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To write Faetar, you have to use the Italian spelling system, because it’s the only system the speakers know.
When you write Faetar, you should use French orthography because that will indicate the Gallic roots of the language.
Of course, the only option is to use the International Phonetic Alphabet to write Faetar, so that linguists around the world are able to understand the details of our unique language.
Introduction
The reconstructed vignette above, based on actual conversations with speakers of Faetar, an endangered language spoken in two small villages in southern Italy (Nagy 2000, 2011a), illustrates some of the many uses that transcription has. Researchers (and the transcribers they hire) may not even be aware of all the potential downstream uses of their transcriptions. The most common understanding of the purpose of transcription in linguistics is contained in the third statement. However, a linguist’s decision to transcribe in a standardized orthography or in the International Phonetic Alphabet (IPA) can influence later uses of the text. Deviations from the traditions of one’s field can even be perceived as ideologically charged. As Kendall (2008: 337) puts it,
the act of transcription [. . .] is often undertaken as a purely methodological activity, as if it were theory neutral. Each decision that is made while transcribing influences and constrains the resulting possible readings and analyses (Ochs 1979; Mishler 1991; Bucholtz 2000; Edwards 2001). Decisions as seemingly straightforward as how to lay out the text, to those more nuanced – like how much non-verbal information to include and how to encode minutiae such as pause length and utterance overlap – have far-reaching effects on the utility of a transcript and the directions in which the transcript may lead analysts.
A common objective of geophysics is to probe the properties of the Earth's interior based on data from observations. Geoscientists often use seismic data to build a model of the subsurface as a representation of various assessments of some simplified key aspects of the real world. The validity of each model depends on its consistency with observations. All observable datasets constitute a data space, and all possible models constitute a model space. Data fitting and model inversion are two complementary approaches in geophysics to relate the data space to the model space. Data fitting uses forward modeling to search for models that fit well with the observed data and satisfy our scientific intuition. Model inversion uses our scientific intuition to set up rules about how the models should behave and then determines the model variations that fit best with the available data. The usefulness of data fitting and model inversion is evident in many applications illustrated in this chapter.
The basic theories of seismic modeling and inverse theory are reviewed here. Data fitting is introduced in the first two sections via several seismic forward modeling methods and a simple example of regression. The basic theories on inverting a system of linear equations are given in the next three sections, in conjunction with the tomographic velocity analysis in Section 8.4. The least squares method as a classic linear inversion is widely applicable in geophysical data analysis and beyond. Some mathematic insights on inversion of linear equations are illustrated via several common ways of matrix decomposition. The common causes of non-uniqueness in geophysical inversion include insufficient constraining power of the data, the non-linear relationship between data and model, and dependency of that relationship on the solution. Several practical inverse solutions discussed here include the Backus–Gilbert method and the LSQR algorithm. Practically, seismic inversion is synonymous with the inverse imaging in Section 8.4. The inverse approach has the advantage of subjectively determining the values of model properties based on the given model parameterization and data. For some applications such as inverse filtering and tomographic velocity analysis, inversion is the preferred method because of its objectiveness in obtaining the solutions.
Linguists, across the subdisciplines of the field, use sound recordings for a great many purposes – as data, stimuli, and a medium for recording notes. For example, phoneticians often record speech under controlled laboratory conditions to infer information about the production and comprehension of speech in subsequent acoustic and perception studies, respectively. In addition to analyzing acoustic data, phoneticians may employ articulatory methods to observe more directly how speech is produced. By contrast, sociolinguists often record unscripted speech outside of a university environment, such as a speaker’s home. Sometimes these recordings themselves constitute the data (e.g., for sociophonetic analysis), while other times they may be transcribed at varying levels of detail (see Chapter 12), with the resultant text serving as the data (e.g., for the analysis of lexical or morphosyntactic variation and discourse analysis). In a similar vein, some language acquisitionists capture naturally occurring conversation in adult–child interactions. The research purposes of these recordings may not be determined until some time after the recordings are made, after a longitudinal corpus for a given child has been collected. It is likewise common for language documentarians to make extensive speech recordings in the field. Some field recordings simply serve as a record of elicitation sessions (e.g., when the researcher is ascertaining phrase structure), while others may be used for acoustic analysis (e.g., if phonetic elements of the language are the object of study). In the latter case, articulatory methods can be employed to more accurately describe phonetic properties of speech, such as a sound’s place of articulation or details of the airstream mechanism. As discussed in Chapter 8, sound recordings can also be used as stimuli in perception studies, where listeners may be asked first to listen to a brief audio recording and then to identify whether a particular string of sounds is a real word (Chapter 8); to evaluate how educated the speaker of a brief utterance sounds (Chapter 6); or to rate how accented an L2 speaker sounds (Chapter 7). Linguists may also make use of archival recordings to investigate questions of language change. Proficiency in making sound recordings is thus an increasingly useful skill for linguists of most persuasions.
Shortly after I arrived in Israel to begin fieldwork on language among Israeli lesbian and gay activists, I went out for a drink with three of my male informants. As we waited for the bartender to bring us our beers, Roee, one of the men I was with, leaned over to me and, indicating the bartender with his head, said wai, eize birz hu, naxon? (‘Wow, he’s a birz, isn’t he?’). Though I could tell that he was commenting on the bartender, I had to admit that I did not understand the word birz, and I asked Roee to translate it for me. Roee began to laugh, and then explained that the word birz meant ‘handsome man’ in an Israeli gay slang variety called oxtchit. My interest was immediately piqued. I had never heard of an Israeli gay slang variety before, and I was eager to know where the variety came from and how it was used. The men I was with that evening explained to me that oxtchit was a variety predominantly used by a specific kind of effeminate gay man in Israel, called oxtchot, though it was also sometimes used by other gay men as a “secret” variety.
From the previous chapters the reader should have become acquainted with many of the basic skills of seismic data analysis. Any practice of seismic data processing utilizes some of these skills to solve particular problems, and uses special tools to address more focused issues. Everyone in this field will encounter special issues in his/her career; hence knowing the common features of some special topics is very useful. In this chapter several special processing topics are reviewed to show the use of the basic data processing skills that we have learned, and to expose the reader to some widely seen processing topics. Each of these topics deals with issues associated with a particular problem or property. The first section introduces the issues involved in four aspects of seismic data acquisition: monitoring of source signals including fracking-induced micro-seismicity; monitoring background noises; seismic illumination analysis; and preservation of low-frequency signals. The second section is on suppression of multiple reflections, which is of service to many conventional seismic imaging methods that use only primary reflections. After defining common types of multiples, three classes of multiple suppression methods are introduced. The first is based on the differential moveout between primaries and multiples; the second exploits the periodicity of the multiples; and the third reduces all surface-related multiple energy via pre-stack inversion. The next section reviews the basics in seismic anisotropy, a property of the medium that causes a variation of the speed of seismic waves as a function of the traversing angle. Information on seismic anisotropy helps in improving the fidelity of seismic imagery in fault imaging, and in detecting the dominant orientations of fractures. The fourth section briefly covers multi-component seismic data processing, with an analysis of its pros and cons and with illustrations in wavefield separation, converted wave processing, and VSP data processing. The final section introduces the processing aspect of seismic attributes, including a variety of localized attributes, geometric attributes, and texture attributes, plus related processing in seismic-to-well tie and impedance inversion. To become an expert in the practice of these and other topics in seismic data processing, the reader must learn the fundamentals of seismic wave and ray theory, common issues in seismic data acquisition, processing and interpretation, and spend some time in processing and utilizing field seismic data.
Seismic data analysis transfers seismic records measured at the surface or along wellbores into imagery, estimates, and models of subsurface structures and properties. It covers the topics of digital seismic data processing, seismic migration, and subsurface model building that are useful in both exploration geophysics and solid Earth geophysics. Although several excellent books have covered these topics either from the viewpoint of exploration geophysics or that of solid Earth geophysics, I was motivated to write this book to deal with common seismic analysis methods for both aspects of geophysics. This book is intended as an introductory text on common and practical methods in seismic data analysis.
Most of the materials for this book originated as lecture notes for graduate courses in geophysics at University of Houston and Texas Tech University. Students on these courses usually have a variety of backgrounds: many are recent graduates from geophysics, geology, engineering, computer sciences, or other physical science disciplines, and others are employees in the petroleum industry. They intend to apply seismic data analysis skills to problems in exploration geophysics, solid Earth geophysics, and engineering and environmental sciences. Although they may have access to some commercial or free software in seismic processing, most of these students have not gone through a systematic review of common approaches to seismic data analysis and the practical limitations of each method. Hence, an effort has been made in this book to emphasize the concepts and practicality of common seismic analysis methods using tutorial and case examples or schematic plots.
As the most widely used subsurface imaging method in petroleum exploration, seismic migration attempts to place seismic reflection data into their correct spatial or temporal reflector positions. Similar to the echo sounding technique to fathom the water bottom from a boat, seismic migration maps the subsurface reflectors in two steps. Step one is to back-project the seismic data measured at the surface downwards using the wave equation and a velocity model, producing an extrapolated wavefield that is a function of space and time. Step two is to use an imaging condition to capture the positions of the subsurface reflectors from the extrapolated wavefield. These two steps are demonstrated by the three common seismic migration methods introduced in this chapter. First, Kirchhoff migration is the most intuitive and flexible migration method, and it uses the ray theory approximation in practice. Second, frequency domain migration is theoretically rigorous and made efficient by taking advantage of the Fourier transform, although it is less effective in the presence of strong lateral velocity variations. Like these two methods, most migrations simplify reality by assuming that the input data contain only primary reflections; hence some pre-processing procedures are necessary to suppress other seismic waves recorded. Third, reverse time migration is a full wave migration method that is capable of using both primary reflections and other waves such as refractions and multiple reflections.
Fundamentally, a velocity model is required for all seismic migration methods. A time migration uses layer-cake models without lateral velocity variations. In contrast, a depth migration may handle a significant level of lateral velocity variations in the velocity model. In the case of gently dipping reflectors, a post-stack migration may be sufficient, using post-NMO stacked traces to approximate zero-offset traces. In the presence of steeply dipping reflectors, a pre-stack migration is usually more suitable but takes many more computational resources. Depending on the complexity of the target structures, we may choose from a suite of migration methods, from the crude but fast post-stack time migration which is not sensitive to velocity variations, to the expensive pre-stack depth migration to handle steep reflector dips and strong lateral variations in the velocity models.
The practice of seismic data processing with digital records has been progressing for over six decades. Today all seismic processing projects are started with a set of scientific and business objectives in mind that often require specific processing flows; usually each flow involves some pre-processed data rather than the raw data. The pre-processing includes all preparation steps through which both major and relatively simple problems in the input data are cleaned up so that the main processing flow can function more effectively. While the pre-processing steps may be standard and even apparently routine, each step can be critical to the final result.
This chapter starts with illustrations of the most common pre-processing tasks. One important aspect of learning seismic data processing is to appreciate the physical processes that the wavelet from a seismic source has experienced, so that we may approximately undo or redo some of the processes in computers. For this reason, the filtering expression of seismic data processing is introduced. As a modern example, the processing of a multi-component dataset from vertical seismic profile is shown. This chapter examines several simple but common processing operators, including normal moveout, stacking, convolution, correlation, and Radon transform. Often the reason for using these techniques is to suppress the most common types of noise. The readers should try to envision the physical processes that each operator attempts to emulate. As an example of preliminary analysis, the effects of surface topography and near-surface velocity variations are analyzed using the concept of near-surface statics.
the importance of knowledge of space in the early years – it enables children to explore the world around them and develop the vocabulary to label and talk about it
the role of shape in children’s understanding of space, and the related concepts of location and transformation
the seven spatial perception skills.
In addition to the ability to work with numbers and reason logically, children need opportunities to develop their spatial skills and understanding of shape, location and transformation, and to engage in geometric or spatial reasoning. This form of knowledge is referred to broadly as spatial sense – an important objective of mathematics education in the 21st century. Some aspects of spatial sense are evident in the drawings from seven-year-old Laura’s journal (see below). Compared to her age peers, Laura has a well-developed spatial sense. However, her drawings suggest that she needs to develop an understanding of the relative size of adults and children. Hence, encouraging children to express themselves through drawing provides an insight into their spatial sense. Comparing a child’s drawings over time is one method of monitoring the progression of his spatial sense.
ways to represent quantity using physical items, words and numerals
activities to encourage children to count, compare and order numbers
ways to foster conceptual understanding of place value in the base 10 number system
how mathematical operations on a quantity increase or decrease its value.
Number knowledge is fundamental to understanding mathematical situations in the everyday world. To develop this understanding, young children need a range of experiences, such as counting, recognising and writing numerals, composing and decomposing numbers, and simple operations. Children’s understandings can be supported by the use of physical materials and tools that aid thinking. For example, the calculator is a useful tool when children are learning to count by twos and fives because children can check what they are saying with what the visual display of the calculator is showing. It is also useful for checking answers when children have completed an operation. Throughout their school years, children are expected to acquire increasingly complex understandings of number. Hence, it is important for children to master simple concepts and gradually build their proficiency with number.
describing, copying, extending and creating repeating patterns
identifying the ‘rule’ in growing patterns, and continuing and creating these patterns
the notion that the rule to extend a growth pattern in number is the same as a function to change the value of a set of numbers
finding key mathematical relationships among numbers or sets of numbers.
Recognising and working with patterns is fundamental to mathematics. Some patterns have units that repeat. Continuing a repeating pattern involves simply copying the repeating unit and adding it onto the existing pattern. There are also growth patterns. In a growth pattern, each new term includes the one before and grows according to an inbuilt ‘rule’. The rule in the growth pattern below is to copy the letters and include the next letter of the alphabet.
activities designed to raise children’s awareness of the role of chance in everyday life
activities focusing on developing children’s knowledge and skills in collecting, organising, representing and interpreting data.
Chance and data is a relatively new concept area in mathematics for young children. Chance includes ideas of randomness and probability that are relevant to everyday life – for example, in games involving spinners. Data includes collecting, organising, representing and interpreting information. For example, data can be collected in a survey, organised in a table and represented on a graph. Someone looking at the graph needs to be able to interpret the information that was collected in the survey. Understanding data is particularly important in the information-rich age of the 21st century. Children’s experiences of chance and data in the mathematics program should enrich their understanding of the world around them, so it is important that these experiences have personal relevance. Playing games with dice or reading a television guide and a bus timetable are examples of children interpreting data in meaningful contexts.
On a visit to a classroom, Nicola (N), an early childhood educator, had the following conversation with Tessa (T), a Year 3 child:
N: What are you doing, Tessa?
T: Another maths sheet.
N: Oh great! I love doing maths. What is this one about?
T: Adding sums [said glumly].
N: Do you like doing maths, Tessa?
T: No. It’s boring and anyway why should I when my teacher hates it too?
N: Does she really hate it? How do you know that?
T: She never smiles when we do maths.
This anecdote indicates the strength of young children’s perceptions of the learning environment. It also highlights the fact that some adults lack confidence in and enthusiasm for mathematics. This book is designed to support teachers, parents and caregivers in providing a rich mathematical environment for children in their early years (birth to eight years of age). Young children who have worthwhile and interesting mathematical experiences have the opportunity to acquire mathematical understandings and positive attitudes towards mathematics. This enables them to become numerate and use mathematics effectively in their daily lives.
activities suitable to encourage the use of the beginning processes for young children in the first five years of life
the importance of using language, children’s literature and playful explorations as sources for mathematical experiences in the early years. This includes traditional materials such as books and manipulatives as well as new technologies.
From the time a baby is born, she uses her five senses (taste, touch, smell, sight and hearing) to investigate the world. In the years from birth to five, there is a dramatic change in her physical growth, capabilities and skills. It is exciting when a baby says her first word or takes her first steps. It is equally wondrous when she successfully makes a tower of blocks or completes a puzzle independently. Building with blocks and puzzle making are two examples of early experiences that facilitate the development of mathematical thinking. Increasingly, from the age of two, young children are also experiencing using new technologies in a range of activities. Tablet technologies can support early multimodal learning which, when supported by parents, caregivers and teachers, not only enables children to link the two-dimensional experience of using these technologies with ‘real-world’ activities and contexts, but also enriches language acquisition. Encouragement from adults and conversations about activities will help children to connect the mathematical understandings that are relevant to their everyday lives. During these early years, parents, caregivers and teachers play an important role in creating contexts for using mathematical language and supporting the use of the beginning processes and concepts of mathematics that children will encounter in a wide variety of situations. These early experiences are fundamental to enabling the young child to feel confident and competent about doing mathematics in school and being numerate in the 21st century.
the key concept areas in mathematics for young learners – number, measurement, space, chance and data, and patterns and algebra – and the way they relate to the ‘Big Ideas’ in mathematics
the mathematical processes that form the basis of the mathematics curriculum in schools
the importance of fostering positive attitudes towards mathematics, particularly through the careful selection and design of tasks
the substantial variation in children’s understanding and performance in mathematics and the need for responsive teaching.
In the years before starting school, the young child has had many experiences that provide the foundation for mathematical understandings. A child stacking pots and pans begins to learn about ordering. When Dad counts with Sam, or Mum reads The Three Little Pigs to Simon, they are helping their children to develop an understanding of numbers. Children also develop an understanding of mathematics through everyday activities. At the shops, seeing people buying groceries provides some understanding of the value of coins and how we exchange coins for goods. Children enjoy acting out everyday mathematical situations that they have seen, such as ‘playing shops’. When children play together they have an opportunity to learn from each other and to use mathematical language, such as ‘price’, ‘money’, ‘how much’ or ‘change’. When the young child goes to school, he will continue to build on these foundations of mathematical learning.