A geomorphological mapping approach for the assessment of seabed geohazards and risk
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- Hough, G., Green, J., Fish, P. et al. Mar Geophys Res (2011) 32: 151. doi:10.1007/s11001-010-9111-z
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Exploration and development of offshore hydrocarbon resources has advanced into remote deepwater regions over the last decade and poses significant technical challenges for the design and installation of wells and facilities at extreme water depths. Seafloor and shallow subsurface processes and conditions in these areas are complex and generally poorly understood, and the geohazards to development are larger scale and fundamentally different to those encountered onshore; consequently the geohazard risk to deepwater development projects is potentially significant and requires careful evaluation and mitigation during the front-end planning and engineering design stages of projects. There are no established industry standards or methods for the assessment of geohazards and engineering-quality geophysical data at the scale of development. The paper describes an integrated and systematic map-based approach for the assessment and mitigation of seabed geohazards and risk to proposed deepwater development. The approach employs a multi-disciplinary team working with engineering-quality field calibrated data to accurately map and assess seafloor ground conditions and ensure that development proposals are not exposed to intolerable geohazard risk. The approach taken is very similar to the practice of establishing geological models for land-based engineering projects, in which the complete geological history of the site is used to characterise and predict the performance of the ground. Such an approach is routine for major projects on land but so far does not seem to be common practice in the offshore industry. The paper illustrates the seafloor geomophological mapping approach developed. The products are being used to optimise development layouts to avoid geohazards where possible and to support site-specific engineering design of facilities based on a detailed understanding of the potential geohazard loadings and associated risk.
KeywordsGeomorphological mappingGeohazard riskGround modelsSeafloor
Introduction and approach
This paper presents an integrated approach to the systematic mapping of seafloor geomorphology to inform geohazard risk assessments of proposed oil and gas development sites. Geohazards are defined as geological materials, features or processes that represent commercial and safety risks to development and/or risks to the environment. Examples described here include landslides, faults, salt diapirism, gas/fluid expulsion, and adverse soil conditions. Typical geohazard triggering events include seismicity, volcanism, climatic events and human activity. Deepwater oil and gas developments are increasingly focused in areas where sediment thicknesses or deposition rates are high, excess pore fluid pressures or overpressures may exist, soil strength is low, and where seabed forms indicate pre-existing seabed instability, surface displacements or fluid escapes. Such conditions pose a potential significant risk to oil and gas exploration and development and can result in construction and operational problems if not properly investigated, assessed and mitigated.
Assessment of geohazards and ground conditions is an integral part of risk assessment for offshore oil and gas projects yet there are no established industry standards or methods for the assessment of geohazards and engineering-quality geophysical data to support development and engineering. Prior and Hooper (1999) provide a good review of past achievements and future directions for engineering geomorphology mapping of the seafloor and Hampton and Lee (1996) provide similar for submarine landslides research. Locat (2001) and Locat and Lee (2002) provide a geomorphological and geotechnical perspective of seafloor instability and submarine landslides along ocean margins. Over the last decade there has been an emerging literature of regional-scale case studies and assessments of submarine landslides as a result of the capture and release of high resolution bathymetry and seismic data for research e.g. McAdoo et al. (2000), Huhnerbach and Masson (2004), Masson et al. (2006), Ten Brink et al. (2006), Gee et al. (2007), Cauchon-Voyer et al. (2008) and Twichell et al. (2009).
The level of detail of an assessment should be proportional to the degree of the anticipated hazard and risk, with a high risk setting requiring a higher level of investigation. It requires a systematic search for geohazards using appropriate data to catalogue geohazard features, ground conditions and seabed processes. Based on a sound understanding of the controls of past natural geohazards and processes, the likelihood of future processes and events can be estimated (e.g. Locat and Lee 2002; Jeanjean et al. 2005). In order to undertake a full quantitative geohazard risk assessment, it is necessary to understand the vulnerability of development and subsea facilities to these geohazard processes (Evans et al. 2007). Such an approach has developed significantly in the last decade, allowing geohazard risk mitigation strategies to be implemented in practice (Jeanjean et al. 2005; Kvalstad 2007; Moore et al. 2007).
Completion of comprehensive geological, geomorphological and geotechnical desk studies of the development area;
Integrated geomorphological mapping of the seabed across the development-area and interpretation of shallow (i.e. less than 1 km below mudline) geohazard features through integration of bathymetry and seismic data;
Development of geohazard ground models;
Preparation of a risk register, screening and assessment of geohazards of significance to development proposals;
Optimisation of seismic surveys and geotechnical data acquisition to support development planning, engineering design and site-specific geohazard investigations and mitigation; and
Guidance and communication on geohazards and ground conditions to wells and facilities engineers during project appraisal, Front-End Engineering and Design (FEED) and construction stages.
A typical sequence of work will begin with a comprehensive desk study based on pre-existing data or published reports covering the area of interest. The work will include a regional geological, geomorphological and geotechnical assessment of the development area to provide important context to the regional setting and its past and future evolution. The desk study is followed by a high-level screening of the more significant potential geohazards that may exist within or affect the proposed development area. These first two stages enable informed decisions to be made on the scope of data acquisition needed to support project appraisal and FEED, and the appropriate scale of seabed mapping and sampling. Detailed interpretation of these data is then performed which may involve completion of multidisciplinary assessments as required by the project, such as fault hazard analysis, pockmark hazard analysis, slope stability assessment and salt diapir analysis. This information allows the development of a series of seismo-stratigraphy, and geohazard ground models and soil models.
A key element of the approach is the integrated seismo-geomorphological mapping of the seabed. This provides a means of integrating data on seabed geomorphology interpreted from bathymetry, with sub-seabed geological data interpreted from seismic data, to give a three dimensional understanding of geohazard processes (Posamentier 2000). The mapping approach developed for the seafloor follows the principles of detailed morphological mapping reported by Savigear (1965), Brunsden and Jones (1972) and Cooke and Doornkamp (1990), and has been developed to incorporate a conceptual understanding of geohazard magnitude and frequency. Since the availability of high resolution sea floor images, with continuous coverage over large areas, investigations into sea floor processes using geomorphological mapping have been undertaken through large collaborative projects, e.g. STRATA-FORM (Nittrouer and Kravitz 1996) and COSTA-Canada (Cauchon-Voyer et al. 2008); large regional studies e.g. across the US continental slope (McAdoo et al. 2000; Twichell et al. 2009); off the coast of northwest Africa (Masson et al. 2006); and for site-specific studies e.g. northwest Borneo (Gee et al. 2007). The approach described in this paper expands on regional terrain assessment style mapping (e.g. Bryn et al. 2005) and more detailed feature mapping (e.g. Micallef et al. 2009) often undertaken for offshore geohazard studies. The morphological map provides a record of the seabed form and features which are not necessarily portrayed by bathymetry or contours. The morphological map provides an important spatial context (framework) of existing seabed forms and potential processes, and how these may interact with development proposals. This spatial framework is used to underpin interpretation and derivative maps including definition of terrain units, geomorphology, geohazards, soil conditions and planning guidance. The integrated seismo-geomorphological approach provides a ground model framework for subsequent work that assesses the magnitude and frequency of potential geohazard events for quantitative risk analysis.
The integrated multi-disciplinary team approach is very similar to the practice of establishing geological models for land-based engineering projects, in which the complete geological history of the site is used to predict the performance of the ground in response to engineering work and to identify the likely presence of geohazards (Brunsden 2002). Such an approach is carried out fairly routinely for major projects on land, but so far does not seem to be common practice in the offshore industry.
Data sources and resolution
Sites can typically cover up to 1,000 km2 and the reliability of geohazard assessments depends on the quality and extent of the geophysical and geotechnical data across the area. 3D exploration-quality data is typically available early on in the project and provides an excellent dataset for the initial assessment and screening of geohazards. High-resolution engineering-quality data is generally not available early on in projects but is used to resolve features and ground conditions in the shallow section and may include Ultra High Resolution (UHR) and Autonomous Underwater Vehicle (AUV) surveys including Multibeam Echosounder (MBES), Side Scan Sonar (SSS) and Compressed High Intensity Radar Pulse (CHIRP) seismic reflection data.
Summary of geophysical dataset resolution and penetration
Penetration (m below seabed)
CHIRP collected by AUV
Multibeam echosounder collected by AUV
Side scan sonar collected by AUV
Table 1 also illustrates the relationship between resolution and penetration depth for geophysical datasets. The highest resolution CHIRP dataset can only resolve the structure of a comparatively shallow section of sediments, while 3D seismic data penetrate to depths of many kilometres but provide poorer resolution of sediment thickness and stratigraphy. Steep seabed topography may limit the quality of sub-bottom imagery collected using an AUV, whilst data artefacts have been noted in very deep water (>2,000 m) in 2D UHR datasets. The positional accuracy of geophysical survey vessels using Differential Global Positioning System (DGPS) may be degraded from <1 m to 5–10 m due to vessel motion and survey equipment laybacks as well as periods of poor satellite coverage.
Other sources of data, such as exploration and development well drilling reports, environmental baseline surveys (still or video footage with limited grab sampling of sea bed materials) using Remotely Operated Vehicles (ROV) and ocean current monitoring, can be incorporated into the geohazard assessment.
Seafloor mapping and characterisation
- 1.Generation of baseline imagery layers: processing of the bathymetry and seismic datasets is carried out to optimise visualisation of the various geophysical survey data, including bathymetry (water depth), shaded relief, seabed slope angle (Figs. 1, 2) as well as seabed aspect and side scan sonar mosaics. The data shown in Figs. 1 and 2 are derived from CHIRP collected from an AUV, with a resolution and penetration depth as outlined in Table 1. The spatial data can be viewed in ArcGIS, and thus compared and thoroughly interrogated. For example the shaded relief can be viewed from a range of sunlight directions to highlight every part of the undulating terrain and seabed features. Seabed slope angles can be grouped into different classes and ranges e.g. focus may be required on seabed angles of engineering importance. Interactive 3D visualisation tools (such as Fledermaus) can be used to view seabed topography, giving a different perspective to the geohazard features which can aid in the mapping and interpretation (Fig. 3). ArcGIS is also used to locate the position of sub-bottom profiler survey lines across the area of interest to compliment seismic data (Fig. 4) viewed in seismic interpretation packages (such as Seisworks or SMT Kingdom).Examples of baseline imagery layers used in this paper (Figs. 1, 2, 3, 4) illustrate the same area of seabed to aid comparison. Fig. 1 shows a section of seabed, viewed using high-resolution engineering-quality MBES data with the bathymetry DEM over the hillshade. The image is of an elevated plateau running vertically down the page with evidence of mass movement to the west and east of the plateau. To the east of the plateau a steep scarp (greater than 10°) has developed with evidence of mass movement associated with the scarp. To the west of the plateau the bathymetric data and sub-surface data reveal a series of tensions cracks, pull-apart windows (i.e. exposed shear surfaces), displaced slabs and compression zones (features highlighted in Fig. 4).
- 2.Morphological mapping: systematic mapping of morphological features observed in seafloor imagery provides a factual dataset for geomorphological interpretation and provides freedom for derivative maps to be superimposed on the same mapped features (Fig. 5). The key objective of morphological mapping is to characterise the form of the seafloor (i.e. scarp slope, smooth convex slope, ridge etc.) and should avoid interpretation of the feature which should be conducted as a separate task (see geomorphological interpretation, next). A bespoke set of slope morphology lines and symbols are used for mapping based on published standards to represent sharp breaks and smooth changes of slope, conical and linear depressions, ridges and areas of variable seabed texture (e.g. Cooke and Doornkamp 1990). Where necessary, new symbols are developed to fit the specific requirements of the seabed environment. Systematic mapping of all features is undertaken at a consistent scale appropriate for the project. Typically a scale of 1:5,000 is used, however larger scales may be needed to map in details of complex landforms, and also smaller scales may be used to better understand the broader context of the site.
- 3.Geomorphological interpretation: geomorphological interpretation of seafloor features and processes is conducted using all the available baseline image layers and seabed morphology factual data (Fig. 6). The interpretation uses classified shading and linework to indicate the distribution and types of existing features and potential processes, which may include for example major terrain features (e.g. plateaus, canyons), mass movement features (e.g. pre-existing landslides, tension and compression features), sediment scour and deposition features (channels, flutes, bedforms, moats) and fluid expulsion features (e.g. mud volcanoes, pockmarks). Interpretation of seafloor features revealed on bathymetry datasets must be integrated with interpretation of sub-surface geophysical data to ensure consistency and quality of interpretation. Figure 6 shows the typical detail of this work showing how landslides have been subdivided into their constituent parts of source, displacement and accumulation zones. The interpretation of existing and potential geohazard processes should be documented in the project risk register and guidance provided to the project and engineering teams.
- 4.Ground models: based on the seismo-geomorphological interpretation, conceptual three dimensional block models are produced to illustrate and communicate the nature of geomorphological and geohazard features and processes present across the development area (Fig. 7). They can be used to illustrate and communicate the modes of potential ground behaviour that could be expected given reactivation or ongoing activity of these features through the life-of-field, enabling the engineering team to understand the range and scale of features and processes that might be encountered by the development. Ground models can be used to illustrate the modes of potential damage to infrastructure associated with predicted ground behaviour. Ground models are also used to show the potential lateral and vertical variability in ground conditions in relation to the features observed and in areas, where ground-truthed data are not necessarily available.
Soil Conditions: an assessment of the expected soil conditions in the development area is initially based on information available from the desk study together with an appreciation of the development-wide geomorphology (Hampton and Lee 1996). Depending on the level of detail of available data, inferred soil conditions can be presented as soil provinces, which are areas of similar soils; predicted soil profiles; and ranges of expected geotechnical parameter values e.g. undrained shear strength, submerged unit weight, water content and plasticity index. This preliminary assessment is then used to optimise the scope of a geotechnical site investigation in order to recover geological and geotechnical data that can be used to calibrate the ground model and provide geotechnical parameters for engineering design. Once the preferred field layout has been determined, a further iteration may be required to provide site-specific geotechnical parameter values using various forms of geological sampling (e.g. piston cores, box cores) and geotechnical testing techniques (e.g. Piezocone Penetration Test (PCPT) and piezoprobe). The supplementary sampling and testing data are used to refine the ground model, and identify any possible impacts of soil conditions on detailed design, installation and operation of facilities across the development area. The results can then be integrated into the project risk register, and appropriate guidance and mitigation determined (Evans et al. 2007; Moore et al. 2007).
Project guidance: seabed mapping, ground modelling and risk assessment
Depending on individual project requirements and the assessed level of geohazard risk to development, a range of thematic baseline and interpretative maps are prepared in ArcGIS and hardcopy format to provide guidance to project end-users. This information forms part of a comprehensive set of deliverables to support the project team’s wells and facilities engineers, particularly during the appraisal and engineering design stages. They provide contextual information on the geohazards and ground conditions observed in the development area as well as site-specific guidance, presented in a common format.
Development-wide planning guidance is used by project engineers to highlight the relative geohazard risks to a development, and identify opportunities for geohazard avoidance. The intention is that geohazards should be avoided if at all possible, but if avoidance is not possible, for example due to cost or inadequate space for facility re-routing, further work can be undertaken to quantify the risk by collecting additional data or undertaking more detailed and site-specific analysis of existing data. With respect to landslides, the guidance is to avoid areas with evidence of potentially active or historical seabed instability. The stability of any seabed will be a function of the site-specific and time-dependent conditions promoting or resisting slope failure and should be properly investigated. Where the seabed has undergone recent slope failure or successive failure in the past there is a relatively high probability of failure of these sites in the future due to the presence of weakened soils and conditions promoting slope failure. In situations where the seabed shows no signs of prior slope failure or evidence of recent instability of previously failed seabed, these areas are likely to have a low probability of failure under present natural conditions. Where tolerable, the geohazard risk can be managed, otherwise engineering mitigation design work can be undertaken. In cases where geohazards cannot be avoided, the maps and associated databases provide the context for comparing potential geohazard loadings on equipment to identify opportunities for geohazard resistant design.
Bathymetry map: This map illustrates the elevation and topography of the seabed across a given development site. This map is a standard product for all seabed investigations, acting as a baseline dataset, providing no interpretation of geohazard risks to facilities, wells or pipelines. The map is valuable in providing the first illustration of seabed conditions, depth information and the basis for seismic profile selection, data point location and referencing. Experienced observers and topographic interpreters gain their first impressions from these data. In combination with slope information, the map can be used to identify topographic constraints to flowline and pipeline routing.
Slope map: This map illustrates the variation in seabed slope angle across a given development site and should always be prepared at slope angle intervals best suited to the portrayal of critical engineering limits. Slope presentation is enhanced by the production of representative slope transects and derivative maps e.g. aspect-slope maps whereby the map simultaneously shows the aspect (direction) and degree (steepness) of the seabed slope. A slope map is a standard product for all seabed investigations, acting as a baseline dataset. It provides no interpretation of geohazard risks to facilities, wells or pipelines, however, the information assists in locating facilities and pipelines to avoid steep terrain.
Terrain units map: This map is a derivative map of the geomorphology interpretation. It provides a summary of the major terrain units of the development site which are considered to be characterised by similar geomorphological features and processes and ground conditions. Terrain units provide a regional understanding to the geohazard setting and ground conditions, and a spatial framework to infer lateral variations in soil characteristics. This information is particularly useful at early stages of field layout planning and geohazard assessment.
Geohazard map: This map is a derivative map of the geomorphology interpretation and presents the distribution of shallow geohazard features and processes across the development area. This is a critical map that highlights both the forms, soil properties and processes which might affect a development.
- 5a.Planning guidance map: This map summarises information from the wider thematic map set to show the distribution of observed and anticipated geohazards at any location in the development area in non-technical detail. The map provides specific recommendations for geohazard avoidance based on the detailed mapping and assessments that underpin the work (Fig. 9). The map may include slope constraints, geotechnical constraints, potential for shallow gas and shallow water flow and other geohazards considered important to the development site and project end-users in a language they can understand and can take account of in their own work. Table 2 outlines general guidance for features observed in Fig. 9. In this hypothetical example, the proposed (pre-geohazard assessment) pipeline route ran across a series of landslide units along the scarp, as well as crossing pockmark clusters and tension cracks. As the position of the two wells was fixed, the pipeline was re-routed to the top of the scarp, away from any landslide units. Placing a pipeline across, or directly downslope, of a landslide will expose the pipeline to potential landslide damage (Table 2). Optimisation of the sub-sea layout and pipeline routing allows for the avoidance of significant geohazard risk (post-geohazard assessment). In this example the pockmarks and tension cracks at the top of the scarp were not considered a threat.Table 2
Geohazard register to compliment the planning guidance map (Fig. 9)
Guidance for shallow foundations––implications to flowlines and flowline structures
Guidance for deep foundations––implications to riser bases, manifolds and FPSO anchors
Areas of disturbed or displaced seabed sediments derived from en-masse lateral soil displacement. May exhibit a retrogression zone of displaced sediments, slabs of un-deformed sediments, exposed shear surfaces of older sediments, compression zones and run-out of deformed or mobile sediments.
First-time failure or re-activation of an existing landslide may cause seabed and shallow sediment displacement (e.g. sliding, heave, extension, deformation, exposure and burial).
Steep slopes, uneven terrain and ground movement.
Recommendation: Careful site selection and routing. Avoid landslides if possible. Otherwise, site investigation and analysis to support geohazard mitigation.
Steep slopes, uneven terrain and ground movement.
Recommendation: Careful site selection. Avoid landslides if possible. Otherwise, site investigation and analysis to support geohazard mitigation.
Buried areas of disturbed or displaced sediments derived from en-masse lateral soil displacement that have subsequently been buried by younger sediments but still have topographic expression at seabed. May exhibit variable soil conditions.
Reactivation may cause landslide, overlying and seabed sediment displacement (e.g. sliding, heave, extension, deformation and burial).
Seabed and shallow sediment displacement (given reactivation or first-time failure).
Recommendation: Avoid footprints of buried landslides if possible. Otherwise, careful routing and siting of inline equipment, and site investigation and analysis to support geohazard mitigation.
Seabed and shallow sediment displacement (given reactivation or first-time failure). Variable soil conditions.
Recommendation: Avoid footprints of buried landslides if possible. Otherwise, careful routing, site investigation and analysis to support geohazard mitigation.
Faults and tension cracks
Sub-vertical fractures of variable lateral extent, which separate sediments displaced relative to one another either a) parallel to the plane of fracture (faults), or b) normal to the plane of fracture (tension cracks). Uneven terrain and unstable sediments may occur at steep, exposed fault surfaces and tension crack sides.
Fault movement is likely to occur as progressive creep rather than sudden dislocation. Creep of sediments about the fault plane may occur. A sudden dislocation could occur on a fault or tension crack in response to rapid loading, e.g. induced by an earthquake or a landslide.
Steep slopes, uneven terrain, unstable sediments, sediment creep.
Recommendation: Careful site selection and routing. Vulnerability assessment if avoidance is impractical. Inspection and maintenance programme to identify signs of movement.
Variable soils and higher soil permeabilities at fault planes (reducing the potential of soils to sustain suction). Sediment creep.
Recommendation: Avoid positioning near faults if possible. Otherwise, vulnerability assessment and site investigation and analysis to support geohazard mitigation. Inspection and maintenance programme to identify signs of movement.
Pockmarks, fluid expulsion depressions, seeps
Pockmarks are conical depressions in the seabed formed by expulsion of fluids from shallow sediments. Fluid expulsion depressions are accumulations of several pockmarks in a single, coalesced depression. Seeps are conical mounds of biogenic carbonate formed from chemosynthetic organisms feeding on seeping gas. Hard grounds (carbonates) and variable soil conditions may be associated with pockmarks and seeps. Uneven terrain and sediment instability may also occur on the flanks of pockmarks, fluid expulsion depressions and seeps.
Continuing expulsion of fluids may release corrosive chemicals and lead to depression/mound growth. Living chemosynthetic communities may exist on seeps and within pockmarks.
Uneven terrain, variable soils, slope instability, environmental sensitivity, corrosive chemicals.
Recommendation: Assessment of individual pockmarks, fluid expulsion depressions and seeps encountered at structure sites.
Uneven terrain, variable soils, slope instability, environmental sensitivity, corrosive chemicals.
Recommendation: Assessment of individual pockmarks, fluid expulsion depressions and seeps encountered at structure sites.
Planning guidance register: project guidance is normally provided in tabular format (see Table 2) to be read in conjunction with the planning guidance map. For each mapped geohazard (e.g. landslide) guidance is presented that characterises the form and potential geohazard processes and the potential implications for facilities and field layout. A landslide, for example, may exhibit features such as a retrogression zone of displaced sediment and exposed shear surface of older sediment. Implications for facilities and field layout provide guidance on the potential impact of each geohazard on field equipment where this is known.
Using the fully integrated seismic datasets, thematic maps and geotechnical knowledge, ground models can be developed as an effective means of communicating geohazard risk. Ground models can provide an illustrative description of the nature of geohazard features, materials, mechanisms and potential processes, for the given development sites. They can be produced at a range of scales (development wide to local) for specific geohazard features (e.g. landslides) to illustrate sediment variability and soil characteristics, and to illustrate key structural features and environmental conditions. For example, a series of landslide type models can be produced to understand more fully their magnitude, frequency, susceptibility and cause (Fig. 7). These models are used to support engineering design including supporting data and information, technical guidance and quality assurance.
The geohazards and risk to deepwater development projects are potentially significant and require careful evaluation and mitigation particularly during field planning and front-end engineering design and construction of subsea systems. The paper illustrates a detailed map-based geomorphological approach which has been refined for the systematic identification and characterisation of seafloor features and processes that can be used to underpin assessment of the potential geohazards and risk to subsea development. The integrated approach employs a multi-disciplinary team working with high-quality field-calibrated data to accurately map and interpret seafloor features and ground conditions to ensure that developments are not exposed to intolerable geohazards and risk: foreseen is forearmed. The approach taken is very similar to the practice of establishing geological models for land-based engineering projects, in which the complete geological history of the site is used to characterise and predict the potential performance of the ground. Such an approach is routine for major projects on land but so far does not seem to be common practice in the offshore industry. The approach presented offers a new standard for the industry in order that the risks associated with seafloor geohazard features and processes are identified, assessed and mitigated, where appropriate, at the early stages of development appraisal and engineering design.
A deeper understanding of geohazard features, causes and mechanisms than could be gained from the study of smaller or more isolated areas, or by using the traditional methods of geophysical interpretation and geotechnical engineering in isolation.
Provision of sufficient information for quantitative risk assessment, such as the calculation of frequency-magnitude relationships for geohazard events.
Determination of the most appropriate geohazard mitigation options (i.e. geohazard avoidance or geohazard-resistant design measures), which could not have been done had the investigations been more superficial.
The authors are grateful to colleagues in Halcrow and Fugro for their assistance and collaboration in developing the integrated mapping approach presented in this paper. The authors are grateful for the comments of Prof Denys Brunsden on the initial draft of the paper. We gratefully acknowledge the comments of the editor and reviewers on an earlier version of this paper.