (f-p) or frequency-velocity

(f-v) dimensions. Common schemes for applying this transform include the intercept

time-slowness (tau-p) transform, also referred to as the slant stack transform (Thorson

and Claerbout, 1985), f-k transform (Nolet and Panza, 1976), frequency domain

beamformer (Johnson and Dudgeon, 1993), or phase shift transform (Park et al, 1998).

Dispersive phases show a distinct pattern of normal modes in low-velocity surface

layers: sloping down from high phase velocities at low frequencies, to lower phase

velocities at higher frequencies. The distinctive slope of dispersive waves is a real

advantage of the 1/p-f analysis; other arrivals, such as body waves and air waves,

cannot have such a slope, so the analyst can “ignore” them by picking only the points

along the sloping maxima.

In our case we used a Geometrics Geode exploration seismograph to collect the data,

and the SeisImager/SW software package developed by Hayashi (2009) to process the

data and develop the 2D tomograms. Unlike the normal dispersive pattern, as shown in

Figure 5, in which phase velocity decreases as frequency increases, the data obtained

in this study shows reversed dispersive character. Phase velocity increases with

frequency, probably due to the seismic velocity inversion in which the high-velocity layer

corresponding to levee embankment overlays the low-velocity layers corresponding to

peat or clay. Inversion based on Love waves is still in the research and development

stage, and there is no commercially available processing software for it. Shear-wave

velocity tomograms were created by a simple wavelength transformation (Xia et al.,

1999), in which wavelength calculated from phase velocity and frequency is divided by

three and plotted at depth. Uncertainty is generally large in the surface wave data

processing, including higher modes, even if the inversion is applied. It should be noted

that accuracy and reliability of shear wave tomograms shown in this paper is limited,

particularly in deeper layers beneath embankment. However, the S-wave velocity

contrasts are large so we believe our interpretation of the results is robust.

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