3G - Geophysical Methods Delivering Input to
Geostatistical Methods for Geotechnical Site
Characterization
Ernst NIEDERLEITHINGERBAM Federal Institute for Materials Research and Testing, Germany
Abstract. Geophysical methods are able to contribute significantly to geotechnical site characterization. In-situ parameters are collected and gaps between boreholes or other direct tests are filled with information. However the limited resolution has to be considered and the indirect geophysical parameters have to be translated into something geotechnically useful. Moreover, the limitations have to be evaluated when including geophysical data into geostatistical models. If done properly, the use of geophysics will help in an efficient and effective site characterization. A comprehensive overview on existing geophysical (mostly seismic) methods is given as well as information on the calibration of geophysical against geotechnical parameters, pitfalls and limitations and some hints how to include these data into geostatistical/geotechnical models.
Keywords. Geophysics, geotechnics, geostatistics, models
1. Introduction
Geophysical methods are used in geotechnical engineering since several decades. A large variety of methods have been applied in site characterization, earthquake engineering, landslide investigation and many other fields. Early applications have been collected e. g. by Ward (1990), more recent ones by Reynolds (2011). Unfortunately in many cases these measurements are not fully integrated into the geotechnical investigation programs. Thus important information may have been lost at the interface between geophysicist and geotechnical engineer. Recently, geotechnical standards and recommendations are starting to include geophysics in more detail to get the best possible value out this kind of methods. On the other hand new methods to combine geophysical and geotechnical techniques have been proposed in recent research projects - many of them using geostatistical methods.
This paper focuses on the use of geophysical methods in geotechnical applications including their characteristics and limitations. Some hints and examples are given for the use of geostatistical methods in geophysics.
2. Geophysical Methods in Geotechnical Engineering
Geophysical methods are using physical fields to probe the earth indirectly and non-destructively. There are numerous methodologies, differing in capabilities, limitations, resolution, type of physical field, use of active or passive sources, frequencies, sensor type and so on. This chapter just gives a rough overview. For more details the reader may refer to Reynolds (2011) or Everett (2013).
2.1. Geophysical Methods and Their Limitations Seismic methods are probably the most used in geotechnical applications. They use elastic waves, which are reflected, refracted (Figure 1) and scattered by in homogeneities in the subsurface. Structures can be delineated and dynamic elastic properties can be determined. Some of the latter are closely related to geotechnical properties as initial (low strain) stiffness G0. Seismic methods
come in lot of variations with different capabilities and limitations. Some of them display a lack of resolution very close to the surface (top few meters).
© 2015 The authors and IOS Press.
This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License.
Figure 1. Example for a geophysical method, probing the earth with surface sensors: Refraction seismics. An impact generates waves traveling downwards. Under certain conditions a part is moving along layer boundaries (e. g. top of bedrock), sending energy back to the surface. From the recordings seismic velocities and layer depth can be determined (from DGZfP, 2013).
Resistivity methods use electrical currents to probe the earth via lines or 2D arrays of electrodes. 2D or 3D subsurface resistivity images are provided via numerical inversion of hundreds or thousands of measurements (ERT: electrical resistivity tomography). Resistivity changes can be related to soil/rock type, moisture content, salinity and various other parameters. Local calibration for depth and material is required in most cases. Correlations to geotechnical parameters are mostly empirical.
Electromagnetic methods work (mostly) contact-less and measure electrical resistivity as well (or conductivity – the reciprocal). Various instruments with different source types and penetrations depths are available. They have in general the speed advantage compared to resistivity, but less accuracy, resolution or depth coverage under respective conditions.
Ground penetrating radar (GPR) uses high frequency electromagnetic waves. It is mainly used to map structures and obstacles in the very near surface (e. g. pipes), but the results may also reflect moisture changes. GPR does not work properly in clay or other conductive soils.
So called potential methods as magnetics or gravity measurements are limited (in geotechnical projects) to obstacle detection, e. g. unexploded ordnance (magnetics) or larger voids (gravity).
There is a variety of other, mostly special purpose methods which might be of benefit for
certain investigations, but can’t be discussed here. For many methods variations using borehole sensors (example in Figure 2) may be applied in case enhanced resolution at depth is required or the subsurface has to be probed beneath structures.
Most methods require sophisticated computer software tools to convert (image, invert) the data acquired at the surface (or in a borehole) to models of the subsurface (a 2D- or 3D-distribution of a certain physical property). This process is here referred to as geophysical model building and is often ill conditioned and/or underdetermined. It greatly benefits from including information from ground truth or the combination of multiple geophysical methods.
An example of the use of a variety of geophysical techniques is shown by Mooney (2015) in the same volume.
Figure 2. Example for a geophysical method, probing the earth with borehole sensors: Seismic tomography. A source in one borehole sends seismic waves to receivers in another borehole. The measurement is repeated with several source depths. Using sophisticated math the distribution of seismic velocities (and from there elastic parameters) between the boreholes can be established (from DGZfP, 2013).
2.2. Errors and Uncertainties in Geophysics The errors and uncertainties of geophysical methods are hard to predict without site and method specific ground truth. No general rules, formulas or numbers can be given here, but some hints.
Measurement (instrumentation errors) can considered to be low or at least approximately known. If possible and appropriate, bias, drift and noise measurements are taken and the results are reported. In most cases, measurements are repeated and stacked. For instance, most resistivity instruments are repeating measurements until certain quality criteria are met, for example a standard deviation of less than 3 %.
Positioning errors of the sensors don’t play a significant role in practice, as modern techniques (GPS, etc.) limit these to the centimeter range, at least if the geophysical contractor works properly.
Of much greater significance is the uncertainty involved in geophysical model building. In many cases, more than one model is able to explain the data. For example, in resistivity the principle of equivalence is known, which says that a thin layer with a very high resistivity looks similar in the data as a slightly thicker, slightly less resistive one. This causes connected uncertainties in position (layer depth in the example given) and material properties at the same time. In addition, the modeling algorithms used have inherent limitations and may not necessarily reflect the full complexity of the real subsurface.
Another point which has to be taken into account is stationarity. Stationarity in a geostatistical sense requires that mean and variance have to be finite and constant in the area under investigation. This is not necessarily the case for geophysical data. Data set may have to be detrended or transformed, e.g., as used in example in section 4.2.
2.3. Geophysical and Geotechnical Parameters Only in a very few cases geophysical and geotechnical parameters are directly related or even identical. Among the exceptions are vs30
(average shear wave velocity in the uppermost 30 m), an important property in earthquake engineering, or G0 (initial stiffness) which is
closely related to G (the dynamic shear modulus). The latter can be measured be determining shear wave velocity vs
= (1)
For most other combinations of geophysical and geotechnical properties, empirical equations have to be (or already have been) established. Most of them are material- or even site-specific. These kind of “calibrations” are mainly performed by fitting simple analytical models (not necessarily reflecting physics) to laboratory or borehole data. Figure 3 shows an example. Great care has to be taken to consider only homogeneous groups of data. For instance, in the example of Figure 3 all weathered or unconsolidated samples showed a different behavior than sound material.
Figure 3. Example for establishing an empirical relationship between a geophysical (compressional wave velocity cp) and
a geotechnical property (undrained shear strength qu) for
limestone samples of a south-west German area (from DGZfP, 2013).
2.4. Standards and Recommendations
In the past two decades, several standards and recommendations have been developed on the use of geophysical methods for geotechnical purposes. However, it is difficult to find general guidance. Some standards as the various ASTM documents are describing specific methods in detail, sometimes without leaving space for proper adaption to the project’s needs (e. g. ASTM D4428, D5777, D7400). Others give just a rough overview on existing methods without proper hints how to apply them and integrate them into geotechnical survey concepts (e. g. DIN EN 1997). Only a few documents (e. g. USACE (1995/2005), Wightman et al. (2003), DGZfP B8 (2013), SEGJ (2014)) are covering the topic in detail. Some of them are outdated.
An exception is the investigation of river embankments. After disastrous events in the past fifteen years, several recommendations and
guidelines have been developed, e. g. by Fauchard & Mériaux (2007) , Weller et al. (2010, English summary in Niederleithinger et al, (2012)), Ciria (2013), which cover geophysical investigations on river embankments in great detail and up to date technology.
To the knowledge of the author, geostatistical concepts have not yet been covered in any of the documents mentioned.
3. Geostatistics in Geophysics
The use of geostatistical methods in geophysics is not new. So far, there have been two main fields of application: mapping and petrophysical parameter estimation, the latter mainly applied in the characterization of hydrocarbon reservoirs. 3.1. Mapping
Producing maps and automatic contouring of geophysical (or other) data is an issue not without problems since decades. The purpose is, in most cases, the interpolation of irregular spaced and often partially sparse data to dense regular grids. This is not only done for mapping purposes but also to collocate data from different types of investigations. Many simple techniques (linear, polynomial or spline interpolation, inverse distance, nearest neighbor, etc.) have been used for a long time.
Since the 1970’s, a statistical method proposed by Krige (1951) has become more and more popular in geophysical mapping; namely, kriging (e.g. Olea, 1974) and its variant cokriging. The significant advantage of these techniques over conventional methods is that the spatial variability is taken into account, spatial clusters of data points are treated well and error estimates for the interpolated points are available. Kriging and cokriging are meanwhile integrated in most relevant mapping software packages. 3.2. Petrophysical Parameter Estimation in Reservoir Geophysics
Seismic reflection methods are well established in hydrocarbon exploration. They are used primarily to identify structures (position, depth, shape) which might contain oil or gas. Seismic
parameters as velocities or acoustic impedance are also used to determine petrophysical data as lithology, porosity or pore fluids.
Conventionally, this is performed according to a sequential procedure. In a first step, the seismic data are inverted to elastic parameters (“seismic inversion”). In a second step, the elastic parameters are converted to petrophysical parameters by using local correlations obtained e. g. from theoretical rock physics or data from well logs.
An early example of introducing geostatistical methods is given by Doyen (1988). Recently Bosch et al. (2010) published a review on these approaches. The information given below was taken from this paper.
Geostatistical methods try to incorporate all information on reservoir properties in the inversion procedure, often in a Bayesian formulation. This guarantees consistency between elastic and reservoir properties. In addition, geostatistical methods help to add constraints of spatial correlation, data conditioning and incorporating different scales.
Figure 4 shows a synthetic example for conventional and geostatistical based reservoir characterization given by Bosch et al. (2010). The shape of the subsurface sandy channels is reproduced much better by geostatistical inversion.
4. 3G – Combining Geophysics and Geotechnics by Geostatistics 4.1. Use of (Geo)Statistical Methods in Integrated Geophysical Model Building
Geophysical model building describes the process to calculate subsurface distributions of (geo)physical parameters (seismic velocities, electrical resistivity or other) from data acquired at the surface or in boreholes. This process is often non-unique, or requires the subjective setting of certain parameters. Different geophysical methods may show different unit (layer, object) boundaries as the physical parameters involved are sensitive to different petrophysical parameters.
The inclusion of existing a priori information (e. g. from boreholes) and the joint
model building from different geophysical datasets are methods to overcome these problems. Many techniques are available to perform these operations. Geostatistical methods recently have been used with good success herein (e.g. Linder et al., 2010, Paasche et al., 2012, Caterina et al., 2014).
Figure 4. Comparison of conventional and geostatistical based methods to estimate petrophysical properties from seismic data. a) Input true model showing spatial distribution of lithology categories (sand and shale, showing a channel type geometry), corresponding compressional velocity vp and
distributions and vp-
lithologies. b) Input seismic data, computed by simulation from the input data, c) acoustic impedance section obtained by conventional seismic inversion and d) probability for sand by geostatistical inversion of the same seismic data. From Bosch et al. (2010).
As an example, the results of using fuzzy c-means clustering in the imaging process to derive a joint subsurface model from seismic and GPR borehole tomography data (Linder et al., 2010) is shown in Figure 5. The datasets have been acquired at a test site used for the validation on non-destructive testing methods for civil engineering close to Horstwalde, Germany (Niederleithinger, 2009). The clustering method not only combines different methods; it also sorts the subsurface into different units, which helps to interpolate layer between boreholes and/or CPT soundings. The method has recently been improved to include not fully co-located data and to include a-priori information (Paasche et al. 2012).
Figure 5. Joint tomographical geophysical model obtained by clustering from seismic and GPR data compared to CPT tip resistance from 2 soundings between the geophysical boreholes. Units with low tip resistance (green and yellow clusters) are well differentiated from those with intermediate (blue, grey) or high values (red). From Linder et al. (2010). 4.2. Estimation of Geotechnical Parameters From Geophysical Models by Geostatistics
As stated earlier, the determination of geotechnical parameters from geophysics is a complex, difficult issue as the dependencies are often non-unique, nonlinear and site specific. Geostatistical methods might be of help, even if the geophysical data sets have been processed and mapped in a conventional way, separately from each other and not using a priori information.
De Benedetto et al. (2012) show an example on producing clay content maps for precision agriculture from a limited number of soil sampling points, using resistivity and GPR measurements as auxiliary information. In this study, a procedure called kriging with external drift (KED) was used to establish relationships between clay content at sampling points and the geophysical values measured as well as to use the results to produce detailed maps for the survey area. Figure 6 shows one of the evaluated geophysical data sets (electromagnetic induction, EMI). Figure 7 shows the results of using KED for clay content mapping. Note that there is limited correlation between the EMI dataset (Figure 6) and the estimated clay content (Figure 7) as the other geophysical data used (not shown here) are influencing the result as well.
Figure 6. One of several geophysical data set used to estimate clay content (electrical conductivity measured by the electromagnetic induction method). From de Benedetto et al. (2012).
4.3. Integrated Geophysical/Geotechnical/ Geostatistical Model Building
The optimal way to derive reliable geotechnical models would of course be to integrate the geophysical/geotechnical model building process as much as possible. Due to the different kind of parameters and data acquisition methods (and positions) this is a quite difficult task.
Figure 7. Clay content estimation (20 – 40 cm depth) by kriging with external drift (KED) from the data set shown in Figure 6, GPR data and a few soil samples. From de Benedetto et al. (2012).
Recently, Rumpf & Tronicke (2014) have published an approach which tries to use statistical based methods both for geophysical and geotechnical model building. However, the process is still divided in two steps.
Data have been collected at the same test site as used by Linder et al. (2010). In a first step, the geophysical data (p- and s-wave seismic and GPR borehole tomographic data) have been converted to subsurface models inverted using a novel technique called particle swarm optimization (PSO). This method mimics the social behavior and delivers not a single, but a large ensemble of models, which explain the data within the frame of measurement accuracy.
In the second step, a method called ACE (alternating conditional expectation) was used to establish relationships between the set of geophysical parameters (seismic velocities vp, vs,
GPR velocity vGPR) and geotechnical properties
(here: CPT sleeve friction fs) obtained from
boreholes or CPTs. ACE determines optimized nonlinear transformations for all parameters to obtain a linear relationship between the transformed dependent (geotechnical) property and the sum of the transformed independent (geophysical) properties without a priori knowledge. Uncertainty is included by using all the models in the ensemble determined by PSO in the first step. Back-transformation delivers the
distribution of the geotechnical parameter in the entire subsurface space covered by geophysics. For details see Rumpf & Tronicke (2014).
Figure 8 shows the result of ACE evaluation of a single geophysical data set obtained by PSO. The transformation of the geotechnical parameter (here: CPT sleeve friction) is bilinear while the geophysical ones are highly nonlinear. The resulting relationship (part e of Figure 8) is linear with a high correlation coefficient (0.98). The same kind of analysis was done using many other PSO models. All results are compared to the real geotechnical at the CPT points in Figure 9 showing a more than sufficient degree of coincidence.
Figure 10 shows the result of the translation of the geophysical tomograms to a geotechnical subsurface model. The model shows a lot of details, reflecting the glacial geology at the test site. Uncertainty in the geotechnical parameter is established as well, giving valuable input for probabilistic geotechnical design. A similar approach using different statistical techniques, is presented by Paasche (2015) in the same volume.
Figure 8. ACE evaluation for CPT sleeve friction fs:
Nonlinear transformations for geophysical parameters (a-c), the geotechnical parameters (d) and the resulting linear relationship between transformed parameters. From Rumpf & Tronicke (2014).
Figure 9. Evaluation of the transformation derived by ACE (Figure 8) at the CPT sites involved. Black line: CPT sleeve friction data. Grey: Bandwidth of ACE results for different training data sets from PSO. Red Line: Median of ACE results. From Rumpf & Tronicke (2014).
Figure 10. Subsurface model of CPT sleeve friction obtained by transforming the geophysical tomograms using the ACE results (Figure 8). a) Distribution of sleeve friction. d) Interquartile range derived from1000 ACE evaluations. From Rumpf & Tronicke (2014).
5. Conclusion and Outlook
Geophysical methods can give valuable input to geotechnical site characterization. Some methods are used since decades by geotechnical engineers. The main advantage of these methods lies in the fact that data are obtained from parts of the subsurface which are not accessible (at least not at reasonable cost) for conventional investigations.
It should be taken into account that geophysical parameters do not necessarily reflect geotechnical properties directly. The relationships might be nonlinear, non-unique and site-specific.
In addition, geophysical methods have limited method- and site-specific accuracy and resolution. The techniques involved in geophysical model building include inaccuracies and eventually ambiguities as well. In most cases, more than one model is able to explain the data. Site and problem specific choice of an appropriate combination of geophysical methods and measurement parameters are prerequisites for success.
Geostatistical techniques play an increasing role at the interface between geophysics and geotechnics. They are used for geophysical model building to include a priori knowledge, to combine results from different methods or to cluster geophysical datasets.
Even more important is the use of geostatistical techniques for the translation of geophysical to geotechnical parameters. By use of modern techniques, geophysical data, despite all the uncertainties involved, can be transformed to detailed and reliable geotechnical models.
References
ASTM D 4428/D 4428M – 00: Standard Test Methods for
Crosshole Seismic Testing.
ASTM D 5777 – 00: Standard Guide for Using the Seismic
Refraction Method for Subsurface Investigation.
ASTM D 7400 - 08, Standard Test Methods for Downhole
Seismic Testing.
Bosch, M.; Mukerji, T.; Gonzalez, E.F. (2010). Seismic Inversion for Reservoir Properties Combining Statistical Rock Physics and Geostatistics: A Review.
Geophysics 75 (5), 75A165–75A176.
doi:10.1190/1.3478209.
Bourges, M.; Mari, J.-L.; Jeannée, N. (2012). A Practical Review of Geostatistical Processing Applied to
Geophysical Data: Methods and Applications: Geostatistical Processing Applied to Geophysical Data.
Geophysical Prospecting 60 (3), 400–412.
doi:10.1111/j.1365-2478.2011.00992.x.
Caterina, D.; Hermans, T.; Nguyen, F. (2014). Case Studies of Incorporation of Prior Information in Electrical Resistivity Tomography: Comparison of Different Approaches. Near Surface Geophysics 12 (4), 451-465. doi:10.3997/1873-0604.2013070.
Ciria (2013). The International Levee Handbook. CIRIA C731 2013. RP957. ISBN: 978-0-86017-734-
De Benedetto, D.; Castrignano, A.; Sollitto, D.; Modugno, F.; Buttafuoco, G.; lo Papa, G. (2012). Integrating Geophysical and Geostatistical Techniques to Map the Spatial Variation of Clay. Geoderma 171–172, 53–63. doi:10.1016/j.geoderma.2011.05.005.
De Benedetto, D.; Castrignanò, A.; Rinaldi, M.; Ruggieri, S.; Santoro, F. ; Figorito, B.; Gualano, S.; Diacono, M.; Tamborrino, R. (2013) An Approach for Delineating Homogeneous Zones by Using Multi-Sensor Data.
Geoderma 199, 117–27.
doi:10.1016/j.geoderma.2012.08.028.
DGZfP (2013). Recommendations for seismic site
characterization (Merkblatt B8). DGZfP, Berlin
DIN EN 1997-2: Eurocode 7, part 2: Ground investigation
and testing. German Version EN 1997-2:2007.
Doyen, P. M. (1988). Porosity from Seismic Data: A Geostatistical Approach. Geophysics 53 (10); 1263– 75. doi:10.1190/1.1442404.
Engdahl, N. B.; Weissmann, G. S.; Bonal, N. D. (2010). An Integrated Approach to Shallow Aquifer Characterization: Combining Geophysics and Geostatistics. Computational Geosciences 14 (2), 217– 29. doi:10.1007/s10596-009-9145-y.
Everett, M. E. (2013). Near-Surface Applied Geophysics. Cambridge University Press.
Fauchard, C.; Mériaux, P. (2007). Geophysical and
geotechnical methods for diagnosing flood protection dikes. Éditions Quae, Paris.
Krige, D. G. (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J. of the
Chem., Metal. and Mining Soc. of South Africa 52 (6):
119–139.
Linder, S.; Paasche, H.; Tronicke, J.; Niederleithinger, E.; Vienken, T. (2010) Zonal cooperative inversion of crosshole P-wave, S-wave, and georadar traveltime data sets. Journal of Applied Geophysics. 72 (4), 254–262 Mooney, M. A. (2015) Spatio-Temporal Characterization of
Earth Dam and Levee Geotechnical Conditions using Geophysical Imaging. Same Volume.
Niederleithinger, E.; Wiggenhauser, H.; Taffe, A. (2009). The NDT-CE test and validation center in Horstwalde. In : NDTCE `09 - 7th International symposium on
nondestructive testing in civil engineering (Proceedings), Nantes, France, Laboratoire Central des
Ponts et Chaussées.
Niederleithinger, E., Weller, A., & Lewis, R (2012). Evaluation of Geophysical Techniques for Dike Inspection, JEEG 17(4), 185-194.
Olea, R. A. (1974). Optimal Contour Mapping Using Universal Kriging. Journal of Geophysical Research 79 (5); 695–702. doi:10.1029/JB079i005p00695.
Paasche, H.; Tronicke, J.; Dietrich, P. (2012) Zonal cooperative inversion of partially co-located data sets constrained by structural a priori information. Near
Surface Geophysics, 10 (1824), 103-116, doi:10.3997/1837-0604.201133.
Paasche, H. (2015) Approaches towards a probabilistic
assessment of geotechnical parameter distributions relying on geophysical imaging. Same Volume.
Reynolds, J. M. (2011). An Introduction to Applied and
Environmental Geophysics. John Wiley & Sons.
Rumpf, M.; Tronicke, J. (2014) Predicting 2D Geotechnical Parameter Fields in near-Surface Sedimentary Environments. Journal of Applied Geophysics 101, 95–107. doi:10.1016/j.jappgeo.2013.12.002.
SEGJ (ed.) (2014): Application Manual of Geophysical
Methods to Engineering and Environmental Problems.
EAGE Publications bv, Houton, NL. ISBN 9789073834880.
Schön, J.H. (2004) Physical Properties of Rocks:
Fundamentals and Principles of Petrophysics. Elsevier,
Amsterdam, ISBN 0-08-041008-1.
USACE (1995/2005): Geophysical Exploration for Engineering and Environmental Investigations.
University Press of the Pacific.
Ward, S. H. (ed.) (1990). Geotechnical and Environmental
Geophysics. Investigations in Geophysics 5. SEG,
Tulsa.
Weller, A., Lewis, R., and Niederleithinger, E., 2008. Geophysikalische Verfahren zur Strukturerkundung und Schwachstellenanalyse von Flussdeichen – Ein Handbuch (Geophysical methods for structural evaluation and weak point detection of river embankments, in German), BAM Forschungsbericht 281, BAM, Berlin, Germany.
Wightman, W.E.; Jalinoos, F.; Sirles, P.; Hanna, K. (2003):
Application of Geophysical Methods to Highway Related Problems. FHWA technical manual, contract
no. DTFH68-02-P-00083.