\r\n\tThis book shall focus on these antisense guided sequence specific silencing molecules with different mechanisms and potency for gene silencing, providing the reader with a comprehensive overview of the current state-of-the-art in ASO based therapeutics, featuring the more recent developments in terms of clinical translation and the use of nanomedicine for the effective delivery of therapeutic nucleic acids towards precision medicine.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"96f256f5bb2e750c7496b3c0b62cb95a",bookSignature:"Prof. Pedro Baptista and Prof. Alexandra R Fernandes",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9571.jpg",keywords:"gene therapy, gene silencing, genome modulation, post-transcriptional modulation, modified oligonucleotides, PNAs, LNAs, siRNA, antisense nucleotides, vectorization of antisense nucleotides, nanotheranostics, clinical translation, nanoparticles for gene delivery",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 25th 2019",dateEndSecondStepPublish:"November 15th 2019",dateEndThirdStepPublish:"January 14th 2020",dateEndFourthStepPublish:"April 3rd 2020",dateEndFifthStepPublish:"June 2nd 2020",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"82671",title:"Prof.",name:"Pedro",middleName:null,surname:"Baptista",slug:"pedro-baptista",fullName:"Pedro Baptista",profilePictureURL:"https://mts.intechopen.com/storage/users/82671/images/system/82671.jpg",biography:"Pedro Viana Baptista (b.1972) holds a degree in Pharmaceutical Sciences (1996) from the Universidade de Lisboa. He obtained his PhD in Human Molecular Genetics from the School of Pharmacy, University of London in 2000. In 2001 moved to FCT-NOVA where he created the Nanomedicine Group, which he leads. Currently, he is Full Professor of Molecular Genetics & Nanomedicine at the Department of Life Sciences, FCT-NOVA and responsible for the NanoImunoTech Group – Nanomedicine in the Applied Biomolecular Sciences Research Unit. His work focuses on the biomedical applications of nanoparticle-based strategies towards light-induced cancer therapy and as gene silencing platforms (including siRNA, antisense and nanobeacons). 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Fernandes is an Assistant Professor at the Department of Life Sciences, FCT-NOVA where she leads the group of Cancer Therapeutics dedicated to assessing novel compounds against tumor cells and elucidate the underlying molecular mechanisms. 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\n\t\t\t
1. Introduction
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The advances in software and hardware technologies have enabled, in an increasing rate, electronic storage of great amounts of data in several formats and fields of knowledge, such as medicine, engineering, biology, financial market, and many others. A correct and fast analysis of these data is essential to guarantee the differential in competitive marketing or progress in investigative sciences.
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Information visualization tools are one of the most used computational resources for a good and fast analysis of data and the associated relationships (Spence, 2001)(Chen, 1999). These tools provide users visual and interactive representations of the data (Card et al, 1999). Currently, the use of multiple views of the data is appreciated in information visualization, for it enables the creation of better-manageable visualizations of the data, i.e., less complex visualizations (Baldonado et al., 2005) (North & Shneiderman, 2000), and improves the perception of the user through diverse perspectives on the data.
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It is important to remark that the great concern is the cognitive overload that the user may suffer when manipulating and analyzing the data by using multiple views. In order to reduce this problem, the user interactions that refer to data manipulation must be coordinated among all views, updating their visual representations coherently, improving the user’s perception of the data and facilitating the discovery of nontrivial relationships.
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The usage of multiple coordinate views brings some current challenges, such as: development of easy interaction mechanisms for coordination, configuration and organization of layouts among views. One of the objectives of the Augmented Reality (AR) as a research area is to provide more natural and intuitive interfaces for the interaction with computational systems (Bimber & Raskar, 2005) (Azuma, 2001).
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Moreover, AR enriches the real environment with virtual information. This allows the user to use objects or to collaborate with other people in the real environment while he or she simultaneously visualizes and interacts with virtual information. Finally, AR provides much more natural and ample environments to organize the information that will be visualized when compared to desktop environments. Thus, AR presents alternatives of solutions for the current challenges on multiple coordinate views applied to information visualization. This chapter presents a prototype that implements coordinated multiple views in information visualization for augmented reality environments. The applied information visualization technique was the 3D scatter plot for each data view, and a modified version of ARToolKit (Kato, 2005) has been used for the visualization of the augmented environment. The prototype was developed based on recommendations for a good information visualization tool (Shneiderman, 1996)(Carr, 1999) and multiple coordinated views (Baldonado et al, 2005), with coordinated characteristics of views, configuration, dynamic filters, selection and details on demand. Finally, this paper presents initial usability tests results after the application of some tasks proposed by (Pillat et al. 2005).
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2. Related work
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This section presents some tools that apply multiple coordinated views or augmented reality to different fields in information visualization.
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(Maple et al. 2004) uses multiple coordinated views in three-dimensional virtual environments to assist navigation and orientation in these environments.
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(Slay et al. 2001) uses augmented reality with the main objective of visualizing a graph information technique. The interface for configuration and generation of view is bidimensional.
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(Meiguins et al. 2006) developed a prototype in augmented reality for visualization and interaction of data by using the 3D scatter plot technique.
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3. Multiple views in information visualization
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3.1. Information visualization (IV)
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Information visualization is an area that studies transformation of abstract data into images that can be visualized and easily understood by human beings (Spence, 2001)(Chen, 1999). Information visualization tools are computational tools that implement data interaction and presentation mechanisms. The tools must offer the user a fast and easy manipulation and visual reorganization of the multidimensional data to assist tasks such as data query or analysis.
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According to Carr’s work (Carr, 1999), a good visualization tool should present characteristics according to possible user tasks. Among them, some can be remarked: general view, zoom, filter and details on demand.
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Systems of multiple views use two or more distinct views to assist the investigation process of a single conceptual entity (Baldonado & Kuchinsky, 2000).
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In order to develop information visualization systems with multiple coordinated views, the most frequent recommendations are (Baldonado & Kuchinsky, 2000):
\n\t\t\t\t
When there is a diversity of attributes, models, user profiles, abstraction levels;
When the different views point out correlations or disparities;
When there is a need to reduce the complexity of the data set, by using simpler multiple views;
Use multiple views minimally; justify the use of multiple views in relation to the cost for the user and visualization space.
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(Pillat et al. 2005) stands out the main possibilities of coordination in multiple views:
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Selection: data items selected in a view are pointed out in other views;
Filter: to reduce dataset for analysis in all views;
Color, Transparency and Size: visual characteristics to represent the variation of values of attributes in all views;
Sort: values of an attribute define the order of the visual representations of the data;
Label: it determines what content the labels will present for each data item of the views;
Manipulation of Attributes: it allows the user to add/remove attributes off the data views.
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4. Augmented reality
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Augmented reality is a system that supplements the real world with computer-generated virtual objects, which seem to coexist in the same space and present the following properties (Bimber, 2005)(Azuma et al., 2001):
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It combines real and virtual objects in real environment;
It executes interactively in real time;
It lines up real and virtual objects;
It is applied to all senses of the user.
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The augmented environment was based on the ARToolKit library (http://jerry.c-lab.de/jartoolkit), developed by the HIT Lab in C Language and distributed as open source, which allows the programmers to develop applications in AR (Kato et al., 2005).
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ARToolKit uses computational view techniques for identification of predefined symbols inserted in the real scene. Once a symbol or a marker is identified, the virtual object is inserted in the real scene in the same position of the identified object. The final scene presented to the user is the visual combination of the real world with virtual objects.
\n\t\t\t
The construction of the objects that are combined with the real world can be made through applications in OpenGL and VRML. There is also an ARToolKit version written in Java (JARToolKit) (Kato et al., 2005) with which JAVA3D can be used (Walsh & Gehringer, 2002).
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5. Prototype
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The prototype uses augmented reality to implement multiple views of 3D scatter plot technique in a coordinated way. The main points of its conception were:
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An environment of easy interaction;
Work with several database types;
Implement the 3D scatter plot technique;
Develop mechanisms of dynamic filters in the augmented environment;
Develop coordination mechanisms among data views, such as: selection, filters, details on demand;
Develop auxiliary graphics, such as pie and bar, also coordinated with data views;
Conception of software architecture that facilitates the inclusion of new information visualization techniques.
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5.1. Architecture
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ARToolKit has three basic modules: Scene Capturer, Augmented Reality (AR) and Augmented Image Generator (Kato et al., 2005). The Scene Capturer module is a set of video routines that captures input frames sent by webcam or any other video device. The Augmented Reality module is responsible for identifying the markers in the scene, tracking the captured markers and associating virtual objects with them. Finally, the Augmented Image Generator module is responsible for generating the augmented image (real scene and virtual objects), and is a set of graphical routines based on OpenGL and GLUT.
\n\t\t\t\t
The modifications made in the ARToolKit in order to implement multiple coordinated views can be seen in Figure 1, and are concentrated in the AR module. The creation of several modules was taken into effect in order to help the maintainability, extensibility, efficiency and reutilization of the code (Figure 1).
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Figure 1.
Summary of the prototype architecture
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A brief description of the implemented modules is presented below:
\n\t\t\t\t
Identification of Interaction Module identifies the type of interaction with markers performed by the user: insertion, occlusion or leaving the scene. It sends a message either to the control module in order to change the view data, or, when interaction is performed only visually and there is no modification in the visible data set, to the coordinated view module;
Control Module is responsible for managing the communication between the coordinated view module and the data module, providing transparency when these module exchange messages;
Data Module is responsible for data access in text files, XML or relational databases;
Coordinated View Module is responsible for managing what each data view must present, and thus assure coordination among all views;
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5.2. Augmented interface
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The augmented interface is formed by the 3D scatter plot view and other virtual objects, as well as the interaction controls based on markers and real objects. The prototype builds two data views by using the 3D scatter plot technique to represent the elements in a dataset. The main view configurations are axis X, Y and Z, 3D Shape, Color and Size. Figure 2 shows an example of the prototype during its execution, pointing out the simultaneous presence of real and virtual objects.
\n\t\t\t\t
Figure 2.
Example of the prototype in executing mode
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Most of the user interaction is directly performed by the occlusion of the markers. The occlusion-based interaction consists of blocking the capture of the marker’s symbol by the video device. This may be performed with his or her own hands. It is possible to apply transformations based on translations, rotations and scale in data views or other virtual objects in the scene just by moving or interacting with the markers. The markers are grouped according to their functionality (Figure 3), and can be freely manipulated in the real environment, enabling an infinite array of layouts to visualize the analyzed dataset.
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An important characteristic of the prototype is its ability to set a fixed position to any generated virtual object in the scene, as a 3D scatter plot, just by occluding the object’s marker (Figure 4). The prototype stores the last register of the transformation matrix in order to place the virtual object in the fixed position in the scene. This is important because it avoids any unintentional interaction of the user with markers.
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Figure 3.
Markers set according to functionality
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Figure 4.
Virtual object fixed in the scene
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5.3. Coordinated views
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Some of the coordinative characteristics of the prototype should be remarked:
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Data: It uses a single dataset for all views;
Layout flexibility: the user may analyze or query data with individual or simultaneous views (Figure 4);
Coordination: It is classified as static, i.e., the coordination between pairs of views is predefined. It may be either strongly coordinated, as color (Figure 2) – once defined, the same color is applied to all views, or loosely coordinated, as semantic zoom or Axis values, which can be used in any data view, but have to be manually configured for each view in the augmented interface.
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The coordinated actions are:
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Strongly Coordinated Actions: filters, environment configuration for color, shape and size attributes, and for selection of objects. They affect directly all views, even if they are not present in the scene (unreachable by the video device);
Loosely Coordinated Actions: axis configuration, semantic zoom (Figure 6) and navigation (translation and rotation). They only affect a view which is present in the scene
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5.4. Filters
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Concepts of dynamic queries have been applied (Shneiderman, 1994) for categorical and continuous values. This type of action allows the user to check databases without needing to use command lines, manipulating only graphic components of interface (Figure 5 and 6).
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Figure 5.
Augmented representation of the categorical attribute filter
\n\t\t\t\t
In the prototype, any filter can perform the following actions:
\n\t\t\t\t
Hiding: Take off the scene a determined item or data items which have a previously selected characteristic;
Isolating: Leave only items which have a previously selected characteristic in the scene;
Restoring: Undo the filtering processes previously performed on data items.
The categorical attribute filters work on configurable characteristics of a data view, such as: color, shape and size. Figure 5 illustrates the filter control for categorical attributes.
The continuous attribute filters specify ranges of values to isolate and hide data items from views (Figure 6).
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Figure 6.
Augmented representation of the continuous attribute filter.
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5.5. Semantic zoom and auxiliary chart
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Semantic Zoom allows the user to visualize the data space more precisely and with additional details as his or her perspective gets closer to the virtual objects (Figure 7). The zoom marker has two faces, one to zoom in and the other to zoom out.
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5.6. Environment configuration
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The prototype allows the user, though an environment configuration control, to freely change the attributes of X, Y and Z Axes and of Shape, Color and Size for each data view. Figure 8 shows a situation in which the user changes the color and shape configuration to another categorical attribute, and the changes are presented in the multiple coordinated views.
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5.7. Details on demand and help
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A resource called “Virtual Pointer” has been developed to select virtual objects and analyze their hidden information. The selected objects in one view are pointed out in the other view (Figure 9).
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This item helps to detail the activities of each marker, in case there is a doubt about its functionality. Its use is simple: while the help marker is visible, all groups of markers present in the scene provide information related to its use mode.
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Figure 7.
Example of Semantic Zoom
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Figure 8.
Changing the color and shape attributes in views
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Figure 9.
Selection of items performed in a strongly coordinated way
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The prototype presents auxiliary bidimensional pie and bar graphics that provide additional information on the visualized data (Figure 10).
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Figure 10.
Example of auxiliary charts (Pie and Bar)
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6. Usability tests
\n\t\t\t
Usability tests were performed to evaluate the use of information visualization techniques in an augmented reality environment with multiple coordinated views. The users were asked to perform a set of tasks previously defined by (Pillat et al. 2005) that demand different actions such as: view configuration, data correlation, and range specification, among others.
\n\t\t\t
Task 1: Are the 4-cylinder Japanese cars usually lighter than the 6-cylinder American cars?
Answer 1: No.
Task 2: Analyze the data and describe the main characteristics of the American cars;
Answer 2: Acceleration is between 8 and 22.2, mainly between 11 and 19. Most of the cars have 8 cylinders. Weight is uniformly distributed. MPG values are also uniformly distributed. Horsepower is concentrated between 88 and 155.
Answer 3: Acceleration between 12.2 and 24.8, and light weight. The horsepower kept stable until 1977 when it rose just to reduce again the next year. There are few 5 or 6-cylinder cars but most of them are 4-cylinder. MPG was between 10 and 31 from 1970 to 1976 and considerably rose since them.
\n\t\t\t
The used dataset contains information about American, Japanese and European cars from 1970 to 1982. (Pillat et al. 2005) There are 8 attributes: 3 categorical and 5 continuous.
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After a 20-minute training in augmented environment and interactive markers, task one was used as a practical example in order to build confidence and improve the users skills. The comparative tests were restricted to tasks 2 and 3 that are similar but with increasing level of difficulty. The tests involved 5 users, all 21-32 male with good computer skills. None of the users had previously interacted with augmented reality environments with markers. All users had previous knowledge on information visualization techniques.
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Each item of user answers was analyzed. For example, for task 2 what was the answer to attribute1, attribute2, and so on. The accuracy rate is based on the total number of correct answers to each item of each task. Figure 11 and Figure 12 present the results in terms of accuracy rate and task execution time, respectively.
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Figure 11.
Accuracy rate in user answers
\n\t\t\t
The accuracy rate plot indicates that 80% of the users had a better or similar accuracy for task 3 that is considered complex (Pillat et al. 2005). All the users spent less time performing task 3 than task 2. So even with a reduced number of tests it is possible to infer that once the user has experience and confidence in the environment he tends to achieve precise and prompt results.
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Figure 12.
Task Execution Times
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7. Final remarks
\n\t\t\t
This chapter presented a prototype that implements multiple coordinate views in augmented reality environments. The main supported views are based on the 3D scatter plot technique. The augmented interface provides coordinated actions control among views, such as dynamic filters for continuous and categorical attributes; details on demand (object selection); environment configuration; auxiliary pie and bar graphics; semantic zoom; and free navigation.
\n\t\t\t
Initial usability tests were performed in order to evaluate the proposed approach to information visualization. During the execution of the tests it was possible to observe the efficient use of the developed controls and the coordinated views to solve the assigned tasks. Usability tests also revealed the high adaptability of the users to the augmented environment. Only one user had major problems performing task one, taking 11 minutes to adapt to the environment and to the marker-based interaction. Other pointed out difficulties were related to the excessive use of markers and video capture or identification problems that made the interface unstable. The following remarks were made by the users on the interview following the tests.
\n\t\t\t
A first experience in AR environments: users highlighted the main advantages, such as the easy adaptation and learning, the more immersive, free and sometimes fun environment, the freedom to move and manipulate virtual and real objects simultaneously and a larger workspace. As disadvantages the users pointed out the lack of precision of some movements because of marker detection failures; the excessive need to repeat interactions; the excessive use of markers.
Use of information visualization techniques in AR: the users pointed out the freedom to manipulate data views and the free workspace to work with virtual and real objects, and the collaborative aspect as the main advantages. The main disadvantage was the need for more appropriate equipment like augmented reality glasses that would, according to the users, significantly improve precision and performance.
The use of a multiple views coordinated environment in AR: the configuration of graphics axis on views and the different information perspectives allowed better and faster data comparisons and analysis.
\n\t\t
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Information visualization (IV)",level:"2"},{id:"sec_5",title:"4. Augmented reality",level:"1"},{id:"sec_6",title:"5. Prototype",level:"1"},{id:"sec_6_2",title:"5.1. Architecture",level:"2"},{id:"sec_7_2",title:"5.2. Augmented interface",level:"2"},{id:"sec_8_2",title:"5.3. Coordinated views",level:"2"},{id:"sec_9_2",title:"5.4. Filters",level:"2"},{id:"sec_10_2",title:"5.5. Semantic zoom and auxiliary chart",level:"2"},{id:"sec_11_2",title:"5.6. Environment configuration",level:"2"},{id:"sec_12_2",title:"5.7. Details on demand and help",level:"2"},{id:"sec_14",title:"6. Usability tests",level:"1"},{id:"sec_15",title:"7. 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Universidade Federal do Pará, Centro Universitário do Pará, Brazil
Universidade Federal do Pará, Centro Universitário do Pará, Brazil
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Ramachandram and Omar Al Jadaan",authors:[{id:"103952",title:"Mr.",name:"Wael",middleName:null,surname:"Abdulal",fullName:"Wael Abdulal",slug:"wael-abdulal"},{id:"149175",title:"Prof.",name:"Ramachandram",middleName:null,surname:"Sirandas",fullName:"Ramachandram Sirandas",slug:"ramachandram-sirandas"}]},{id:"36785",title:"Efficient Parallel Application Execution on Opportunistic Desktop Grids",slug:"efficient-parallel-application-execution-on-opportunistic-desktop-grids",signatures:"Francisco Silva, Fabio Kon, Daniel Batista, Alfredo Goldman, Fabio Costa and Raphael Camargo",authors:[{id:"105124",title:"Prof.",name:"Francisco José",middleName:null,surname:"Da Silva E Silva",fullName:"Francisco José Da Silva E Silva",slug:"francisco-jose-da-silva-e-silva"},{id:"113707",title:"Prof.",name:"Fabio",middleName:null,surname:"Kon",fullName:"Fabio Kon",slug:"fabio-kon"},{id:"113709",title:"Prof.",name:"Fabio",middleName:null,surname:"Costa",fullName:"Fabio Costa",slug:"fabio-costa"},{id:"113710",title:"Prof.",name:"Raphael",middleName:null,surname:"Camargo",fullName:"Raphael Camargo",slug:"raphael-camargo"},{id:"113712",title:"Prof.",name:"Daniel",middleName:null,surname:"Batista",fullName:"Daniel Batista",slug:"daniel-batista"},{id:"127903",title:"Prof.",name:"Alfredo",middleName:null,surname:"Goldman",fullName:"Alfredo Goldman",slug:"alfredo-goldman"}]},{id:"36786",title:"Research and Implementation of Parallel Cache Model Through Grid Memory",slug:"research-and-implementation-of-parallel-cache-model-through-grid-memory",signatures:"Qingkui Chen, Lichun Na, He Jia, Song Lin Zhuang and Xiaodong Ding",authors:[{id:"110692",title:"Dr.",name:"Qingkui",middleName:null,surname:"Chen",fullName:"Qingkui Chen",slug:"qingkui-chen"},{id:"147355",title:"Dr.",name:"He",middleName:null,surname:"Jia",fullName:"He Jia",slug:"he-jia"}]},{id:"36787",title:"Hierarchy-Aware Message-Passing in the Upcoming Many-Core Era",slug:"hierarchy-aware-message-passing-in-the-upcoming-many-core-era",signatures:"Carsten Clauss, Simon Pickartz, Stefan Lankes and Thomas Bemmerl",authors:[{id:"108932",title:"Dr.",name:"Carsten",middleName:null,surname:"Clauss",fullName:"Carsten Clauss",slug:"carsten-clauss"},{id:"113718",title:"Dr.",name:"Stefan",middleName:null,surname:"Lankes",fullName:"Stefan Lankes",slug:"stefan-lankes"},{id:"113722",title:"Prof.",name:"Thomas",middleName:null,surname:"Bemmerl",fullName:"Thomas Bemmerl",slug:"thomas-bemmerl"},{id:"137686",title:"BSc.",name:"Simon",middleName:null,surname:"Pickartz",fullName:"Simon Pickartz",slug:"simon-pickartz"}]},{id:"36788",title:"Grid Computing in High Energy Physics Experiments",slug:"grid-computing-in-high-energy-physics-experiments",signatures:"Dagmar Adamová and Pablo Saiz",authors:[{id:"107786",title:"Dr.",name:"Dagmar",middleName:null,surname:"Adamova",fullName:"Dagmar Adamova",slug:"dagmar-adamova"},{id:"138329",title:"Dr.",name:"Pablo",middleName:null,surname:"Saiz",fullName:"Pablo Saiz",slug:"pablo-saiz"}]},{id:"36789",title:"Using Grid Computing for Constructing Ternary Covering Arrays",slug:"using-grid-computing-for-constructing-ternary-covering-arrays",signatures:"Himer Avila-George, Jose Torres-Jimenez, Abel Carrión and Vicente Hernández",authors:[{id:"106782",title:"Dr.",name:"Himer",middleName:null,surname:"Avila-George",fullName:"Himer Avila-George",slug:"himer-avila-george"},{id:"138115",title:"Dr.",name:"Jose",middleName:null,surname:"Torres-Jimenez",fullName:"Jose Torres-Jimenez",slug:"jose-torres-jimenez"},{id:"138249",title:"MSc.",name:"Abel",middleName:null,surname:"Carrión",fullName:"Abel Carrión",slug:"abel-carrion"},{id:"138250",title:"Dr.",name:"Vicente",middleName:null,surname:"Hernández",fullName:"Vicente Hernández",slug:"vicente-hernandez"}]},{id:"36790",title:"Grid Infrastructure for Domain Decomposition Methods in Computational ElectroMagnetics",slug:"grid-infrastructure-for-domain-decomposition-methods-in-computational-electromagnetics",signatures:"Olivier Terzo, Pietro Ruiu, Lorenzo Mossucca, Matteo Alessandro Francavilla and Francesca Vipiana",authors:[{id:"109381",title:"Dr.",name:"Olivier",middleName:null,surname:"Terzo",fullName:"Olivier Terzo",slug:"olivier-terzo"},{id:"111672",title:"Dr.",name:"Francesca",middleName:null,surname:"Vipiana",fullName:"Francesca Vipiana",slug:"francesca-vipiana"},{id:"111673",title:"Dr.",name:"Matteo Alessandro",middleName:null,surname:"Francavilla",fullName:"Matteo Alessandro Francavilla",slug:"matteo-alessandro-francavilla"},{id:"111674",title:"Dr.",name:"Lorenzo",middleName:null,surname:"Mossucca",fullName:"Lorenzo Mossucca",slug:"lorenzo-mossucca"},{id:"111681",title:"Dr.",name:"Pietro",middleName:null,surname:"Ruiu",fullName:"Pietro Ruiu",slug:"pietro-ruiu"}]},{id:"36791",title:"Characterization of Hepatic Lesions Using Grid Computing (Globus) and Neural Networks",slug:"characterization-of-hepatic-lesions-using-grid-computing-globus-and-neural-networks",signatures:"Sheng Hung Chung and Ean Teng Khor",authors:[{id:"113164",title:"Dr.",name:"Shenghung",middleName:null,surname:"Chung",fullName:"Shenghung Chung",slug:"shenghung-chung"},{id:"113498",title:"Dr.",name:"Ean",middleName:null,surname:"Teng",fullName:"Ean Teng",slug:"ean-teng"}]},{id:"36792",title:"Applications Exploiting e-Infrastructures Across Europe and India Within the EU-IndiaGrid Project",slug:"applications-exploiting-e-infrastructures-across-europe-and-india-within-the-eu-india-grid-project",signatures:"Alberto Masoni and Stefano Cozzini",authors:[{id:"114545",title:"Dr.",name:"Alberto",middleName:null,surname:"Masoni",fullName:"Alberto Masoni",slug:"alberto-masoni"},{id:"115480",title:"Dr.",name:"Stefano",middleName:null,surname:"Cozzini",fullName:"Stefano Cozzini",slug:"stefano-cozzini"}]},{id:"36793",title:"Open Development Platform for Embedded Systems",slug:"open-development-platform-for-embedded-systems",signatures:"E. Ostúa, A. Muñoz, P. Ruiz-de-Clavijo, M.J. Bellido, D. Guerrero and A. Millán",authors:[{id:"114135",title:"MSc.",name:"Enrique",middleName:null,surname:"Ostua",fullName:"Enrique Ostua",slug:"enrique-ostua"},{id:"147933",title:"MSc.",name:"Alejandro",middleName:null,surname:"Muñoz",fullName:"Alejandro Muñoz",slug:"alejandro-munoz"},{id:"147934",title:"Dr.",name:"Paulino",middleName:null,surname:"Ruiz-De-Clavijo",fullName:"Paulino Ruiz-De-Clavijo",slug:"paulino-ruiz-de-clavijo"},{id:"147935",title:"Prof.",name:"Manuel J.",middleName:null,surname:"Bellido",fullName:"Manuel J. 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\n
1. Introduction
\n
The propagation of seismic waves through the Earth’s subsurface is described by the wave equation, one of the partial differential equations (PDEs), which describe many of the fundamental natural laws. When the subsurface earth structure is complex, it is difficult to obtain the analytic results. The finite difference (FD) method is one of most widely used numerical methods for wave equation modeling because of its high efficiency, smaller memory requirement, and easy implementation [1–7].
\n
The first application of the FD method to wave equation modeling can be possibly traced back to Alterman and Karal [1]. Alford et al. took the grid dispersion analysis for the second-order and fourth-order FD operators and stated that it is necessary to use high-order FD operators [8]. Kelly et al. further illustrated the grid dispersion, absorbing boundary condition, and other implementation aspects of the FD method [9].
\n
Madariaga developed a staggered grid FD scheme to solve a rupture propagation problem [10]. Virieux adapted this scheme to elastic SH waves and P-SV waves in a 2D Cartesian system [2, 3]. Levander introduced a fourth-order staggered grid FD operator in the space domain to improve accuracy [11].
\n
Grid dispersion is one of the key numerical problems affecting practical usage when utilizing the FD method. Since the traditional FD coefficient obtained in the space domain with the Taylor expansion method is only accurate for a very limited wavenumber range [4], many efforts are paid to reducing the grid dispersion with optimized FD coefficient. Yang et al. proposed the nearly analytic discrete method for wave equation and later improved this method [12, 13]. Chen proposed high-order time discretization method to reduce the dispersion caused by the temporal discretization [14, 15]. The Fourier FD was introduced by Song and Fomel with the combination of fast Fourier transform and finite difference operators [16]. Chu and Stoffa improved the FD methods with a scaled binomial windowed FD scheme that leads to more precise discrete operators [17]. Fomel et al. introduced low-rank approximation of the wave propagator matrix to reduce the cost of wave extrapolation [18].
\n
Generally, the FD coefficients of the spatial derivative are determined only in the spatial domain. However, wave equations are solved in the temporal and spatial domains simultaneously. Finkelstein and Kastner propose a systematic design methodology for obtaining FD coefficients to reduce dispersion, which allows the exact phase velocity or (and) group velocity dispersion relationship to be satisfied at some designated frequencies in the temporal-spatial domain [19, 20]. Etgen proposed minimizing the phase velocity error using the least squares (LS) method [21]. Liu and Sen propose a new time-space domain method to determine the higher order FD coefficients for 1D, 2D, and 3D wave equations [22], and then they use this method to get the staggered grid FD coefficients [23]. Zhang and Yao proposed the use of the simulated annealing algorithm and gave an error limitation for determining the FD coefficients in the space or the time-space domain [24]. Liang et al. proposed utilizing the linear method to determine the FD coefficient in the time-space domain [25]. Ren and Liu developed a novel optimal time-space domain staggered grid FD scheme and used least squares method to get the FD coefficients [26]. Wang et al. proposed the regularized optimization method to get the staggered grid FD coefficient in the time-space domain [27]. Chen et al. used K space operator-based high-order staggered grid FD method to improve accuracy [28]. Yong et al. proposed using the optimized equivalent staggered grid FD method with three sets of FD coefficients to improve the simulation accuracy [29]. Compared with the traditional high-order staggered grid FD coefficient obtained by the Taylor expansion method, these methods greatly improved the accuracy with the optimized FD coefficient.
\n
Another way to improve the accuracy and efficiency of the FD methods is using new FD stencil. Liu and Sen studied the rhombus stencil and found that it can reach high-order accuracy along all directions [30]. Liu et al. formulated an explicit time evolution scheme with high temporal accuracy by using a new FD stencil for the second-order wave equation [31]. Tan and Huang propose a staggered grid FD stencil with added points in the diagonal direction for the first-order wave equation [32, 33]. Compared with the traditional staggered grid FD stencil, these methods improved the efficiency by using a larger time step while still preserving high accuracy.
\n
\n
\n
2. Acoustic/elastic wave equations
\n
The first-order velocity-stress acoustic wave equation can be described as
where (vx\n, vz\n) is the velocity vector,(τxx\n, τzz\n, τxz\n) is the stress vector, and α and β are the P- and S wave propagation speeds, respectively.
\n
Substituting Eqs. (7)–(9) into Eqs. (5)–(6), the second-order elastic wave equation can be written as
where M\n1 and M\n2 are the length of the FD operators, cm\n is the staggered grid FD coefficient to be determined, and h is the spatial grid interval.
\n
\n
\n
4. Optimizing finite difference operators
\n
\n
4.1. Optimizing finite difference operators for the acoustic wave equation
where r = vΔt/h, M1 = M2 = M, and(kx\n, kz\n) = k(cosθ, sinθ). It can be observed from Eq. (24) that the dispersion relation is complex and optimized methods are needed to address this problem.
\n
Let c be the vector form of the FD coefficients, and denote the left side of Eq. 24 by [27]:
The upper limit of the wavenumber range used for calculating the FD coefficients is based on the source frequency, the space grid interval, and the wave propagation speed [25]:
The direct minimization of the objective function Φ for the FD coefficient may lead to unstable results. Therefore, regularizing technique was applied to restore stability. The regularization model is established as
where α > 0 is a user-defined regularization parameter and D is a scale operator. The new task is the minimization of J(c), and then the regularized optimization staggered grid FD coefficient can be obtained.
\n
Another way to improve the efficiency and accuracy of the staggered grid FD methods is the utilization of the new staggered grid FD scheme. Different with the previous staggered grid FD scheme, the simplest centered second-order staggered grid FD operator can be used for the spatial derivatives in Eqs. (2) and (3), for example,
The staggered grid FD scheme in Eqs. (30)–(32) can be seen as a new staggered grid FD scheme for the first-order acoustic wave equation. The new staggered grid FD scheme is exactly the same as the traditional staggered grid FD scheme except if the staggered grid FD operator length is shorter for Eqs. (31) and (32). By carefully comparing Eqs. (12) and (14) with Eqs. (30) and (32), we find that the new staggered grid FD scheme is more efficient and can save about 45% of simulation time when M equals 7. It looks like the particle velocities vx\n and vz\n in Eqs. (31) and (32) are inaccurate since only the second-order staggered grid FD operators are used. However, this is not true since the staggered grid FD coefficient in Eq. (30) is optimized with Eqs. (31) and (32) in consideration. In the following, the huge advantage of the new staggered grid FD scheme will be demonstrated because it can reduce the simulation time while still preserving high accuracy compared with the traditional staggered grid FD scheme.
\n
To get the staggered grid FD coefficient in Eq. (30), we substitute Eqs. (31) and (32) into Eq. (30), using the plane wave theory. Then we get
where \n\n\n\nk\nx\n\n\nk\ny\n\n\nk\nz\n\n\n=\nk\n\n\nsin\nθ\ncos\nφ\n\n\nsin\nθ\nsin\nφ\n\n\ncos\nθ\n\n\n.\n\n\n
\n
Compared with the traditional dispersion relation in Eq. (24), the new dispersion relation in Eqs. (36) and (37) is linear and much simpler.
\n
We assume that there are M equally distributed wavenumber points satisfying the dispersion relation within the wavenumber range specified by Eq. (28). Then, we establish the linear equation from Eq. (37) for the 3D case [25]:
where \n\n\na\n\n\nk\nl\n\n,\nm\n\nh\n\n=\ncos\n\n\n\nmk\nl\n\nh\n\n\n−\ncos\n\n\n\n\nm\n−\n1\n\n\n\nk\nl\n\nh\n\n\n\n, the ith component of kl\n(l = x, y, z) is represented as k\n\ni, l\n, kx\n = k cos θ cos φ, ky\n = k cos θ sin φ, kz\n = k sin θ, and k(i) for each i = 1,2,…,M + 1 is equally distributed between 0 and Ratio × π / h, where Ratio is determined by Eq. (28). In the following, we will demonstrate that the new staggered grid FD scheme in Eqs. (30)–(32) has similar accuracy compared with the computational intensive traditional staggered grid FD scheme in Eqs. (12)–(14).
\n
The 2D dispersion error δ of the new staggered grid FD scheme is defined as
\n\nFigures 1\n and \n2\n show the dispersion error curves of the traditional and the new staggered grid FD schemes for the homogeneous acoustic model in 2D. All the FD coefficients are determined in the time-space domain with M = 7. From \nFigures 1\n and \n2\n, we get the conclusion that the new staggered grid FD scheme can also preserve the dispersion relation in a pretty wider range compared with the traditional staggered grid FD methods. For example, with r = 0.0075 in the 2D case, both of them can preserve the dispersion error under 10−5 within 80% of kh range. However, the new staggered grid FD scheme saves wave equation simulation time because Eqs. (31) and (32) are much simpler than Eqs. (13) and (14).
\n
Figure 1.
Dispersion error curves of the traditional staggered grid FD schemes. (a) r = 0.075 and (b) r = 0.225.
\n
Figure 2.
Dispersion error curves of the new staggered grid FD schemes. (a) r = 0.075 and (b) r = 0.225.
\n\nFigure 3\n shows the stability condition of the traditional and the new staggered grid FD scheme in 2D. We can see that the stability condition becomes stricter with the increase of the FD operator length. It also shows that the new staggered grid FD scheme’s stability condition is a little bit better than the previous staggered grid FD scheme. For example, the stability conditions are r < 0.54 and r < 0.57, respectively, for the traditional and the new staggered grid FD scheme with M = 7.
\n
Figure 3.
Stability condition in 2D. (a) The traditional staggered grid FD scheme and (b) the new staggered grid FD scheme.
\n
\n
\n
4.2. Optimizing finite difference operators for the elastic wave equation
Usually, Eq. (48) is used to determine the FD coefficient. For the first-order staggered grid FD scheme, the following dispersion relation can be obtained from Eq. (48):
where r = βΔt/h, M1 = M2 = M, and (kx\n, kz\n) = k(cosθ, sinθ). It can be observed from Eq. (49) that the dispersion relation is nonlinear and regularized optimized methods can address this problem similarly.
\n
Different with previous staggered grid FD scheme for the first-order elastic wave equation, the simplest centered second-order staggered grid FD operator can be used for the spatial derivatives in Eqs. (7)–(9):
The staggered grid FD scheme in Eqs. (52)–(54) is more efficient than the staggered grid FD scheme in Eqs. (19)–(21). It will be demonstrated later that the staggered grid FD scheme in Eqs. (52)–(54) is accurate for the stress vector (τxx\n, τzz\n, τxz\n) even when only second-order staggered grid FD operator is used.
\n
Then, the new dispersion relation can be obtained from Eq. (49) in the frequency-wavenumber domain:
The staggered grid FD coefficient can be obtained similarly using the linear method.
\n
\n
\n
\n
5. Experiments
\n
\n
5.1. Acoustic wave equation
\n
\n
5.1.1. Numerical modeling in the layered velocity model
\n
We first consider a layered velocity model. The velocity is 1500 m/s for the first layer and 2500 m/s for the second layer as shown in \nFigure 4\n. The sponge boundary code in CREWES Toolbox is used to reduce artificial reflection waves [34]. A Ricker wavelet with the main frequency as 14.3 Hz was used as the seismic source. The seismic source position is denoted as a asterisk, and the receivers A and B are denoted as a circle and a diamond from top to bottom, respectively. The space grid interval is 20m, the FD operator length M is 7 and the time step is 1.5 ms. The staggered grid FD coefficients used in \nFigure 4\n are shown in \nTable 1\n.
\n
Figure 4.
Velocity model.
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n\n
\n
\n
c1\n
\n
c2\n
\n
c3\n
\n
c4\n
\n
c5\n
\n
c6\n
\n
c7\n
\n
\n\n\n
\n
\n
1.22861
\n
−0.102384
\n
0.0204768
\n
−0.00417893
\n
0.000689454
\n
−0.0000769225
\n
0.00000423651
\n
\n
\n
\n
1.25438
\n
−0.1235307
\n
0.03467231
\n
−0.01192915
\n
0.00405709
\n
−0.001191005
\n
0.0002263204
\n
\n
\n
v = 1500 m/s
\n
1.57866
\n
−0.296598
\n
0.0949307
\n
−0.0344762
\n
0.0120067
\n
−0.00344529
\n
0.000605554
\n
\n\n
Table 1.
Staggered grid FD coefficient used to obtain the seismograms in \nFigure 4\n with the space grid interval equals 20 m, and the time step equals 1.5 ms. In the first row is the traditional staggered grid FD coefficient obtained from Table 3 of Chu and Stoffa [17]; in the second row is the least squares staggered grid FD coefficient obtained from Table 3 of Liu [35]; and in the last rows are the staggered grid FD coefficients used for Eq. (30). Eqs. (31) and (32) use the simplest second-order staggered grid FD operator.
\n
The seismograms recorded at positions A and B by different methods are presented in \nFigure 5\n. \nFigure 5(a)\n is obtained with the traditional staggered grid FD scheme with the FD coefficient obtained in the space domain by Taylor expansion method [17]. The grid dispersion is obvious. \nFigure 5(b)\n is obtained with the traditional staggered grid FD scheme with the coefficient obtained in the space domain by the least squares method [35]. The staggered grid FD coefficient provided by Liu is one of the best staggered grid FD coefficient provided in recent years [35]. \nFigure 5(c)\n is obtained with the new staggered grid FD scheme with the coefficient determined in the time-space domain by the linear method. \nFigure 5(d)\n is obtained with the pseudo-spectrum method with the second-order acoustic wave equation. We observe that the grid dispersion in \nFigure 5(b)\n and \n(c)\n is similar to each other and is close to the nearly analytic results obtained with the pseudo-spectrum method in \nFigure 5(d)\n. However, the required simulation time is reduced by using the new staggered grid FD scheme because Eqs. (31) and (32) are much simpler than Eqs. (13) and (14).
\n
Figure 5.
Seismograms recorded by different simulation methods. (a) The traditional staggered grid FD scheme with FD coefficients determined in the space domain by Taylor expansion method, (b) the traditional staggered grid FD scheme with FD coefficients determined in the space domain by least squares method, (c) the new staggered grid FD scheme with FD coefficients determined in the time-space domain by the linear method, and (d) the pseudo-spectrum method.
\n
\n
\n
5.1.2. Numerical modeling in the salt model
\n
\n\nFigure 6\n shows the salt model from Society of Exploration of geophysicists with variations of velocities from 1486 to 4790 m/s. The seismic source function is the same as the previous example. The spatial sampling interval is 20 m, temporal step is 1 ms, and M = 7 for the staggered grid FD operators in \nFigure 7(a)\n and \n(b)\n. In \nFigure 7(c)\n, the parameters are M = 7 for the spatial derivatives in Eq. (1), and M = 1 for the spatial derivatives in Eqs. (2) and (3). The pseudo-spectrum method is used for the second-order acoustic wave equation as shown \nFigure 7(d)\n.
\n
Figure 6.
SEG BP salt model.
\n
Figure 7.
Seismic records obtained with different methods. (a) The traditional staggered grid FD scheme with FD coefficients determined in the space domain by Taylor expansion method, (b) the traditional staggered grid FD scheme with FD coefficients determined in the time-space domain by least squares method, (c) the new staggered grid FD scheme with FD coefficients determined in the time-space domain by the linear method, and (d) the pseudo-spectrum method.
\n
\n\nFigure 7(a)\n is obtained the with the traditional staggered grid FD scheme with the coefficient obtained in the space domain by Taylor expansion method. The grid dispersion is obvious. \nFigure 7(b)\n is obtained with the traditional staggered grid FD scheme with the coefficient obtained in the time-space domain by the least squares method [27]. Most of the grid dispersion is suppressed. \nFigure 7(c)\n is obtained the with the new staggered grid FD scheme with the coefficient obtained in the time-space domain by the linear method. The grid dispersion in \nFigure 7(c)\n is very similar to the grid dispersion in \nFigure 7(b)\n. However, the simulation time to get \nFigure 7(c)\n is reduced compared with the simulation time to get \nFigure 7(b)\n. Both seismic records in \nFigure 7(b)\n and \n(c)\n are close to seismic record in \nFigure 7(d)\n. We want to mention that the linear method is faster than the LS method to determine the FD coefficients.
\n
\n\nFigure 8\n Further compares the seismograms in \nFigure 7\n at position x/dx = 400. It is also observed that with the coefficient obtained in the space domain by Taylor expansion method, the grid dispersion is serious in the simulation result. The simulation results are almost overlapped for the traditional staggered grid FD scheme and new staggered grid FD scheme with optimized FD coefficient. However, the required simulation time is reduced by using the new staggered grid FD scheme because Eqs. (31) and (32) are much simpler than Eqs. (13) and (14).
\n
Figure 8.
Seismograms at x/dx = 400 from \nFigure 4(a)–(d)\n.
\n
\n\nFigure 9\n compares snapshots of particle velocity vx\n with the different staggered grid FD schemes at 2500 ms. it is also observed that with the coefficient obtained in the space domain by Taylor expansion method, the grid dispersion is most serious. The grid dispersion in \nFigure 9(c)\n is very similar to the grid dispersion in \nFigure 9(b)\n. It demonstrated that the new staggered grid FD scheme is accurate for the particle velocities in Eqs. (32) and (33) even when only second-order staggered grid FD operator is used.
\n
Figure 9.
Particle velocity snapshots vx\n obtained with different methods. (a) The traditional staggered grid FD scheme with the traditional FD coefficients, (b) the traditional staggered grid FD scheme with FD coefficients determined in the time-space domain by the least squares method, and (c) the new staggered grid FD scheme with FD coefficients determined in the time-space domain by the linear method.
\n
\n
\n
\n
5.2. Elastic wave equation
\n
\n
5.2.1. Numerical modeling in the homogeneous media
\n
We first consider a homogeneous model. The P wave propagation speed is 2598 m/s, and the S wave velocity is 1500 m/s. The seismic source position is at the center of the model. The grid space interval is 20 m, the time step is 1 ms, and the operator length M is 7. A Ricker wavelet with the main frequency as 14.3 Hz was used as the seismic source.
\n
The snapshots of the horizontal component obtained by different staggered grid FD methods are presented in \nFigure 10(a)–(c)\n. \nFigure 10(a)\n is obtained with the traditional staggered grid FD scheme with the traditional FD coefficient. The grid dispersion is obvious. \nFigure 10(b)\n is obtained with the traditional staggered grid FD scheme with the new FD coefficient. Compared with \nFigure 10(a)\n, the grid dispersion is suppressed. \nFigure 10(c)\n is obtained with the new staggered grid FD scheme. The grid dispersion curves in \nFigure 10(b)\n and \n(c)\n are very similar, which is further demonstrated in \nFigure 10(d)\n. However, with the new staggered grid FD scheme, we can save about 45% of the modeling time.
\n
Figure 10.
Snapshots and slices of snapshots of the horizontal component at 698 ms obtained by different simulation methods. (a) The traditional staggered gird FD scheme with traditional FD coefficient, (b) the traditional staggered gird FD scheme with new FD coefficient, (c) the new staggered grid FD scheme with new FD coefficient, and (d) slices of snapshots at x/dx = 125.
\n
\n
\n
5.2.2. Numerical modeling in the homogeneous media
\n
\n\nFigure 11\n shows the salt model from Society of Exploration of geophysicists. The S wave velocity is obtained from the P wave velocity. The seismic source function is plotted as a red asterisk. The spatial sampling interval is 12.5 m, the temporal step is 1 ms, and M = 7 for staggered grid FD operators.
\n
Figure 11.
SEG BP salt model. (a) P wave velocity and (b) S wave velocity.
\n
\n\nFigure 12\n displays the seismic records of the horizontal component obtained by different staggered grid FD methods. \nFigure 12(a)\n is obtained with the traditional FD scheme with the traditional staggered grid FD coefficient. The grid dispersion is severe. \nFigure 12(b)\n is obtained with the traditional FD scheme with the staggered grid FD coefficient obtained by the least squares method. \nFigure 12(c)\n is obtained the with the new FD scheme with the staggered grid FD coefficient obtained by the linear method. It is observed that the grid dispersion in \nFigure 12(b)\n and \n12(c)\n is smaller than the grid dispersion in \nFigure 12(a)\n. \nFigure 12(d)\n is seismograms obtained from \nFigure 12(a)–(c)\n. It further demonstrated that the grid dispersion in \nFigure 12(b)\n and \n(c)\n is similar to each other and smaller than the grid dispersion in \nFigure 12(a)\n. However, with the new FD scheme, the simulation time is reduced about 45%. In our simulation, there are 525 grids in the z direction and 850 grids in the x direction. With the traditional FD scheme, the simulation time is 920 seconds. With the new staggered FD grid scheme, the simulation time is 530 seconds. The huge reduction in simulation time is due to using the shorter staggered FD operator for the spatial derivatives in Eqs. (7)–(9). \nFigure 13\n is the seismic records of the vertical component obtained by different FD methods. The same pattern can be observed from \nFigure 13(a)–(d)\n.
\n
Figure 12.
Seismic records of the horizontal component obtained with different staggered grid FD methods. (a) Seismic records obtained by traditional FD scheme with traditional staggered grid FD coefficient, (b) seismic records obtained by the traditional FD scheme with new staggered grid FD coefficient, (c) seismic records obtained by the new FD scheme with new staggered grid FD coefficient, and (d) seismograms obtained from (a) to (c) at position x/dx = 355.
\n
Figure 13.
Seismic records of the vertical component obtained with different staggered grid FD methods. (a) The traditional FD scheme with traditional staggered grid FD coefficient, (b) the traditional FD scheme with new staggered grid FD coefficient, (c) the new FD scheme with new staggered grid FD coefficient, and (d) seismograms obtained from (a) to (c) at position x/dx = 200.
\n
\n
\n
\n
\n
6. Discussion and conclusion
\n
The FD method is the most commonly used numerical method for wave equation modeling. Suppressing the grid dispersion is an important research area. Optimization method is usually used to determine the FD coefficients which could preserve the dispersion relation in a wider range of wavenumber (Zhang and Yao [24]; Ren and Liu [26]; Tan and Huang [32, 33]). We introduced the regularized optimization method to determine the FD coefficient which would be more robust for extreme conditions. The other way to suppress the grid dispersion is the utilization of the new FD scheme for the spatial derivatives. We introduce to use different FD operators for different spatial derivatives in the first-order wave equation. With the new staggered grid FD scheme, the wave equation modeling speed was accelerated while still preserving high accuracy. Through numerical modeling, we conclude that the introduced methods are more efficient while still preserving high accuracy for the first-order acoustic/elastic wave equation modeling. As a result, the introduced methods can be a substitute for the traditional FD methods used in acoustic/elastic wave equation modeling, which are essential in forward seismic wave modeling and reverse-time migration.
\n
\n
Acknowledgments
\n
This work is supported by the National Natural Science Foundation of China under grant numbers 41325016, 41704120, and 91630202.
\n
\n',keywords:"finite difference scheme, optimized finite difference coefficient, staggered grid, regularization, wave equation",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/57674.pdf",chapterXML:"https://mts.intechopen.com/source/xml/57674.xml",downloadPdfUrl:"/chapter/pdf-download/57674",previewPdfUrl:"/chapter/pdf-preview/57674",totalDownloads:1082,totalViews:562,totalCrossrefCites:0,dateSubmitted:"July 28th 2017",dateReviewed:"October 12th 2017",datePrePublished:"December 20th 2017",datePublished:"January 4th 2018",dateFinished:null,readingETA:"0",abstract:"The finite difference (FD) methods are widely used for approximating the partial derivatives in the acoustic/elastic wave equation. Grid dispersion is one of the key numerical problems and will directly influence the accuracy of the result because of the discretization of the partial derivatives in the wave equation. Therefore, it is of great importance to suppress the grid dispersion by optimizing the FD coefficient. Various optimized methods are introduced in this chapter to determine the FD coefficient. Usually, the identical staggered grid finite difference operator is used for all of the first-order spatial derivatives in the first-order wave equation. In this chapter, we introduce a new staggered grid FD scheme which can improve the efficiency while still preserving high accuracy for the first-order acoustic/elastic wave equation modeling. It uses different staggered grid FD operators for different spatial derivatives in the first-order wave equation. The staggered grid FD coefficients of the new FD scheme can be obtained with a linear method. At last, numerical experiments were done to demonstrate the effectiveness of the introduced method.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/57674",risUrl:"/chapter/ris/57674",signatures:"Yanfei Wang and Wenquan Liang",book:{id:"5708",title:"Computational and Experimental Studies of Acoustic Waves",subtitle:null,fullTitle:"Computational and Experimental Studies of Acoustic Waves",slug:"computational-and-experimental-studies-of-acoustic-waves",publishedDate:"January 4th 2018",bookSignature:"Mahmut Reyhanoglu",coverURL:"https://cdn.intechopen.com/books/images_new/5708.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"15068",title:"Dr.",name:"Mahmut",middleName:null,surname:"Reyhanoglu",slug:"mahmut-reyhanoglu",fullName:"Mahmut Reyhanoglu"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"218676",title:"Prof.",name:"Yanfei",middleName:null,surname:"Wang",fullName:"Yanfei Wang",slug:"yanfei-wang",email:"yfwang@mail.iggcas.ac.cn",position:null,institution:{name:"Institute of Geology and Geophysics",institutionURL:null,country:{name:"Azerbaijan"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Acoustic/elastic wave equations",level:"1"},{id:"sec_3",title:"3. Finite difference operators",level:"1"},{id:"sec_4",title:"4. Optimizing finite difference operators",level:"1"},{id:"sec_4_2",title:"4.1. Optimizing finite difference operators for the acoustic wave equation",level:"2"},{id:"sec_5_2",title:"4.2. Optimizing finite difference operators for the elastic wave equation",level:"2"},{id:"sec_7",title:"5. Experiments",level:"1"},{id:"sec_7_2",title:"5.1. Acoustic wave equation",level:"2"},{id:"sec_7_3",title:"Table 1.",level:"3"},{id:"sec_8_3",title:"5.1.2. Numerical modeling in the salt model",level:"3"},{id:"sec_10_2",title:"5.2. Elastic wave equation",level:"2"},{id:"sec_10_3",title:"5.2.1. Numerical modeling in the homogeneous media",level:"3"},{id:"sec_11_3",title:"5.2.2. Numerical modeling in the homogeneous media",level:"3"},{id:"sec_14",title:"6. Discussion and conclusion",level:"1"},{id:"sec_15",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'\nAlterman Z, Karal FC. Propagation of elastic waves in layered media by finite difference methods. Bulletin of the Seismological Society of America. 1968;58(1):367-398\n'},{id:"B2",body:'\nVirieux J. SH-wave propagation in heterogeneous media: Velocity-stress finite- difference method. Geophysics. 1984;49(11):1933-1942\n'},{id:"B3",body:'\nVirieux J. P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method. Geophysics. 1986;51(4):889-901\n'},{id:"B4",body:'\nDablain MA. The application of high-order differencing to the scalar wave equation. Geophysics. 1986;51(1):54-66\n'},{id:"B5",body:'\nRobertsson JO, Blanch JO, Symes WW. Viscoelastic finite-difference modeling. Geophysics. 1994;59(9):1444-1456\n'},{id:"B6",body:'\nBohlen T, Wittkamp F. Three-dimensional viscoelastic time-domain finite-difference seismic modeling using the staggered Adams-Bashforth time integrator. Geophysical Journal International. 2016;204(3):1781-1788\n'},{id:"B7",body:'\nEtemadsaeed L, Moczo P, Kristek J, Ansari A, Kristekova M. A no-cost improved velocity-stress staggered-grid finite-difference scheme for modelling seismic wave propagation. Geophysical Journal International. 2016;207(1):481-511\n'},{id:"B8",body:'\nAlford RM, Kelly KR, Boore DM. Accuracy of finite-difference modeling of the acoustic wave equation. Geophysics. 1974;39(6):834-842\n'},{id:"B9",body:'\nKelly KR, Ward RW, Treitel S, Alford RM. Synthetic seismograms: A finite-difference approach. Geophysics. 2012;41:2-27\n'},{id:"B10",body:'\nMadariaga R. Dynamics of an expanding circular fault. Bulletin of the Seismological Society of America. 1976;66(3):639-666\n'},{id:"B11",body:'\nLevander AR. Fourth-order finite-difference p-sv seismograms. Geophysics. 1988;53(11):1425-1436\n'},{id:"B12",body:'\nYang D, Teng J, Zhang Z, Liu E. A nearly analytic discrete method for acoustic and elastic wave equations in anisotropic media. Bulletin of the Seismological Society of America. 2003;93(2):882-890\n'},{id:"B13",body:'\nYang D, Lu M, Wu R, Peng J. An optimal nearly analytic discrete method for 2D acoustic and elastic wave equations. Bulletin of the Seismological Society of America. 2004;94(5):1982-1992\n'},{id:"B14",body:'\nChen JB. High-order time discretizations in seismic modeling. Geophysics. 2007;72(5):SM115-SM122\n'},{id:"B15",body:'\nChen JB. A stability formula for lax-Wendroff methods with fourth-order in time and general-order in space for the scalar wave equation. Geophysics. 2011;76(2):T37-T42\n'},{id:"B16",body:'\nSong X, Fomel S. Fourier finite-difference wave propagation. Geophysics. 2011;76(5):T123-T129\n'},{id:"B17",body:'\nChu C, Stoffa PL. Determination of finite-difference weights using scaled binomial windows. Geophysics. 2012;77(3):W17-W26\n'},{id:"B18",body:'\nFomel S, Ying L, Song X. Seismic wave extrapolation using low-rank symbol approximation. Geophysical Prospecting. 2013;61(3):526-536\n'},{id:"B19",body:'\nFinkelstein B, Kastner R. Finite difference time domain dispersion reduction schemes. Journal of Computational Physics. 2007;221:422-438\n'},{id:"B20",body:'\nFinkelstein B, Kastner R. A comprehensive new methodology for formulating FDTD schemes with controlled order of accuracy and dispersion. IEEE Transactions on Antennas and Propagation. 2008;56:3516-3525\n'},{id:"B21",body:'\nEtgen J. T. A tutorial on optimizing time domain finite-difference scheme: Beyond Holberg: Stanford Exploration Project Report. 2007;129:33-43\n'},{id:"B22",body:'\nLiu Y, Sen MK. A new time-space domain high-order finite difference method for the acoustic wave equation. Journal of Computational Physics. 2009;228:8779-8806\n'},{id:"B23",body:'\nLiu Y, Sen MK. Scalar wave equation modeling with time-space domain dispersion-relation-based staggered-grid finite-difference schemes. Bulletin of the Seismological Society of America. 2011;101(1):141-159\n'},{id:"B24",body:'\nZhang JH, Yao ZX. Optimized finite-difference operator for broadband seismic wave modeling. Geophysics. 2013;78:A13-A18\n'},{id:"B25",body:'\nLiang WQ, Yang CC, Wang YF, Liu HW. Acoustic wave equation modeling with new time-space domain finite difference operators. Chinese Journal of Geophysics. 2013;56(6):840-850\n'},{id:"B26",body:'\nRen Z, Liu Y. Acoustic and elastic modeling by optimal time-space-domain staggered-grid finite-difference schemes. Geophysics. 2014;80(1):T17-T40\n'},{id:"B27",body:'\nWang Y, Liang W, Nashed Z, Li X, Liang G, Yang C. Seismic modeling by optimizing regularized staggered-grid finite-difference operators using a time-space-domain dispersion- relationship-preserving method. Geophysics. 2014;79(5):T277-T285\n'},{id:"B28",body:'\nChen H, Zhou H, Zhang Q, Chen Y. Modeling elastic wave propagation using K space operator-based temporal high-order staggered-grid finite-difference method. IEEE Transactions on Geoscience and Remote Sensing. 2017;55(2):801-815\n'},{id:"B29",body:'\nYong P, Huang J, Li Z, Liao W, Qu L, Li Q, Liu P. Optimized equivalent staggered-grid FD method for elastic wave modelling based on plane wave solutions. Geophysical Journal International. 2017;208(2):1157-1172\n'},{id:"B30",body:'\nLiu Y, Sen MK. Time-space domain dispersion-relation-based finite-difference method with arbitrary even-order accuracy for the 2D acoustic wave equation. Journal of Computational Physics. 2013;232(1):327-345\n'},{id:"B31",body:'\nLiu H, Dai N, Niu F, Wu W. An explicit time evolution method for acoustic wave propagation. Geophysics. 2014;79(3):T117-T124\n'},{id:"B32",body:'\nTan S, Huang L. An efficient finite-difference method with high-order accuracy in both time and space domains for modelling scalar-wave propagation. Geophysical Journal International. 2014a;197(2):1250-1267\n'},{id:"B33",body:'\nTan S, Huang L. A staggered-grid finite-difference scheme optimized in the time-space domain for modeling scalar-wave propagation in geophysical problems. Journal of Computational Physics. 2014b;276:613-634\n'},{id:"B34",body:'\nMargrave GF. Numerical Methods of Exploration Seismology with Algorithms in Matlab. Calgary: Department of Geology and Geophysics, the University of Calgary; 2001\n'},{id:"B35",body:'\nLiu Y. Optimal staggered-grid finite-difference schemes based on least-squares for wave equation modelling. Geophysical Journal International. 2014;197(2):1033-1047\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Yanfei Wang",address:"yfwang@mail.iggcas.ac.cn",affiliation:'
Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, People’s Republic of China
Institutions of Earth Science, Chinese Academy of Sciences, People’s Republic of China
University of Chinese Academy of Sciences, People’s Republic of China
College of Resource Engineering, Longyan University, People’s Republic of China
'}],corrections:null},book:{id:"5708",title:"Computational and Experimental Studies of Acoustic Waves",subtitle:null,fullTitle:"Computational and Experimental Studies of Acoustic Waves",slug:"computational-and-experimental-studies-of-acoustic-waves",publishedDate:"January 4th 2018",bookSignature:"Mahmut Reyhanoglu",coverURL:"https://cdn.intechopen.com/books/images_new/5708.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"15068",title:"Dr.",name:"Mahmut",middleName:null,surname:"Reyhanoglu",slug:"mahmut-reyhanoglu",fullName:"Mahmut Reyhanoglu"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}}},profile:{item:{id:"206346",title:"Dr.",name:"Partida",middleName:null,surname:"Ruvalcaba Leopoldo",email:"parpolo@yahoo.com.mx",fullName:"Partida Ruvalcaba Leopoldo",slug:"partida-ruvalcaba-leopoldo",position:null,biography:null,institutionString:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",totalCites:0,totalChapterViews:"0",outsideEditionCount:0,totalAuthoredChapters:"1",totalEditedBooks:"0",personalWebsiteURL:null,twitterURL:null,linkedinURL:null,institution:{name:"Instituto Tecnológico de Culiacán",institutionURL:null,country:{name:"Mexico"}}},booksEdited:[],chaptersAuthored:[{title:"Biorational Insecticides and Diatomaceous Earth for Control Sustainability of Pest in Chickpea and Mexican Bean Weevil",slug:"biorational-insecticides-and-diatomaceous-earth-for-control-sustainability-of-pest-in-chickpea-and-m",abstract:"Sustainability involving the conservation and/or enhancement of natural resources and environmental protection can be practiced with biorational insecticides or diatomaceous earth. Two researches were carried out; in one, the objective was to determine the efficacy of biorational insecticides in controlling chickpea leaf miner, Liriomyza sativae Blanchard, without completely inhibiting the presence of parasitoids of this pest. Biorational insecticides were chlorantraniliprole, cyromazine and spinosad, and conventional insecticide was chlorpyrifos, which were similarly effective to control adults and larvae of Liriomyza. Most chickpea production in 2012–2013 (1993.3 and 1806.8 kg ha−1) was obtained where chlorantraniliprole and chlorpyrifos were applied, respectively, and where spinosad and cyromazine were applied also exceeded the performance of absolute control (1213.6 kg ha−1). In 2013–2014, the increased production was 1621.9 kg ha−1 with chlorantraniliprole and 1556.3 kg ha−1 with chlorpyrifos, significantly different from the absolute control that produced 1136.5 kg ha−1. Earnings were MX$ 21011.7 in 2012–2013 and MX$ 16036.7 in 2013–2014 with chlorantraniliprole, while in the absolute control, earnings were MX$ 12305.1 and MX$ 11083.5. Chlorantraniliprole was the biorational insecticide that caused greater effect in the management of this pest of chickpea and crop yields. While in another research, the objective was to determine the efficacy of different doses of diatomaceous earth against Mexican bean weevil Zabrotes subfasciatus Boheman. An experiment was carried out in two phases: in first, one tested diatomaceous earth at doses of 1.0, 2.0, 3.0, 4.0, and 5.0 g kg−1 of seed, with samples at 15, 30, 45, and 60 days after application (daa), while in the second, the doses were 0.2, 0.4, 0.6, 0.8, and 1.0 g kg−1 and samples at 10, 20, 30, and 40 daa. The parameters evaluated were weevil mortality and seed germination. The results indicated that the doses from 0.8 to 5.0 g kg−1 of diatomaceous earth efficiently controlled the Mexican bean weevil. 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He received his M.Sc. in 2010 from IARI, New Delhi along with a gold medal for his outstanding contribution. He joined the Agricultural Research Service (ARS) in 2011 as a scientist. He completed his Ph.D in 2020 from Visva Bharati University in Soil Science and Agricultural Chemistry and worked on integrated organic nutrient management. He has published 27 national and 40 international research articles, 10 review articles in national and international journals, 30 popular articles, 28 extension folders, 2 books, and 25 book chapters in edited books. He received a DST-INSPIRE fellowship in 2010 from DST, Govt. of India. He has been awarded the best scientist award by the ICAR RC for the NEH Region, Umiam, Meghalaya in 2018. He received six young scientist awards and 3 best oral presentation awards from different reputable societies. 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Our platform – IntechOpen is the world’s leading publisher of OA books, built by scientists, for scientists.
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Our reputation – Everything we publish goes through a two-stage peer review process. We’re proud to count Nobel laureates among our esteemed authors. We meet European Commission standards for funding, and the research we’ve published has been funded by the Bill and Melinda Gates Foundation and the Wellcome Trust, among others. IntechOpen is a member of all relevant trade associations (including the STM Association and the Association of Learned and Professional Society Publishers) and has a selection of books indexed in Web of Science's Book Citation Index.
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Our expertise – We’ve published more than 4,500 books by more than 118,000 authors and editors.
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Our reach – Our books have more than 130 million downloads and more than 146,150 Web of Science citations. We increase citations via indexing in all the major databases, including the Book Citation Index at Web of Science and Google Scholar.
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Our services – The support we offer our authors and editors is second to none. Each book in our program receives the following:
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A Creative Commons license, so authors always keep their copyright;
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A dedicated Author Service Manager to guide the publication process from submission to publication;
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Professional copyediting and language editing;
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An open access e-book, plus beautifully produced hardcover and affordable paperback print-on-demand editions;
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Professional cover design;
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Access to our online Manuscript Tracking System;
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A dedicated landing page;
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DOI for every book and every individual chapter;
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