Cite this article as Haney, M. M., K. M. Ward, V. C. Tsai, and B. Schmandt (2020). Bulk Structure of the Crust and Upper Mantle beneath Alaska from an Approximate Rayleigh-Wave Dispersion Formula, Seismol. Res. Lett. XX, 1–12, doi: 10.1785/0220200162. Supplemental Material We introduce a method for estimating crustal thickness and bulk crustal and uppermantle shear-wave velocities directly from high-quality measurements of fundamental-mode Rayleigh-wave dispersion in the period range from 10 to 40 s. The method is based on an approximate Rayleigh-wave dispersion formula and provides fast results with minimal model parameterization. We apply the method to Rayleigh-wave phase maps in Alaska to reveal first-order structure in a region that had not been systematically and densely instrumented prior to the Transportable Array (TA). To demonstrate the consistency of the results, we also apply the same method to existing Rayleighwave phase maps derived from TA data in the conterminous United States, where crustal and upper mantle structures are better known. We contrast features observed in maps of crustal thickness and bulk shear-wave velocity between the Cascadia and Alaska-Aleutian subduction zones to highlight differences in the two regions. Our results show that, contrary to conventional wisdom, first-order information on the location of major depth discontinuities (e.g., the Moho) can be extracted in a fast, straightforward manner from measurements of Rayleigh-wave dispersion alone. Introduction Crustal thickness is a fundamental geophysical parameter needed to understand the dynamic forces responsible for mountain building and to constrain properties of the deep crust. Yet prior to the deployment of the Earthscope Transportable Array (TA) in Alaska (Incorporated Research Institutions for Seismology [IRIS] Transportable Array, 2003) knowledge of crustal thickness (i.e., depth of the Moho) across much of the state was limited. Figure 1 shows the expansion of the TA in Alaska between 2014 and 2017, with stations from 2016 and 2017 filling in regions of western and northern Alaska that had previously only been sparsely instrumented. Subsequently, research on crustal and upper mantle structure in Alaska has grown considerably in recent years with the availability of TA data (Jiang et al., 2018; Martin-Short et al., 2018; Miller and Moresi, 2018; Miller et al., 2018; Ward and Lin, 2018; Feng and Ritzwoller, 2019; Zhang et al., 2019; Berg et al., 2020). In addition to the structural implications of the Moho, its depth is also noteworthy because it formally marks the lower boundary of the transcrustal magma systems underlying volcanoes in Alaska. For example, deep long-period (DLP) earthquakes beneath Alaskan volcanoes are often observed to cluster around the depths of the Moho (Power et al., 2004, 2013). Tamura et al. (2016) have shown evidence for crustal thickness determining magma type in the western Aleutians as well as the Izu-Bonin arc. Receiver functions are the most widely used approach for determining crustal thickness from passive seismic data (Schmandt et al., 2015; Miller and Moresi, 2018; Zhang et al., 2019). Based on multicomponent analysis of teleseismic bodywave scattering at the Moho, receiver functions provide estimates of crustal thickness and the ratio of P-wave velocity to S-wave velocity in the crust, which is itself related to the bulk Poisson’s ratio of the crust. In this article, we present an alternative approach for obtaining the depth to the Moho, or crustal thickness, from the dispersion of Rayleigh waves. Traditionally, surface waves have been utilized to find 1. U.S. Geological Survey, Alaska Volcano Observatory, Anchorage, Alaska, U.S.A., ORCID ID: 0000-0003-3317-7884; 2. Department of Geology and Geological Engineering, South Dakota School of Mines and Technology, Rapid City, South Dakota, U.S.A., ORCID ID: 0000-0002-2938-4306; 3. Department of Earth, Environmental, and Planetary Sciences, Brown University, Providence, Rhode Island, U.S.A., ORCID ID: 0000-0003-1809-6672; 4. Department of Earth and Planetary Sciences, University of New Mexico, Albuquerque, New Mexico, U.S.A., ORCID ID: 0000-0003-1049-9020 *Corresponding author: mhaney@usgs.gov © Seismological Society of America Volume XX • Number XX • – 2020 • www.srl-online.org Seismological Research Letters 1 Downloaded from https://pubs.geoscienceworld.org/ssa/srl/article-pdf/doi/10.1785/0220200162/5125978/srl-2020162.1.pdf by walryd on 12 August 2020 the thickness of the crust (e.g., Evison et al., 1959); however, as comprehensively discussed by Lebedev et al. (2013), there are pitfalls and tradeoffs involved in mapping the Moho with surface waves. We develop a method suitable for obtaining a first-order approximation of the Moho interface and the bulk shear-wave velocity of the crust and upper mantle from fundamental-mode Rayleigh waves and discuss both the advantages and limitations of the method. Detailed Moho mapping, beyond a first-order approximation, requires more advanced surface-wave methods as described by Lebedev et al. (2013). Feng and Ritzwoller (2019), for example, have recently implemented a Bayesian Monte Carlo inversion of surface-wave dispersion in Alaska for depth models parameterized by 15 unknowns, including the Moho, at each lateral grid point. In contrast, our simplified method only solves for three parameters: the depth of the Moho and the bulk shear-wave velocities of the crust and upper mantle. In this way, our method bridges a gap between receiver functions, which estimate two parameters at each receiver (Moho and bulk crustal Poisson’s ratio), and more advanced surface-wave methods that can image heterogeneities within the crust and upper mantle. The method is similar in principle to the grid search technique used by Pasyanos and Walter (2002) to map out crustal and uppermantle structure in North Africa, Europe, and the Middle East. We additionally use an approximation for Rayleigh-wave dispersion that allows the grid search to run over only a single parameter, the thickness of the crust. In fact, the approximate Rayleigh-wave dispersion formula we use was discovered by Jeffreys (1935). The new aspect of our work lies in the use of this approximate formula, which Jeffreys (1935) referred to as the “first approximation,” within an inversion scheme. The lack of full dispersion modeling and the reduced dimensions of the grid search make our method an extremely fast way to gain estimates of crustal and upper-mantle structure, including the Moho, from Rayleigh waves alone. Data and Methods We analyze fundamentalmode Rayleigh-wave phase velocity maps between 10 and 40 s period to determine the depth of the Moho as well as bulk crustal and upper-mantle structure. The method we use is based on an approximate formula for Rayleigh-wave dispersion (Jeffreys, 1935; Haney and Tsai, 2015), which we describe later. In addition to Alaska, we also analyze phase maps determined with TA data from the conterminous United States to show the method we develop captures the known crustal and upper-mantle structure there. We select the period range from 10 to 40 s based on the findings of Lebedev et al. (2013) that Rayleigh waves have maximum sensitivity to the Moho within this band. This can be understood from the fact that the sensitivity depth of Rayleigh waves is roughly one-half of a wavelength (Haney and Tsai, 2015). For an average phase velocity of 3:5 km=s, the period range from 10 to 40 s corresponds to the typical depth range of the Moho from 18 to 70 km. The phase maps for the conterminous United States and Alaska have been published previously by Ekström (2014, 2017) and Ward and Lin (2018), respectively, and utilized correlations of ambient noise to recover the Rayleigh-wave portion of the interstation Green’s functions for input to tomography. Finite-frequency effects and off-great-circle propagation, or ray-bending, were not taken into account in these phase maps. To extract depth information from the phase velocity maps, we exploit recent results by Haney and Tsai (2015, 2017) demonstrating that an analogy to the Dix equation used in reflection seismology (Dix, 1955) exists for surface waves. Figure 1. Regional map of the Transportable Array in Alaska with stations color-coded by year of installation between 2014 and 2017. The color version of this figure is available only in the electronic edition. 2 Seismological Research Letters www.srl-online.org • Volume XX • Number XX • – 2020 Downloaded from https://pubs.geoscienceworld.org/ssa/srl/article-pdf/doi/10.1785/0220200162/5125978/srl-2020162.1.pdf by walryd on 12 August 2020 The defining characteristic of the Dix equation for seismic reflections is the proportionality of squared stacking velocities, used to maximize hyperbolic stacking, with the squared velocities of the layers. Such a relation follows from the approximation that, above a reflector, the subsurface can be replaced by a homogeneous medium with velocity equal to the root mean square (rms) velocity over that depth interval. Thus, each reflector has a different effective homogeneous medium overlying it. For fundamental-mode Rayleigh waves in a medium with a Poisson’s ratio of 0.25, a similar approach means that at each frequency the Rayleigh wave can be taken to propagate in a different effectively homogeneous medium with shear-wave velocity given by 1/0.9194 multiplied by the phase velocity at that frequency. Other values of Poisson’s ratio can be used for this approximation besides 0.25 (Haney and Tsai, 2017); however, Poisson’s ratio has a minor effect on Rayleigh-wave phase velocity compared to shear-wave velocity and so we take it to be 0.25 in this study. Chevrot and van der Hilst (2000) report crustal Poisson’s ratio values between 0.23 and 0.29 in Australia, showing minor variability around 0.25. The analogy to the Dix equation for fundamental-mode Rayleigh waves leads to the following propo

中文翻译：

---

从近似瑞利波色散公式看阿拉斯加下地壳和上地幔的整体结构

将本文引用为 Haney、MM、KM Ward、VC Tsai 和 B. Schmandt（2020 年）。阿拉斯加下方地壳和上地幔的整体结构，来自近似瑞利波色散公式，地震。水库 莱特。XX, 1–12, doi: 10.1785/0220200162。补充材料 我们介绍了一种直接从 10 到 40 秒周期范围内对基模瑞利波色散的高质量测量来估计地壳厚度和大块地壳和上地幔横波速度的方法。该方法基于近似的瑞利波色散公式，并以最少的模型参数化提供快速结果。我们将该方法应用于阿拉斯加的瑞利波相位图，以揭示在可移动阵列 (TA) 之前尚未进行系统和密集仪器检测的区域中的一阶结构。为了证明结果的一致性，我们还将相同的方法应用于现有的从美国本土 TA 数据导出的瑞利波相位图，那里的地壳和上地幔结构更为人所知。我们对比了在卡斯卡迪亚和阿拉斯加-阿留申俯冲带之间的地壳厚度和整体剪切波速度图中观察到的特征，以突出两个地区的差异。我们的结果表明，与传统观点相反，主要深度不连续性（例如，莫霍面）位置的一阶信息可以仅从瑞利波色散的测量中以快速、直接的方式提取。引言 地壳厚度是一个基本的地球物理参数，需要了解造成山体形成的动力和约束地壳深层的特性。然而，在阿拉斯加（地震学联合研究机构 [IRIS] 可移动阵列，2003 年）部署 Earthscope 可移动阵列 (TA) 之前，对该州大部分地区的地壳厚度（即莫霍面深度）的了解是有限的。图 1 显示了 2014 年至 2017 年阿拉斯加 TA 的扩展，2016 年和 2017 年的站点填补了阿拉斯加西部和北部以前仅配备稀少仪器的地区。随后，随着 TA 数据的可用，近年来对阿拉斯加地壳和上地幔结构的研究有了长足的发展（Jiang 等，2018；Martin-Short 等，2018；Miller 和 Moresi，2018；Miller 等，2018）。 ，2018；Ward 和 Lin，2018；Feng 和 Ritzwoller，2019；Zhang 等，2019；Berg 等，2020）。除了莫霍面的结构影响，它的深度也值得注意，因为它正式标志着阿拉斯加火山下的跨地壳岩浆系统的下边界。例如，经常观察到阿拉斯加火山下方的深长周期 (DLP) 地震聚集在莫霍面深处（Power 等人，2004 年，2013 年）。田村等人。(2016) 已经证明了地壳厚度决定了阿留申群岛西部以及伊豆-波宁弧的岩浆类型。接收器函数是从被动地震数据确定地壳厚度的最广泛使用的方法（Schmandt 等，2015；Miller 和 Moresi，2018；Zhang 等，2019）。基于对莫霍面远震体波散射的多分量分析，接收器函数提供地壳厚度和地壳中 P 波速度与 S 波速度之比的估计值，这本身与地壳的体积泊松比有关。在本文中，我们提出了一种从瑞利波的色散中获得莫霍面深度或地壳厚度的替代方法。传统上，表面波已被用于寻找 1. 美国地质调查局，阿拉斯加火山观测站，美国阿拉斯加州安克雷奇，ORCID ID：0000-0003-3317-7884；2. 美国南达科他州拉皮德城南达科他矿业技术学院地质与地质工程系，ORCID ID：0000-0002-2938-4306；3. 美国罗德岛州普罗维登斯布朗大学地球、环境和行星科学系，ORCID ID：0000-0003-1809-6672；4. 新墨西哥大学地球与行星科学系，美国新墨西哥州阿尔伯克基市，ORCID ID：0000-0003-1049-9020 *通讯作者：mhaney@usgs.gov © Seismological Society of America Volume XX • Number XX • – 2020 • www.srl-online.org Seismological Research Letters 1 下载自 https://pubs.geoscienceworld.org/ssa/srl/article-pdf/ doi/10.1785/0220200162/5125978/srl-2020162.1.pdf 由 walryd 于 2020 年 8 月 12 日撰写的地壳厚度（例如，Evison 等人，1959 年）；然而，正如 Lebedev 等人全面讨论的那样。(2013)，用表面波映射莫霍面存在陷阱和权衡。我们开发了一种适用于从基模瑞利波获得莫霍面界面以及地壳和上地幔体剪切波速度的一阶近似值的方法，并讨论了该方法的优点和局限性。详细的莫霍面映射，超越一阶近似，需要更先进的表面波方法，如 Lebedev 等人所述。(2013)。例如，Feng 和 Ritzwoller（2019 年）最近对阿拉斯加的表面波色散进行了贝叶斯蒙特卡罗反演，用于在每个横向网格点由 15 个未知数（包括莫霍面）参数化的深度模型。相比之下，我们的简化方法仅求解三个参数：莫霍面深度以及地壳和上地幔的体横波速度。通过这种方式，我们的方法弥合了接收器函数之间的差距，接收器函数估计每个接收器的两个参数（莫霍面和大块地壳泊松比），以及更先进的表面波方法，可以对地壳和上地幔内的不均匀性进行成像。该方法在原理上类似于 Pasyanos 和 Walter (2002) 用来绘制北非、欧洲和中东地壳和上地幔结构的网格搜索技术。我们另外使用瑞利波色散的近似值，它允许网格搜索仅运行单个参数，即地壳厚度。事实上，我们使用的近似瑞利波色散公式是由 Jeffreys (1935) 发现的。我们工作的新方面在于在反演方案中使用了这个近似公式，Jeffreys (1935) 将其称为“第一近似”。缺乏全色散建模和网格搜索维度的减少使我们的方法成为一种极快的方法，可以仅从瑞利波获得地壳和上地幔结构的估计，包括莫霍面。数据和方法 我们分析了 10 到 40 秒周期之间的基模瑞利波相速度图，以确定莫霍面以及大块地壳和上地幔结构的深度。我们使用的方法基于瑞利波色散的近似公式（Jeffreys，1935；Haney 和 Tsai，2015），我们将在后面介绍。除了阿拉斯加，我们还分析了用来自美国本土的 TA 数据确定的相位图，以展示我们开发的方法捕获那里已知的地壳和上地幔结构。我们根据 Lebedev 等人的发现选择了 10 到 40 秒的周期范围。(2013) 认为瑞利波对该波段内的莫霍面具有最大灵敏度。这可以从瑞利波的敏感深度大约为波长的二分之一来理解（Haney and Tsai，2015）。对于 3:5 km=s 的平均相速度，10 到 40 s 的周期范围对应于 18 到 70 公里的典型莫霍面深度范围。Ekström (2014, 2017) 和 Ward and Lin (2018) 之前分别发布了美国本土和阿拉斯加的相位图，并利用环境噪声的相关性来恢复站间格林函数的瑞利波部分断层扫描的输入。在这些相位图中没有考虑有限频率效应和离大圆传播或光线弯曲。为了从相速度图中提取深度信息，我们利用 Haney 和 Tsai（2015 年，2017 年）的最新结果证明，表面波存在与反射地震学中使用的 Dix 方程（Dix，1955 年）的类比。图1。阿拉斯加可移动阵列区域地图，站点在 2014 年至 2017 年之间按安装年份进行颜色编码。此图的彩色版本仅提供电子版。2 地震研究快报 www.srl-online.org • 第 XX 卷 • 第 XX 号 • – 2020 下载自 https://pubs.geoscienceworld.org/ssa/srl/article-pdf/doi/10.1785/0220200162/5125978/srl- 2020162.1.pdf 由 walryd 于 2020 年 8 月 12 日发布 地震反射 Dix 方程的定义特征是叠加速度平方的比例，用于最大化双曲线叠加，与层的平方速度。这种关系源自近似值，即在反射器上方，地下可以被均匀介质替换，其速度等于该深度间隔内的均方根 (rms) 速度。因此，每个反射器都有不同的有效均匀介质覆盖在它上面。对于泊松比为 0.25 的介质中的基模瑞利波，类似的方法意味着在每个频率，瑞利波可以在不同的有效均匀介质中传播，剪切波速度为 1/0.9194 乘以该频率下的相速度。除了 0.25（Haney 和 Tsai，2017）之外，泊松比的其他值也可用于此近似值；然而，与横波速度相比，泊松比对瑞利波相速度的影响较小，因此我们在本研究中将其取为 0.25。Chevrot 和 van der Hilst (2000) 报告了澳大利亚的地壳泊松比值介于 0.23 和 0.29 之间，显示出大约 0.25 的微小变化。