Density and magnetic susceptibility values for Figure 9.
\r\n\tIn this book the amperometry principles, instrumentation, cells (including flow cells), and functional materials used in amperometric sensors are presented together with the numerous applications of the amperometric (bio)sensors and the amperometric titrations in the environmental, food, and clinical analysis.
",isbn:null,printIsbn:null,pdfIsbn:null,doi:null,price:0,priceEur:null,priceUsd:null,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"502756538d952207e98c5b53b0f8c6ed",bookSignature:"Dr. Margarita Stoytcheva and Dr. Roumen Zlatev",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8638.jpg",keywords:"Voltammetry, Direct Amperometry, Pulse Amperometry, Amperometric Sensors, Functional Materials, Amperometric Biosensors, Electrode Modification, Cells, Flow Cells, Amperometric titration, Amperometric Detection, Application",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"August 16th 2018",dateEndSecondStepPublish:"September 6th 2018",dateEndThirdStepPublish:"November 5th 2018",dateEndFourthStepPublish:"January 24th 2019",dateEndFifthStepPublish:"March 25th 2019",remainingDaysToSecondStep:"3 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"170080",title:"Dr.",name:"Margarita",middleName:null,surname:"Stoytcheva",slug:"margarita-stoytcheva",fullName:"Margarita Stoytcheva",profilePictureURL:"https://mts.intechopen.com/storage/users/170080/images/system/170080.jpg",biography:"Prof. Margarita Stoytcheva has graduated from the University of Chemical Technologies and Metallurgy of Sofia, Bulgaria with titles of Chemical Engineer and Master of Electrochemical technologies. She obtained PhD and DSc degrees in Chemistry and Technical Sciences. She has participated in research and teaching in several universities in Bulgaria, Algeria, and France. From 2006 to the present, she has participated in activities of scientific research, technological development, and teaching at the Autonomous University of Baja California (Mexicali, Mexico) as a full-time researcher. Since 2008, she has been a member of the National System of Researches of Mexico, and since 2011 she has been a regular member of the Mexican Academy of Sciences. Her interests and area of research are analytical electrochemistry and biotechnology.",institutionString:"Autonomous University of Baja California",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"5",totalChapterViews:"0",totalEditedBooks:"4",institution:{name:"Autonomous University of Baja California",institutionURL:null,country:{name:"Mexico"}}}],coeditorOne:{id:"128534",title:"Dr.",name:"Roumen",middleName:null,surname:"Zlatev",slug:"roumen-zlatev",fullName:"Roumen Zlatev",profilePictureURL:"https://mts.intechopen.com/storage/users/128534/images/system/128534.jpeg",biography:"Dr. Roumen Zlatev is a full-time researcher at the Engineering Institute of the Autonomous University of Baja California (UABC) (Mexicali, Mexico). He obtained his Bachelor’s and Master’s degrees from the University of Chemical Technology and Metallurgy of Sofia, Bulgaria, and his Ph.D. degree from the National Polytechnic University of Grenoble, France. He was a fulltime researcher in the Bulgarian Academy of Sciences and a part-time professor at Sofia University before accepting the position of full-time senior researcher in UABC in 2005. Dr. Zlatev is a member of the Mexican National System of Researchers and a regular member of the Mexican Academy of Sciences. He participates in research projects in France, Germany, and Mexico. He is the author of more than 170 publications, book chapters and reports in scientific congresses, and holds 14 patents in the field of the electrochemical and spectroscopic methods of analysis, corrosion, and materials, electrochemical and analytical instrumentation.",institutionString:"Autonomous University of Baja California",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Autonomous University of Baja California",institutionURL:null,country:{name:"Mexico"}}},coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"8",title:"Chemistry",slug:"chemistry"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"220811",firstName:"Anita",lastName:"Condic",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/220811/images/6068_n.jpg",email:"anita.c@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"5725",title:"Applications of the Voltammetry",subtitle:null,isOpenForSubmission:!1,hash:"36586695f01005ffab50415baba4de15",slug:"applications-of-the-voltammetry",bookSignature:"Margarita Stoytcheva and Roumen Zlatev",coverURL:"https://cdn.intechopen.com/books/images_new/5725.jpg",editedByType:"Edited by",editors:[{id:"170080",title:"Dr.",name:"Margarita",surname:"Stoytcheva",slug:"margarita-stoytcheva",fullName:"Margarita Stoytcheva"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"5182",title:"Lab-on-a-Chip Fabrication and Application",subtitle:null,isOpenForSubmission:!1,hash:"f4c8e226ea2612f5ecceb7e6311581d4",slug:"lab-on-a-chip-fabrication-and-application",bookSignature:"Margarita Stoytcheva and Roumen Zlatev",coverURL:"https://cdn.intechopen.com/books/images_new/5182.jpg",editedByType:"Edited by",editors:[{id:"170080",title:"Dr.",name:"Margarita",surname:"Stoytcheva",slug:"margarita-stoytcheva",fullName:"Margarita Stoytcheva"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"6690",title:"Arsenic",subtitle:"Analytical and Toxicological Studies",isOpenForSubmission:!1,hash:"5d829bc54fef4d7062ab1d4c403a0895",slug:"arsenic-analytical-and-toxicological-studies",bookSignature:"Margarita Stoytcheva and Roumen Zlatev",coverURL:"https://cdn.intechopen.com/books/images_new/6690.jpg",editedByType:"Edited by",editors:[{id:"170080",title:"Dr.",name:"Margarita",surname:"Stoytcheva",slug:"margarita-stoytcheva",fullName:"Margarita Stoytcheva"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9012",title:"Applications of Nanobiotechnology",subtitle:null,isOpenForSubmission:!1,hash:"8412775aad56ba7350a6201282feb1ec",slug:"applications-of-nanobiotechnology",bookSignature:"Margarita Stoytcheva and Roumen Zlatev",coverURL:"https://cdn.intechopen.com/books/images_new/9012.jpg",editedByType:"Edited by",editors:[{id:"170080",title:"Dr.",name:"Margarita",surname:"Stoytcheva",slug:"margarita-stoytcheva",fullName:"Margarita Stoytcheva"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"314",title:"Regenerative Medicine and Tissue Engineering",subtitle:"Cells and Biomaterials",isOpenForSubmission:!1,hash:"bb67e80e480c86bb8315458012d65686",slug:"regenerative-medicine-and-tissue-engineering-cells-and-biomaterials",bookSignature:"Daniel Eberli",coverURL:"https://cdn.intechopen.com/books/images_new/314.jpg",editedByType:"Edited by",editors:[{id:"6495",title:"Dr.",name:"Daniel",surname:"Eberli",slug:"daniel-eberli",fullName:"Daniel Eberli"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"58517",title:"Basement Tectonics and Fault Reactivation in Alberta Based on Seismic and Potential Field Data",doi:"10.5772/intechopen.72766",slug:"basement-tectonics-and-fault-reactivation-in-alberta-based-on-seismic-and-potential-field-data",body:'During the last decade, exploitation of unconventional resources, including low-permeability hydrocarbons, has been a major focus of oil and gas development in North America. One emerging area of concern is induced seismicity, which has led to a renewed interest in faults as well as the structural architecture of Precambrian basement. Recent studies of injection-induced seismicity in parts of Western Canada [1, 2, 3] have highlighted the probable role of pre-existing basement faults in controlling the distribution of induced earthquakes. Although some basement-related faults in this region have been identified using seismic-reflection images (for example, see [4, 5, 6]), faults that may control the location of induced earthquakes are often challenging to detect using seismic-reflection images alone. Problematic cases include faults with a geometry that is unfavourable for seismic mapping in horizontally stratified rocks, such as sub horizontal thrust faults or vertical strike-slip faults, or brittle faults hosted within crystalline basement rocks that lack clear marker reflections. The latter is particularly true in the shallow crystalline basement in Western Canada, where basement structure may be difficult to discern in the presence of strong multiple reflections [7].
Modelling and interpretation of regional gravity and magnetic data can provide valuable insights for understanding crustal structure beneath sedimentary basins [8, 9] including constraints for understanding geological risk factors for induced seismicity [10]. Models derived from magnetic and gravity data, due to their non-uniqueness, are usually combined with other geological and geophysical information (e.g. seismic and well data), to provide insights into the geometry of the subsurface [9]. The Western Canada Sedimentary Basin (WCSB) is a mature hydrocarbon basin, where extensive public-domain datasets are available, including regional-scale gravity and magnetic anomaly data as well as crustal seismic profiles. To complement the potential field data, this study uses crustal seismic-reflection data from the Alberta Basement Transects (ABT) Peace River Arch Industry Seismic Experiment (PRAISE) project [11], part of Canada’s LITHOPROBE program [12].
The objective of this contribution is to present new insights arising from geophysical imaging and mapping of representative basement fault structures, together with a discussion of how they may be significant as a framework for understanding induced seismicity. The LITHOPROBE seismic profiles intersect structural boundaries that are seen on the regional aeromagnetic and gravity mapping. Our interpretation approach involves mapping and identification of basement structures, followed by 2D gravity and magnetic modelling for selected features. Since the gravity and aeromagnetic data span a large geographical area they are useful to characterize large-scale trends, whereas the 2D seismic lines give detailed constraints for building a model, such as fault throw and timing. Potential field data thus give a more complete tectonic picture of the area by filling in the gaps between areas of seismic coverage, providing an opportunity to improve our understanding of the structural framework.
The Precambrian basement beneath Alberta was formed by amalgamation of disparate domains that were assembled by the plate-tectonic processes of subduction and collision [13, 14, 15]. The crystalline basement in Alberta can be subdivided into three broad regions (Figure 1). Southern Alberta is dominated by Archean domains, bounded to the north by the Vulcan Low; central Alberta consists of the domains of the Hearne Province that surround the Snowbird Tectonic Zone (STZ); and, northern Alberta consists of the domains that surround the early Proterozoic Great Slave Lake shear zone (GSLsz). Basement domains that are the focus of this study occur between the STZ and GSLsz and have Paleoproterozoic crystallization ages (1.9–2.4 Ga).
Location map showing tectonic domains of the Precambrian basement from [
Subdivision of the crystalline basement underlying the WCSB into tectonic domains is based on sparse drillcore samples from hydrocarbon exploration wells, coupled with potential-field interpretation [14, 15]. The drillcore samples are described by [15] in terms of location, rock type, mineralogy and crystallization age based on U-Pb geochronology. Our study area is underlain by basement rocks of the Ksituan, Chinchaga, Buffalo Head and Wabumum domains (Figure 1), which are composed of igneous, metaigneous and less commonly metasedimentary rocks of Paleoproterozoic age (2.4–1.9 Ga). The 1.90–1.98 Ga Ksituan domain is defined by its strong, positive magnetic expression, which is typical of calc-alkaline magmatic belts due to the presence of magnetite as an accessory mineral phase [15]. Crustal imbrication and pervasive ductile deformation of the Ksituan domain is evident from well-developed seismic-reflection fabrics, in the form of panels of dipping reflections in the upper and middle crust [4]. To the east, the slightly older (2.0–2.32 Ga) Buffalo Head Terrane is characterized by sinuous aeromagnetic patterns and discrete subdomains, composed of metaplutonic and subordinate felsic metavolcanic rocks [14]. The eastern edge of the Buffalo Head is defined by the Kimiwan anomaly, a linear magnetic high ~250 km in length. The origin of this magnetic anomaly has been interpreted as either a decapitated calc-alkaline pluton, or a broad zone of hydrothermal alteration and enhanced susceptibility above a crustal-scale extensional fault [9]. The former interpretation is more consistent with oxygen isotope signature of basement samples [16].
To the south, the Chinchaga domain overlaps in age with the Buffalo Head Terrane and is delineated by a negative magnetic anomaly pattern that reflects the absence of calc-alkaline granitic rocks. As discussed below, we distinguish between the northern and southern Chinchaga domains based on potential-field evidence. The southern Chinchaga domain is of particular interest as it underlies the Kaybob-Duvernay region where induced seismicity is concentrated. Finally, the Wabamun domain is interpreted as a structurally bound wedge-shaped block that is enclosed by strands of the Snowbird Tectonic Zone (STZ; [14]), possibly analogous (in terms of structural style) to Archean crustal-scale lozenges formed by annealed mylonites where the STZ is exposed at the surface [17].
Throughout the study area, dipping reflection fabrics observed on LITHOPROBE profiles in the upper and middle crust are cross-cut by the Winagami Reflection Sequence (WRS), a set of prominent, sub-horizontal reflections with an estimated areal extent of ~120,000 km2 [18]. These reflections are interpreted as sheet-like mafic intrusions that record a ca. 1.8 Ga magmatic event. At several locations, the reflections can be followed around perpendicular bends in survey lines with no change in apparent dip, confirming that the reflectors are approximately horizontal [18]. As illustrated in Figure 2, at some locations individual reflections appear to be truncated and offset, suggestive of post-intrusive fault displacement [9].
Representative seismic expression of the Winagami Reflection Sequence (WRS) from LITHOPROBE deep seismic profiles. The WRS is comprised of subparallel high-amplitude reflections that form an anastomosing fan that converges toward the southeast [
Sedimentary units in this part of the WCSB are broadly divisible into three major stratigraphic successions that were deposited in three distinct phases [19]. From Cambrian to mid-Devonian time this region was situated near a passive margin, with non-deposition in the emergent Peace River Arch over a large region in the northern part of this study area [4]. During the Devonian, extensive carbonate shelf complexes formed, locally capped by linear reef chains, isolated reefs or reef complexes [20]. It has been suggested that sedimentation patterns, including abrupt facies changes, the development of fracture porosity and the orientation of reef trends or clastic strandlines, may have been influenced by small topographic features on the basement surface [21] that were transferred up section through a process of tectonic inheritance [20]. During the next major phase, the topographic expression of the Peace River Arch reversed to form the Peace River Embayment. Within the embayment, the formation of a network of satellite grabens caused localized subsidence during the Carboniferous, followed by more widespread subsidence during Permian and Triassic time [22]. The final major depositional phase was characterized by enhanced Mesozoic subsidence within a foreland basin in front of advancing Laramide thrust sheets [23].
In the 1990s, the Canadian LITHOPROBE program acquired a series of long 2D seismic-reflection transects as part of the Alberta Basement Transects program, with the objective of identifying structures present in the sedimentary basin and deeper levels of the crust [11]. The data were acquired using vibroseis sources and recorded to 18 s two-way time (TWT). In the case of the ABT-PRAISE program, acquisition parameters included a 25-m receiver group interval, 480 channels and unusually long offsets (>6 km) that are conducive to attenuation of multiple reverberations [4]. A representative 2D migrated data example is shown in Figure 2, where the approximate depth in the crystalline basement is calculated assuming an average P-wave velocity of 6 km/s.
Terrestrial gravity data used in this study were compiled on a 1 km grid by the Canadian Geodetic Survey and made available through the Geoscience Data Repository for Geophysical Data. Although the grid is sampled at 1 km, the raw data were acquired using an irregular distribution of stations with an average inter-station spacing of >5 km. Despite dense sampling along LITHOPROBE profiles [9], anomaly wavelengths that can be resolved without aliasing (based on the Nyquist criterion) are thus greater than 10 km. A Bouguer gravity anomaly map of Western Canada derived from this dataset contains a conspicuous gravity low (~ −200 mGal) associated with the isostatic root coincident with areas of high elevations in the Rocky Mountains (Figure 3a). This anomaly obscures most of the basement domains that are of interest in this study. One exception is the Snowbird Tectonic Zone (STZ), which is almost perpendicular to the deformation front and forms the southern boundary of basement domains in our study area. The isostatic residual gravity anomaly map (see [24]) is plotted in Figure 3b. By removing most of the gravitational effects of the isostatic root, the isostatic anomaly map reveals a distinct basement fabric parallel to the STZ that is truncated by orogen-parallel anomalies. A residual positive isostatic anomaly with an amplitude of ~25 mGal is caused by flexural support of the Rocky Mountain front ranges, which is not accounted for by the isostatic correction [2].
(a) Bouguer gravity anomaly map of Western Canada, showing a −200 mGal anomaly associated with the isostatic root beneath high elevations in the Rocky Mountains as well as a linear anomaly along the Snowbird Tectonic Zone (STZ). (b) Isostatic gravity anomaly map, highlighting a positive residual associated with lithospheric flexural support for high topography [
An enlargement of the isostatic gravity map for our study area is shown in Figure 4a. The area is characterized by positive anomalies with ovoid shape and peak amplitudes of ~10 mGal, which produce overall weak NE–SW fabric wavelengths in the ranges of 25–50 km. The only basement tectonic domain boundary that is clearly expressed in this map is the boundary between the southern Chinchaga domain, characterized by positive isostatic gravity residual, and the Wabamun domain which has a weakly negative character.
(a) Enlargement of isostatic residual gravity anomaly map within the area outlined in
The aeromagnetic dataset used in this study is a 200-m residual total-field intensity grid obtained from the national aeromagnetic database (Geoscience Data Repository for Geophysical Data). This grid was compiled from different vintages of survey data, including public-domain and industry surveys flown over several decades [9]. Figure 4b shows an aeromagnetic anomaly map of the study area derived from this dataset. In contrast to the gravity anomaly map (Figure 4b), basement domain boundaries are prominently expressed in the aeromagnetic map. This is expected, since at a regional scale, the shape and intensity of the magnetic anomalies is primarily controlled by the magnetic susceptibility of the basement domains [15]. Apart from the loss of short-wavelength content toward the southwest due to thickening of the sediment cover, short-wavelength basement topography is muted by the high flexural strength of the lithosphere [21] and thus has a relatively minor influence on the magnetic anomalies.
There are a number of prominent magnetic features in Figure 4b. The Ksituan domain (K) is characterized by elongate positive magnetic anomalies with wavelengths ~5–10 km that converge northwards toward the GSLsz, located in the northwest corner of the map. An abrupt rectilinear high-gradient zone separates the Ksituan domain from the southern Chinchaga domain, which is characterized by muted, longer-wavelength negative magnetic anomalies. A “conjugate” rectilinear boundary, geometrically identical to the northern rectilinear boundary, marks the southern edge of the Chinchaga magnetic low. The Kimiwan anomaly (KA) is a NW-trending positive magnetic anomaly that merges with the arcuate western margin of the Buffalo Head high (B). Unlike other parts of the WCSB [9, 24], there is remarkably little correlation between the anomaly fabrics evident in the gravity and magnetic maps. The Kaybob-Duvernay region, where a high-concentration of induced seismicity exists, is underlain by basement rocks of the southern Chinchaga domain. Although the epicentral distribution in Figure 4b reveals a diffuse cloud that is elongate in an east-west direction, the location uncertainty for individual events is ~20 km. In contrast, recent studies that feature high-resolution epicentre locations [2] and well-resolved focal mechanisms [3] indicate that individual fault planes are approximately vertical with a likely north-south strike direction. Thus, local potential-field anomaly fabrics in this region with a roughly north-south trend may be of particular relevance for understanding induced seismicity.
The first example that we consider is the Tangent fault, a Carboniferous normal fault that bounds a half-graben within the Peace River Embayment [4]. This fault has not generated any induced seismicity, but it provides a useful template for interpretation of the geophysical expression of other faults. Figure 5 shows a LITHOPROBE profile across the Tangent fault, which is characterized by a clearly defined down-to-the-east displacement of the top of the Precambrian basement. After correlating stratigraphic picks using a well tie, it is evident that overlying Paleozoic marker reflections (Wabamun, Banff, Debolt) exhibit a folded (or draped) character across the Tangent fault. This deformation style is consistent with a case study by [6], who argued that curvature attributes derived from seismic data are well suited to identify subtle faults in the Kaybob-Duvernay region. In addition to the main Tangent fault, an antithetic fault and a smaller fault are visible in the profile.
Seismic profile across the Tangent fault as well as a smaller fault to the west, showing the density well log used to obtain a stratigraphic tie. This section was used to build the 2D model in
Figure 6 shows a simple gravity model for the Tangent fault, based on geometrical constraints derived from the seismic profile (Figure 5). The 2D gravity modelling method is based on the computed gravitational response of polygonal prisms of uniform density [25]. The model comprises three lithostratigraphic successions: Carboniferous-Mississippian (Debolt and Banff), Devonian (Wabamum) and Precambrian (Top of the crystalline basement). An average density was used from the available density log in the area as a constraint. The density of each layer is indicated on the profile. A good fit between observed and modelled gravity was achieved; however, the faults in this profile have a very small gravitational response. While this may reflect the coarse sampling of the raw gravity data, it demonstrates that the public-domain gravity data are primarily useful for regional interpretations, rather than investigation of small-scale structures such as individual faults. This can be observed with the gravity anomaly profile replicating the topmost layer of the crystalline basement.
2D gravity model across the Tangent fault as well as a smaller fault to the east. Layer boundaries are defined based on seismic profile data (
The well-documented basement faulting illustrated above provides an interpretative template for basement faults in the Kaybob-Duvernay region. Figure 7 shows a 1.7–2.4 s time window of data from the ABT-PRAISE transect in this region, which is prone to induced seismicity. The profile is plotted with a vertical exaggeration of ~8:1. There are several interpreted basement faults in this profile, as marked by the black lines. These faults are interpreted based on observed reflection discontinuities. These features share some characteristics with the Tangent fault, including similar, albeit lower amplitude, expression of folding/drape within the sedimentary layers. One of the inferred basement faults is in close proximity to the edge of the Bigstone Leduc reef, while another inferred fault appears to correlate with a positive topographic feature that coincides with a downlap reflection termination (Z-marker) in the Upper Devonian Ireton formation [26]. Due to the effects of contamination by multiple reverberations below the top of basement at ~2100 ms, it is not clear if these interpreted faults merge at depth in the crystalline basement.
LITHOPROBE seismic profile showing sedimentary layers (vertical exaggeration ~8:1) from the Kaybob-Duvernay region, where induced seismicity has occurred. Several basement faults are evident, as indicated by the black lines. Circle highlights a Leduc reef (Bigstone). Previous workers have suggested that basement faulting may have been influenced the locations of Leduc reefs [
Figure 8 shows the same seismic profile as in Figure 7b, but for a larger time window of 1.5–6.25 s, plotted with a vertical exaggeration of ~1.4. This profile contains strong but discontinuous WRS reflections, with a gentle southwest apparent dip within an approximate depth extent of 11–16 km (based on an assumed average basement velocity of 6.0 km/s). Individual WRS reflection show apparent truncations as they approach a listric corridor where these mid-crustal reflections are absent. This pattern of disrupted WRS reflections resembles a similar disrupted pattern described by [9] for a crustal seismic profile across the Kimiwan Anomaly. Based on this reflection geometry, a crustal-scale reverse fault is tentatively interpreted that extends to the top of crystalline basement, at a point where faulting is seen in Figure 7. The apparent fault offsets of Paleozoic reflections are considerably smaller in amplitude than the apparent offset evident in the middle crust. The interpreted crustal geometry in Figure 8 was used to develop a gravity and magnetic model (Figure 9), with layer parameters in Table 1.
LITHOPROBE seismic data from the same spatial location as in
Gravity and magnetic model constructed based on seismic data in
Modelled layers | Density (g/cc) | Magnetic susceptibility (SI) |
---|---|---|
Sedimentary package | 2.17 | 0 |
Leduc reef (pink) | 2.08 | 0.00017 |
WRS (blue) | 2.64 | 0.02 |
Basement (brown) | 2.82 | −0.027 |
WRS (green) | 2.64 | 0.063 |
Basement (red) | 2.79 | 0.05 |
Density and magnetic susceptibility values for Figure 9.
Like the gravity modelling, the magnetic modelling was performed using a 2D algorithm based on uniformly magnetized polygonal prisms. Only induced magnetization was considered, based on local parameters for the geomagnetic field. The 2D gravity and magnetic modelling depicted in Figure 8 shows that a good fit can be achieved between measured and observed potential-field profiles, using polygon vertices derived from the seismic interpretation. Following [9], no regional-residual separation was applied to permit assessment of the influence of features at various crustal levels. The dominant wavelength of the anomalies (>20 km) implies that the depth of features that give rise to the anomalies is considerably deeper than the top of the crystalline basement (~4 km). In this model, the sedimentary package overlaying the crystalline basement (light brown) was treated as one uniform unit with no magnetic susceptibility (k = 0 SI). Hence, the magnetic sources were attributed only to the crystalline basement. The model showed the structure of the basement on a regional scale. Hence, high-frequency anomalies were not modelled. This example also demonstrates that the seismic structural interpretation is consistent with the observed gravity and magnetic anomalies.
A final modelling example is presented in Figure 10. Here, magnetic and gravity profiles are extracted from the total-intensity aeromagnetic and isostatic gravity anomaly grids, along profile A-A’ (Figure 4). This profile cross-cuts the Kimiwan Anomaly as well as a north-south trending positive magnetic anomaly within the southern Chinchaga domain. The Kimiwan Anomaly has a positive magnetic signature (Figure 4) about 40 km in width with a northwest orientation. In the isostatic gravity map, this feature is difficult to map. The observed magnetic profile was extracted from the total field intensity magnetic map by getting a profile perpendicular to the two features of interest. Since no seismic constraint is available along this profile, the purpose of this simple forward model is to examine the applicability of the alteration-zone model for the Kimiwan Anomaly [9] to the north-south trending magnetic anomaly from the southern Chinchaga domain. The data was fitted with the anomalous regions situated in the middle crust (Figure 10). The observed gravity profile is included for reference. It is not modelled, as the gravity anomaly has a different and non-orthogonal strike direction from the magnetic anomaly so the 2D modelling assumptions would be violated. This example shows that the north-south trending Chinchaga magnetic anomaly, near the region of induced seismicity, can be fit using an anomalous region in the middle crust with susceptibility, depth extent and geometry that is similar to (albeit with a narrower than) the alteration-zone model for the Kimiwan Anomaly [9].
Magnetic model and observed gravity along profile A-A’ (location shown in
In this study, potential-field methods are combined with seismic and well data to investigate basement structure in Alberta. Our analysis shows that regional gravity anomaly patterns primarily reflect large-scale crustal features, such as a Bouguer gravity low that marks the isostatic root beneath the Rocky Mountains (Figure 3a), an isostatic gravity high that reflects a flexurally supported topographic load in the Rock Mountain front ranges of Alberta (Figure 3b), and NE-SW linear fabrics associated with the Snowbird Tectonic Zone (STZ). On the other hand, magnetic-anomaly maps provide the primary method for delineating the extent of basement tectonic domains [14]. Isostatic-residual gravity anomalies (Figure 4a) are characterized by longer wavelength than magnetic anomalies (Figure 4b). While the magnetic anomalies predominantly reflect the magnetic susceptibility of the uppermost basement [15], due to the wavelength difference the gravity anomalies are primarily sensitive to deeper crustal levels. This difference in depth sensitivity may explain why the observed isostatic gravity and magnetic intensity fabrics are poorly correlated (Figure 4). Moreover, based on the available regional datasets the (likely subtle) magnetic and gravity expression of basement faults appears to be overwhelmed by anomalies produced by large-scale crustal features. This suggests that a good strategy to improve the sensitivity of potential-field methods to detect and constrain basement faults is to acquire densely sampled data and apply a well-characterized regional-residual separation.
There is evidence to suggest that the southern Chinchaga domain is a distinct block from the northern Chinchaga domain, although basement drillcore samples are too sparse to either validate or falsify this interpretation. The Chinchaga domain has primarily negative magnetic anomaly values throughout its north-south extent, but there are distinct characteristics of the magnetic anomalies in the southern part that are dissimilar from magnetic-anomaly characteristics in the north. Specifically, the southern Chinchaga domain has a more muted negative character, with distinct internal positive anomalies that are absent in the north. In contrast, the northern Chinchaga domain is characterized by high-amplitude negative anomalies. In addition, the southern Chinchaga domain has strikingly rectilinear boundaries, in contrast to the arcuate nature of internal and bounding fabrics in the north. There are north-south trending magnetic anomalies in the southern Chinchaga domain that have an orientation consistent with observed induced-seismicity focal mechanisms, so this distinction may be important in terms of fully understanding the relationships of magnetic anomalies to induced seismicity.
As indicated by a LITHOPROBE seismic profile across the Tangent fault in the Peace River Embayment, despite a sharp offset at the top of crystalline basement, the seismic expression of faulting of Paleozoic layers is dominated by folding. This draped seismic expression supports the use of seismic curvature attribute analysis [6] for mapping potential fault structures. In the shallow basement, faults in the WCSB are difficult to map due to the lack of coherent reflections and the obscuring effects of multiple reverberations. On the other hand, disruption and offset of reflections within the Winagami Reflection Sequence (WRS) provides a potential opportunity to pinpoint loci of crustal-scale faulting at depth as an aid in the interpretation of basement faults. This interpretation approach relies on an assumption that these bright reflections represent mafic sills that were originally more laterally continuous than at present, such that observed offsets can be reasonably interpreted as post-intrusion fault deformation. Extrapolation to the top of basement of the tentatively interpreted crustal-scale reverse fault (Figures 6 and 7) would bring this fault to the base of the WCSB close to several interpreted faults in close proximity to a major Leduc reef edge.
We are grateful for support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and Chevron for the Industrial Research Chair (IRC) in Microseismic System Dynamics. Warner Miles is thanked for helping with access to gridded aeromagnetic data, and Brian Roberts is thanked for providing LITHOPROBE data. CGG is gratefully acknowledged for licensing of the Geoview suite and LCT software through CGG’s worldwide university program. Patrick Quist CGG Houston is thanked for help with answering questions relating to the LCT software and troubleshooting of the seismic and magnetic data. Geosoft software was also used for visualization and interpretation of potential field data. Lydia Dicaprio and Andrew Poulin are thanked for help with GMT and ArcGIS softwares.
The term “dark energy” refers to the cosmological constant
Dark energy is widely regarded as one of the biggest problems in contemporary physics (for a review, cf. [4]). All conceivable ways to modify gravity have been tried. Different approaches to model the observational data have been explored, e.g. [5]. Elaborate laboratory experiments have been performed in the search for new scalar fields that would modify gravity [6]. On top of this, evidence against the earlier interpretation of the supernova observations in terms of dark energy has been discovered [7].
Recently [8] it was shown that there is an alternative way to explain the need for a cosmological constant, namely, as the result of a global cosmic boundary constraint instead of through the introduction of some new physical field. This approach leads to a new cosmological framework that brings a resolution to several outstanding enigmas, including the cosmic coincidence problem. Without the use of any free parameters,
In Section 2 we review the arguments that have been presented in [8] for the origin of the global constraint that governs the value of
In standard cosmological models, the universe is assumed to be homogeneous and isotropic on the largest scales, because this is what observations tell us. The cosmological evolution can then conveniently be described in terms of a scale factor
where
Besides “proper time”
In terms of the temporal coordinates
The conformal metric of the first of these two equations shows that the metric coefficients are proportional to
The word “Euclidian” as the term for the second metric in Eq. (3) does not refer to the flatness assumption but to the signature of the metric: (
The transformation to Euclidian spacetime leads to remarkable advantages and insights, which have found important applications in various areas in the form of Euclidian field theory, e.g., in solid-state physics [10]. The Hamiltonian in ordinary spacetime becomes the Lagrangian in Euclidian spacetime. Quantum field theory QFT in Euclidian spacetime has the structure of statistical mechanics in ordinary spacetime. The oscillating phase factors in QFT become the Boltzmann factors, while the path integral becomes the partition function. Euclidian spacetime has long been known to provide a direct and elegant route to the derivation of the Hawking temperature of black holes, cf. [8, 11].
In the following we will show how the oscillating phase factors of the Euclidian metric field contain a resonance that fixes the value of the cosmological constant
This is the appropriate form to be used with the weak-field approximation, because the right-hand side of Eq. (4) represents the source term for gravitational waves when making a Fourier expansion, while the left-hand side describes the evolution of the vacuum fields, cf. [12]. We have here adopted the standard sign convention with (
In the weak-field approximation and the harmonic gauge,
While the vacuum fields without physical sources (the
With the period of the oscillation given by
In standard cosmology
where
Inserting the value of
In standard cosmology
The existence of such a physical link means that we need to single out, among all the solutions of the oscillator equation in Eq. (5), the Fourier component with a wavelength that corresponds to the conformal age of the universe. This only makes sense if time is bounded between the Big Bang and the Now, which seems to contradict the Einsteinian view that all future times somehow “already preexist” and that the experienced split between past, present, and future is just a stubborn illusion. Here we will argue (for details, see Section 3) that the Einsteinian view only makes sense in a universe devoid of observers and that this is not the universe that we inhabit. Like in quantum physics the observer plays a fundamental role in defining the nature of reality. The split between past, present, and future is not some illusion that we need to come to terms with, but is deeply physical. As soon as we introduce an observer (which can be a test particle, without brains or consciousness!) in Einstein’s universe, the split occurs. In any observable universe the future does not exist, even in principle. The only accessible region is between the Big Bang and the Now, and this region is bounded. The theory has to be applied to the observable universe, not to some idealized universe without observers. This is not just some alternative philosophical viewpoint but has profound physical consequences. It leads to a very different cosmological framework, as will be made clear in the following sections.
The existence of a metric resonance with respect to Euclidian time
Note that the Euclidian metric and scale factor have here been treated like a quantum field by allowing them to have an analytical continuation into the complex plane. When we however convert back to ordinary conformal time
According to Euclidian field theory, the oscillating QFT phase factors in Euclidian spacetime become Boltzmann factors in ordinary spacetime, if the field has periodic boundary conditions. When interpreted as due to a cosmic resonance, our finding that
It gives us the temperature
The identical result can be obtained with the help of Heisenberg’s uncertainty principle. For a system in thermal equilibrium at temperature
Inserting the value for
Alternatively we could have started from Eqs. (13) and (14) to obtain Eq. (12).
Replacing
it follows from Eq. (12) that
This comparison serves to demonstrate that the temperature
We have shown how
The nature of the boundary condition is however fundamentally different in our
The value of
The choice of observer defines the observable universe and its age. The observer is by definition always located at redshift
Although Einstein’s opinion on the split between past, present, and future seems to have been somewhat ambivalent, his most quoted statement on the subject is that this split is an illusion, “but a very stubborn one.” He tended to regard all temporal instants along the infinite timeline as somehow already preexisting as part of a 4D map. This map contains both past and future, in spite of the fact that no observer is able to directly experience any other time than what we refer to as “Now.” Nevertheless the physical meaning of the concept of “Now” remained elusive to him.
The Einsteinian view of a 4D spacetime that maps all times is meaningful only in a universe devoid of observers. As soon as one introduces an observer, the timeline automatically splits up, because the presence of an observer implies a “Here” and “Now.” This split is profoundly physical, because we know from experience that the future is not part of the observable universe. It is not accessible to any observer, even in principle. This is the only universe in which our cosmological theories can be tested, not in some idealized universe devoid of observers, to which nobody can belong.
We are not merely dealing with an alternative philosophical viewpoint, because the introduction of observers leads to a different physical theory with different testable consequences. In the observable universe, time is always bounded, between the Big Bang as one edge and the Now as the other edge. In contrast, in the Einsteinian universe, time is unbounded in the future. The finite temporal dimension allows a global boundary constraint that leads to the emergence of a
A fundamental difference between classical and quantum physics concerns the role of observers. We can introduce test observers in classical physics, but they are not participatory in the way that they are in quantum physics. The classical world represents an objective reality that exists in a form that is independent of the presence of observers. It is the Einsteinian universe. In contrast, the quantum reality comes into existence through the participation of observers. It is the reason for the fundamental quantum fuzziness or uncertainty, the probabilistic causality, and the irreversibility through the collapse of the wave function. While the evolution of the wave function is time symmetric and deterministic, the act of “observation” or “measurement” leads to the profoundly different nature of quantum reality.
Although the role of our cosmological observers is very different from that of quantum theory, the comparison with quantum physics serves to indicate ways in which observer participation profoundly affects the nature of the theory. While abandoning the traditional classical view by allowing observer participation, we transform the theory into something that in at least this respect is closer to the nature of quantum physics. The consequence in our case is that the value of the cosmological constant gets uniquely determined in a way that leads to a very different cosmological framework.
The presence of participating observers also changes our interpretation of spacetime in a profound way by introducing a distinction between local and nonlocal time, a distinction that is absent in a universe without observers. With nonlocal time we here mean the same thing as look-back time. In contrast, dynamical time is the same as local time, because it is the only time that an observer can experience directly. The observables are redshifts, apparent brightnesses, structuring of celestial objects, etc. The observer is by definition always at redshift
In both standard cosmology and our alternative theory, the value of
The choice of observer defines the age
The dynamical time scale is the local time scale that is experienced by a comoving observer and which characterizes the age
In both standard cosmology and AC theory, the expansion rate of the universe, as represented by the Hubble constant, is governed by the equation
if we assume zero spatial curvature (see Section 4.2 for a justification of this assumption). Since
as follows from Eqs. (7) and (8). In standard cosmology
The scale factor normalized to epoch
The redshifts
which satisfies the requirement of Eq. (17) that
The values of
according to Eq. (6). It is the fundamental equation that sets AC theory apart from standard theory.
Because the conformal age
Here the dimensionless parameter
While observations support our assumption of vanishing spatial curvature, AC theory requires it on theoretical grounds, in contrast to standard theory. Since curvature is induced by the presence of matter-energy sources, which may include the vacuum energy
Because the value of the conformal age
From the relation
To find the
The
First of all, the value of
where
cf. [13].
When going to a different epoch with a different
During the iteration we enforce the correct
Besides
The scale factor
We further note that the scale factor uniquely determines the temperature of the cosmic radiation background through
which is valid back to a temperature
Because
In Figure 1 the parameters
The left panel shows
The next step of the calculation is to use the solution for
The proper age
It can be solved by integration to obtain the proper age
The present age
which readily follows from the definition of
The left panel of Figure 2 shows
In the left panel, the log of the scale factor
Note also that the evolutionary time scales are quite different in the two theories. While both curves coincide at the present epoch, simply because they share the same normalization
Since the AC evolution is so close to linear in the log–log diagram, it is meaningful to represent it in the form of a power law:
For clarity we have explicitly written the exponent
Comparison with Eq. (30) shows that
Since
Overall the temporal variations of
Note that the level
Cosmic acceleration parameter
Similar to Eq. (32) we obtain from the definition of
Alternatively we may replace time
Knowing both
In the right panel of Figure 2, the Hubble time
While the solid and dashed curves for
This huge difference has major implications for our understanding of BBN physics. At a first glance, it might seem that it would make AC theory incompatible with the constraints imposed by the observed abundances of the light chemical elements, because the BBN predictions depend on the value of the expansion rate. However, a closer look at the BBN problem shows that the situation is much more complex, because we are in a totally different regime. AC theory may still be compatible with the observational constraints, but this remains an open question. At the time of writing, the required BBN modeling with AC theory is still work in progress.
Similarly the significantly slower expansion rate in AC theory around the epochs of equipartition and recombination will require a reevaluation of the processes that govern the formation of the CMB spectrum. This is needed to allow AC theory to be confronted with the constraints that are imposed by the observed CMB signatures.
Let us next determine the cosmic acceleration parameter
Its derivative with respect to
In contrast, in standard cosmology
Figure 3 shows how standard theory (represented by the dashed curve) has three distinct levels for
In AC theory there is only a gentle transition around equipartition from a level of
It may seem confusing that the universe is currently accelerating according to standard cosmology, while both Figure 3 and the right panel of Figure 1 show it to be decelerating according to AC theory. The reason is that
When we throughout this chapter have referred to the “observed acceleration” of the cosmic expansion, we have implicitly meant the acceleration that is inferred when the observational data are interpreted with the Friedmann-Lemaître models, because no other framework has been available for describing the observations in terms of an evolving scale factor. The discovery with the supernova observations was that a positive cosmological constant
The inference of an acceleration from redshift data depends on the way in which redshift
In standard cosmology an inflationary period in the early universe has been postulated to provide a solution to two fundamental cosmological problems: the horizon and the flatness problem [14]. The remarkable smoothness of the observed CMB tells us that the universe was homogeneous and isotropic on large scales to an extremely high degree (of order
In a decelerating universe, the radius of the cosmic horizon (e.g., the Hubble radius
The described properties are illustrated in Figure 4, where we have plotted the comoving Hubble radius
Plots of the comoving Hubble radius
Causal contact is only possible over distances that are smaller than the comoving horizon size. As seen by the dashed curve in Figure 4, the largest scales that we observe today (of order 10 Gly, the approximate present Hubble radius) only came into causal contact very recently, well after the time of recombination (
To solve this problem, an early inflationary phase without known physical origin was postulated [14]. With its negative slope for
After the inflation idea was introduced, there have been a plethora of theoretical papers on the subject, which now has a prominent place in all modern cosmology textbooks. Still, four decades after its invention, the hypothetical inflaton field that is assumed to be responsible for the phenomenon has not been identified, in spite of an abundance of searches with string theory, supersymmetric grand unified theories, or other exotic alternatives. The existence of a violently inflationary phase around the GUT era, when the universe was a tiny fraction of a second old, is often treated as a fact, while fundamental arguments against it, like in [15, 16], are largely ignored.
In contrast, the solid curve of the AC theory in Figure 4 shows that the comoving Hubble radius
In the right panel of Figure 4, we have let AC theory be represented by two curves. The solid curve is based on the use of a value 73.5 km s
The linear representation of the right panel of Figure 4 again highlights how the present epoch is singled out by the standard model as something extraordinarily special. The comoving Hubble radius has one single narrow peak throughout all of cosmic history, and this peak is located where we happen to live in cosmic time.
The cosmological constant
Forty years ago another inflationary phase was postulated to occur in the GUT era of the very early universe, in order to answer the question why the universe is observed to be so homogeneous and isotropic on large scales [14]. The scalar inflaton field needed to drive the inflation has however not been identified in spite of a profusion of papers on this topic.
In the present work, we show that both these problems are connected and can be solved, if the
We have derived and solved the mathematical equations that follow from this approach. It leads to a very different cosmological framework, which we refer to as the “AC theory” (AC for alternative cosmology). Some implications of this theory have been highlighted: The cosmic coincidence problem disappears, our epoch is not special in any way, and we are not privileged observers. The boundary constraint leads to an evolving scale factor that describes an accelerating, inflating phase from the beginning of the Big Bang throughout the entire radiation-dominated era. There is no need to postulate some early violent inflation driven by some hypothetical inflaton field, because the boundary constraint automatically causes the universe to inflate. The theory reproduces the observed value of
As the cosmic expansion rate is found to have been much slower in the past than it was according to standard cosmology, the various observational data need to be reinterpreted with the new framework, in particular the BBN predictions of the abundances of the light chemical elements, and the observed signatures in the cosmic microwave background. The confrontation of the theory with such observational constraints represents work in progress that may ultimately determine the viability of the theory in its present form.
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