Writing your paper’s introduction is the rare task that benefits from procrastination.
Although the introduction comes first in your paper, write it last. Until you have finalized your paper’s scope and conclusions, you don’t know what you are introducing, so early efforts will be speculative and require revision. But once you have the rest of the paper, produce an introduction for that content and no more.
Your introduction should explain why your problem is important, why it is hard, and what you have done to advance the field. Your readers almost certainly have some background in your area if they opened your paper to read, so skip the most elementary ideas (in my field of disaster risk, authors sometimes open with a self-evident statement such as “Recent history has shown that earthquakes can be very destructive”). It will be more helpful to position your work in the context of more contemporary developments.
A safe Introduction format is to provide one paragraph on each of the following topics:
Context: What problem are you studying, and why is it broadly important? Start with relevant general trends and problems in your field, and then present your specific question in that broader context. This will help readers understand the relevance of your problem.
State of the art: What do people do at present? Aim to establish that there is a need for the contribution that you will later provide, and what limitations there are in current approaches.
Gaps: Are there problems or controversies that haven’t been resolved, or new resources that haven’t been utilized? This overlaps with the state-of-the-art but gets into more detail to provide context for your contributions. This is a chance to introduce similar prior papers. Rather than fully summarize those papers, point out specific parts of their approach or scope that will differ from yours, so that you can easily explain later what your contribution is.
Scope: What key components and approaches will you use, and what is your contribution? The contributions should provide a resolution to the gaps that you identified in previous paragraphs. Your first sentence of this paragraph should be of the form, “This paper demonstrates…,” and should be followed by a description of the study’s scope, methods, and outcomes. If the structure of the paper is nonstandard, you might consider describing it as well.
Start with the assumption that each numbered item is one paragraph, and thoughtfully deviate from that as needed. When considering adjustments, review good papers from the venue where you intend to publish. Conference papers and some broad-audience journals may have very short introductions. Other journals may expect an extended literature review in the introduction, where you provide a few paragraphs of detail about related prior studies of the problem.
Regardless of length, keep the above topics in distinct paragraphs. It is a common impulse to write a paragraph stating, “problem ___ is important, so in this paper I did ___,” followed by another paragraph stating, “but we are limited in data regarding ___, so I addressed this by ___.” This mixing of topics burdens the reader with disentangling the current state of the art from your contribution. Instead, step the reader through those topics one by one, so they finish convinced that the problem is interesting, your approach is promising, and they should keep reading to find out how it all turned out.
Don’t bring up problems that you aren’t going to resolve in the paper. If you write “we lack experimental evidence,” in the gaps paragraph, your paper should provide new experimental evidence. Otherwise, the reader will finish the paper confused as to whether they missed something or disappointed that the challenge you raised was never resolved. There may truly be a lack of experimental evidence regarding your problem, but introducing this is irrelevant if you don’t address it. This idea is referred to as “Chekhov’s gun,” after the writer Anton Chekhov, who advised, “If in the first act you have hung a pistol on the wall, then in the following one it should be fired. Otherwise don’t put it there.”
To illustrate the above structure, consider the following examples (lightly edited for clarity of illustration). Each paragraph from the paper is preceded by a comment to indicate the topic addressed in that paragraph. The second is longer than the first, but both contain the above topics in the same order, and neither mixes topics within paragraphs. I suggest adding labels like this to your draft paper’s paragraphs, to check that you are staying on topic.
Baker J.W. (2007). "Quantitative classification of near-fault ground motions using wavelet analysis," Bulletin of the Seismological Society of America, 97 (5), 1486-1501. DOI
[General commentary: This very short introduction hits the key topics in one paragraph each, so I thought it was a useful example. It does have an unusual feature of including a figure in the introduction. I rarely do that, but in this case it was helpful because the concept I was discussing was very visual. Deviations like this are fine—just be thoughtful about why you are doing it.]
[Context — pulse-like ground motions are important]
Near-fault ground motions containing strong velocity pulses are of interest in the fields of seismology and earthquake engineering. A quantitative approach for identifying these ground motions is proposed here and used to perform a variety of basic studies of their properties. These ground motions, which are here referred to as “pulse-like ground motions,” have been identified as imposing extreme demands on structures to an extent not predicted by typical measures such as response spectra (e.g., 1-10). Theoretical considerations also provide an indication of seismological conditions that may result in occurrence of velocity pulses due to, for example, directivity effects (11-13). While the effect is relatively well studied, a hindrance to incorporating these effects in probabilistic seismic hazard analysis and engineering building codes is that a quantitative method for identifying these velocity pulses does not yet exist. This means that a variety of researchers have assembled sets of pulselike or near-fault ground motions, but these classifications are not easily re- producible (e.g., 14-17).
[State of the art — current pulse-like classifications depend on judgment]
The ground motions identified in past studies are typically selected because the velocity time history of the ground motion is dominated by a large pulse, as seen, for example, in Figure 1a, and/or because source–site geometry suggests that a directivity pulse might be likely to occur at the site where the motion was recorded. Selection of pulselike ground motions using these approaches requires some level of judgment, and for many ground motions, such as those shown in Figure 1b and c, the classification may not be obvious. Identification of non-pulselike motions at near-fault locations (such as the one shown in Fig. 1d) is also challenging for the same reasons, although it has not received as much attention.
[Gap — we can’t solve several problems without quantitative classification]
The lack of a quantitative classification scheme for recorded ground motions has hindered progress toward obtaining results such as the probability that a ground motion with a given earthquake magnitude, distance, and source–site geometry will contain a velocity pulse. Knowledge of this probability is useful for applications such as probabilistic seismic hazard analysis (18,19). The lack of quantitative classifications also means that electronic libraries of recorded ground motions do not list any statistics indicating whether a given ground motion contains a velocity pulse, and this limits the ability of the science and engineering communities to access these ground motions and study their effects for research or practical applications.
In this article, an approach for detecting pulses in ground motions is proposed and investigated. The procedure uses wavelet-based signal processing to identify and extract the largest velocity pulse from a ground motion; if the extracted pulse is “large” relative to the remaining features in the ground motion, the ground motion is classified as pulse-like. The period of a detected velocity pulse, a parameter of interest to engineers, is also easily determined. The classification algorithm is computationally inexpensive, so large libraries of recorded ground motions can be (and have been) analyzed. Although some of the identified pulses are likely not caused by directivity effects, the approach is useful for identifying a set of records potentially exhibiting directivity effects, which can then be manually considered more carefully. Alternatively, the ground motions could be used (without further classification) for structural response calculations, under the assumption that pulses will cause similar effects regardless of their causal mechanism.Baker, J. W., and Chen, Y. (2020). “Ground motion spatial correlation fitting methods and estimation uncertainty.” Earthquake Engineering & Structural Dynamics, 49(15), 1662–1681. DOI
[General commentary: This introduction has three “gaps” paragraphs because there were several distinct problems that we aimed to address, and because this allowed us to do a literature review of related studies. So there are a few more paragraphs than the basic format above, but we still step through the key topics in a standard order.]
[Context — spatial correlations in ground motions are important]
Spatial correlations in ground motion intensities have been studied for nearly two decades [e.g., 1,2,3,4,5,6,7]. These studies calibrate models using statistical analysis of recorded data from past earthquakes, in a manner similar to ground motion prediction models. The resulting models are important for estimating risks to distributed systems such as portfolios of insured properties and distributed infrastructure systems [e.g., 8,9,10,11,12].
[State of the art — current studies draw differing conclusions about causes of correlations]
As our library of recorded ground motions grows over time, spatial correlation studies have grown in refinement, with several studies exploring factors that may cause spatial correlation to vary from one earthquake to another. Goda and Hong  report differences in correlations between California and Taiwan ground motions, but no effect of earthquake magnitude. Jayaram and Baker [ 14] and Sokolov et al.  speculate that soil condition heterogeneity may influence spatial correlation. Goda  and Heresi and Miranda  report that spatial correlations vary from individual earthquake to earthquake, but find no earthquake characteristic that clearly predicts this variation. Schiappapietra and Douglas  report high variability in correlations amongst a sequence of earthquakes in Central Italy, and list local site effects or path and azimuthal effects as possible causes, noting Sokolov et al.’s  similar speculation. Other studies note a possible trend with earthquake magnitude [18,19] or variation regionally . Other studies group data from multiple earthquakes into a single data set, making the assumption that correlations from the earthquakes are equivalent [4,7,6,21,22] .
[Gap — we have limited data and no way to quantify uncertainty in results]
Several issues make it difficult to definitively identify important factors. First, because the spatial correlation estimation is empirical and requires many observed ground motions from an earthquake, it is difficult to obtain sufficient data under the conditions of interest. Second, there are no closed-form results from spatial correlation estimation that allow for a quantitative assessment of the uncertainty in a given estimate. Bootstrap estimation is another popular technique to quantify estimation uncertainty. However, it is difficult to apply to spatial data because of challenges with maintaining spatial dependence structure in the replicates while avoiding resampling the same location within a replicate (which provides no information about spatial structure). Some studies have proposed bootstrap techniques that resample from an estimated nonparametric distribution  or resampling transformed data24, but the methods are somewhat complex and have not been adopted widely. For the above reasons, no results have been presented in previous studies to quantify the estimation uncertainty in spatial correlations computed from individual earthquakes.
[Gap — model fitting techniques differ in previous studies]
Another issue that has not been evaluated in this literature is the role of the method used to fit parameters for the models, and relative performance of alternative methods. Fitting methods used in prior ground motion studies include manual visual fitting , least squares regression on transformed data [16,7], and least squares regression with weighting according to distance or number of data . One general study evaluated several fitting methods using Monte Carlo simulation of spatial data with a known correlation structure , and found that the above fitting methods produce systematic differences in results. But that study considered a small number of observed data (16 or 36 stations) on a regular grid–a situation very different than ground motion data coming from greater numbers of irregularly spaced stations. A recent study examined this issue for realistic numbers of stations in earthquake ground motion studies, but the locations in that study were randomly simulated . There are no general statistical results for estimators under arbitrary station configurations .
[Gap — unknown relationship between data sample size and estimation uncertainty]
Exact estimation of a correlation model from data (i.e., consistency in statistical estimation language) requires a large number of observations at closely spaced distances, with the dense locations not too concentrated at a single location . The above-cited studies of ground motions consider well-recorded earthquakes, but none systematically study the impact of well-recorded versus more-poorly-recorded earthquakes on resulting spatial correlation estimates. Further, the above-cited studies use different methods to fit models to data, and it is unknown what impact those fitting methods have on estimation uncertainty. The baseline estimation uncertainty is important as it establishes a threshold at which variability in observed correlations can be credibly linked to some causal source rather than being due to estimation variability.
[Our study’s scope]
To address the above issues, this paper proposes a framework to quantify uncertainty in spatial correlation models, and uses the framework to evaluate estimation uncertainty associated with individual earthquakes and model fitting methods. Section 2 introduces the basic framework for characterizing ground motion amplitudes using ground motion models, and introduces the semivariogram as a tool for quantifying spatial correlations. Methods for fitting semivariogram models are also introduced. Section 3 then introduces a model to describe the various components of apparent uncertainty in semivariogram parameters. A method is proposed for quantifying estimation uncertainty, by synthetically simulating ground motion amplitudes with a known spatial correlation model but observed only at locations corresponding to those of past earthquakes. This method is then applied to the considered earthquakes and fitting methods. The results are then discussed, along with the limitations and broader implications of the work.
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