Dataset and Software for the Radial Reference Earth Model REM1D

What are the Earth's average physical properties (e.g. density, shear/bulk attenuation, velocity, anisotropy)? Can astronomic-geodetic and full-spectrum seismological data (~1-3200 seconds) be reconciled? How can strong lateral variations (e.g. crust) be accounted for (i.e. theory, observations) in radial models? What can we robustly interpret about the Earth's interior based on its radial features? Is the outer core well mixed and undergoing adiabatic compression? Can spin transitions in iron-bearing minerals be detected in the lower mantle? What is the bulk composition of different regions? Is it pyrolitic everywhere? Is there a pervasive thermo-chemical boundary layer atop the core-mantle boundary? What is the radial extent and origin of large-scale anisotropy in the mantle? Where does the most energy dissipation occur and what is its dominant mechanism? The spherically-averaged profiles of elasticity, density, and attenuation reflect the bulk composition, temperature profile, and dominant processes of the Earth's heterogeneous interior. The two exhaustive manuscripts below describe the new radial (one-dimensional) reference Earth model (REM1D), which serves as the update to the preliminary reference Earth model (PREM; Dziewonski and Anderson, Phys. Earth Planet. Inter., 1981). The first manuscript describes new modeling concepts and reference datasets while features of REM1D and geological interpretations are discussed in the second manuscript. We extend the Full Spectrum Tomography (FST) technique, which is necessary for constructing reference models that account for lateral heterogeneity and geographic bias in diverse data. Summary Figure: REM1D_summary.png Project Website: rem3d.org Feedback/Questions? Please get in touch with Raj Moulik rajmoulik.com at [e-mail] Reference: Please cite the following works if you use this data or software. Moulik P. & G. Ekström (2025) Radial Structure of the Earth: (I) Model Concepts and Data, Phys. Earth Planet. Inter. doi:10.1016/j.pepi.2025.107319 Moulik P. & G. Ekström (2025) Radial Structure of the Earth: (II) Model Features and Interpretations. Phys. Earth Planet. Inter. doi:10.1016/j.pepi.2025.107320 You can also cite the dataset and software from this Zenodo page (Optional). Moulik, P. (2025) Dataset and Software for the Radial Reference Earth Model REM1D. In Phys. Earth Planet. Inter. (v1.0). Zenodo. doi: 10.5281/zenodo.8407693 Highlights: Features and Interpretations (Graphic_abstract_I.png) Radial reference Earth model (REM1D) is introduced for average physical properties Peak anisotropy (aS=3.90%) & attenuation (Qmu~60-80,Qkappa~386) in the upper mantle Consistent with pyrolitic mantle (<800 km) and basal thermo-chemical boundary layer Lower mantle (mu/kappa, Poisson's ratio) consistent with spin transitions in Fe-bearing minerals Outer core is neutrally stable, well mixed and undergoing adiabatic compression Concepts and Data (Graphic_abstract_II.png) New framework for radial reference models as the spherical average of heterogeneity Reference data of astronomic-geodetic constants, body/surface waves & normal modes Theoretical limitations, geographic biases & non-linear crustal effects are quantified Parameterization is adjusted to satisfy datasets & expectations from mineral physics Rapid convergence is achieved using analytical kernels & recent a priori constraints Summary Abstracts: Features and Interpretations: A new reference model is presented for the spherically-averaged profiles of elasticity, density and attenuation, which reflect the bulk composition, temperature profile and dominant processes of the Earth's heterogeneous interior. This study discusses the features of REM1D and geological interpretations while the underlying modeling concept and reference datasets are described in a companion manuscript. All physical parameters in REM1D vary smoothly between the Mohorovicic and 410-km discontinuity, thereby excluding the 220-km discontinuity in earlier models. REM1D predicts arrival times of major body-wave phases in agreement (±0.8 s, normalized misfit ψpb ≤ 0.25 s) with widely used but theoretically incomplete isotropic models optimized for earthquake location. Substantial radial anisotropy is present only in the shallowest mantle (∼250 km) with peak values of shear-wave (aS = 3.90% , ξ = 1.08) and compressional-wave anisotropy (aP = 3.78% , φ = 0.93) between ∼125–150 km, consistent with textures that can form by the alignment of intrinsically anisotropic minerals in this deforming region. The upper mantle (24.4-410 km) is the most dissipative region with a finite bulk attenuation (Qκ ~ 386) and strong shear attenuation (Qµ ~ 60–80) that peaks at a depth of ~150–175 km in the mechanically weak asthenosphere. An olivine-rich pyrolitic composition is broadly consistent with REM1D structure in the upper mantle and extended transition zone (<800 km) with step changes across the 410-km and 650-km discontinuities. Features of the lower mantle can be reconciled with: (i) effects of thermally driven convection throughout the central lower mantle (771–2741 km) leading to an apparent subadiabaticity in the stratification parameter ηB, (ii) effects of spin transitions in iron-bearing minerals that manifest as distinct linear segments in modulus and Poisson’s ratios (µ/κ, σP) on either side of a complex transition region (~1300–1700 km, 52–73 GPa), (iii) a thermal boundary layer with steeper superadiabatic gradients than near the surface, which ultimately exceed the critical gradients for both vP and vS (but not for density ρ) at a depth of 2741 km, and (iv) chemical stratification in the bottom ~500–750 km of the mantle that acts to suppress the thermal effects. Signatures of this thermo-chemical boundary layer are: (i) a gradual increase of density and steep positive gradients with depth (dρ/dz) in the lower mantle, (ii) large values of the stratification parameter (ηB > 1.03) followed by an abrupt reduction to values below one near the core-mantle boundary (CMB), (iii) variations in bulk modulus with pressure κl = dκ/dp that are inconsistent with Equations of state (EoS) expectations of a uniform composition, (iv) very steep negative vP and vS gradients that form a low-velocity zone in the Dll region. The vP and ρ variations in the outer core have steep and the derivative properties are consistent with a neutrally stable region comprising a well-mixed iron alloy undergoing adiabatic compression (ηB ~1, N 2~0, negative κll). REM1D is readily extendable due to its modular construction and represents the average physical properties, features essential for geological interpretations and the construction of a three-dimensional reference Earth model. Concepts and Data: A framework is introduced for developing a radial reference model that incorporates diverse observations and techniques for improving the constraints on bulk Earth structure. This study describes new modeling concepts and reference datasets while features of the reference Earth model REM1D and geological interpretations are discussed in a companion manuscript. Recent measurements from various techniques have improved in precision and are broadly consistent, and are summarized as best estimates with uncertainties. We construct a reference dataset comprising normal-mode eigenfrequencies and quality factors, surface-wave dispersion curves, impedance constraints and travel-time curves from body waves, and astronomic-geodetic observations. Classical radial reference models do not account for the theoretical effects and observational biases resulting from heterogeneity in the crust and mantle. We address three issues that account for lateral variations in the modeling of average elastic, anelastic and density structure. First, current ray coverage of traveling waves is biased towards structure in the northern hemisphere, leading to faster velocities especially in the lower mantle. Second, horizontal wavelength of the heterogeneity that a traveling wave encounters is assumed to be much greater than that of the corresponding normal mode in most ray-theoretical and finite-frequency formulations of wave propagation. Effects of the full volumetric sensitivity on local eigenfrequencies and phase velocities that are ignored with this approximation exceed the data uncertainty for both fundamental spheroidal (Rayleigh waves, T ≥ 220 s) and toroidal modes (Love waves, T ≥ 120 s); waves at these longer periods cannot be modeled solely in terms of radial variations along the ray path. Third, non-linear effects from the strongly heterogeneous crustal structure are substantial for shorter-period waves (T ≤ 100 s) and need to be accounted for while deriving radial models. After accounting for these issues on heterogeneity, rapid convergence for average structure is facilitated by utilizing a priori constraints from recent literature, analytical sensitivity kernels that account for physical dispersion, and a flexible parameterization comprising polynomial functions and cubic B-splines. By adopting a higher-order polynomial for density than the elastic structure, artifacts that imply strong inhomogeneity and non-adiabaticity are avoided in potentially well-mixed regions like the outer core. Derivative properties like the gradient of bulk modulus with pressure (κl = dκ/dp) and the Bullen’s stratification parameter (ηB) are adjusted in the core to match expectations from mineral physics without deteriorating the fits to reference datasets. A cubic polynomial parameterization in the lower mantle is adequate to capture possible changes in the gradients of the modulus ratio (µ/κ) associated with spin transitions in iron-bearing minerals. Radial reference models need to account for lateral heterogeneity and prior geological information in their construction to accurately represent the bulk average properties of a heterogeneous Earth. Data Products: REM1D Model Coefficients Elastic/density structure (REM1D.elas), anelastic structure (REM1D.anelas), and corresponding card deck file listing properties in 750 concentric layers/shells (REM1D.cards). These files are appropriate for various normal-mode, surface-wave and astronomic-geodetic calculations. A summary highlight figure is also provided for the REM1D model (REM1D_summary.png). Same as above but modified for calculating body-wave arrivals (REM1D_TT.elas, REM1D_TT.anelas, REM1D_TT.cards). Values in the upper crust are extended to the surface and ocean is removed. These files are appropriate only for the body-wave calculations. All physical parameters (VPH,VSH,VPV,VSV,VP,VS,Eta,A,C,N,L,F,Eta,Rho,Qmu,Qkappa) and derivative properties (Poisson's ratio, Pressure, dK/dP, Bullen, Gravity) from REM1D evaluated in 750 concentric layers/shells inside the Earth (REM1D_layer_properties.txt). These values are evaluated at the reference period of 1 second from the model coefficients listed in the files above (REM1D.elas, REM1D.anelas) using the equations in Paper II. Elastic properties at other periods after accounting for physical dispersion can be calculated following equation 8 in Paper II and using the Python script below. Python Script A pure Python 3 script (evaluate_REM1D.py) to evaluate REM1D physical parameters at any depth and period accounting for physical dispersion. This script needs coefficient files (REM1D.elas, REM1D.anelas) in the same directory. Some examples from the command line: Help: evaluate_REM1D.py -husage: evaluate_REM1D.py [-h] [-m MODEL] [-T PERIOD] [-p PARAMETER [PARAMETER ...]] [-b BOUNDARY] -d DEPTH_IN_KM [DEPTH_IN_KM ...]Evaluates REM1D physical parameters at the reference period of the default 1 second e.g. to calculate all parameters at150 km, enter: evaluate_REM1D.py -d 150options: -h, --help show this help message and exit -m MODEL, --model MODEL Radial reference Earth model defined at the reference period (default: 1 second) -T PERIOD, --period PERIOD Reference period (default: 1 second) -p PARAMETER [PARAMETER ...], --parameter PARAMETER [PARAMETER ...] Physical parameter. Can give multiple values e.g. rho vpv vsv qkappa qmu vph vsh eta -b BOUNDARY, --boundary BOUNDARY If the depth queried is an internal boundary, + evaluates the value above while - evaluates the value below the discontinuity. Ignored and assumed to be + if depths queried have repeated values. -d DEPTH_IN_KM [DEPTH_IN_KM ...], --depth_in_km DEPTH_IN_KM [DEPTH_IN_KM ...] Depth queried in km. Can give multiple values e.g. 24.4 75. 150. 225. 300. 410. 530. 650. 650. 820. 1320. 1820. 2320. 2550. 2791. 2891. If depth is repeated, then values above and bottom are queried assuming the user has queried a discontinuity. Calculate all parameters at 150 km: evaluate_REM1D.py -d 150 Calculate density at 100 km: evaluate_REM1D.py -d 150 -p rho Calculate all parameters at 150 km and 200 seconds accounting for physical dispersion following equation 8 in Paper II: evaluate_REM1D.py -d 150 -T 200 Calculate all parameters at 100, 150, 650, 1500, and 2891 km. Note that the discontinuities are repeated to evaluate above (+) and below (-) the internal boundary; if not repeated, the code will only provide values above (+) by default: evaluate_REM1D.py -d 100 150 650 650 1500 2891 2891 Calculate all parameters explicitly below (-) the 650-km discontinuity: evaluate_REM1D.py -d 650 -b - Reference Normal Mode/Surface Wave Data Reference datasets of phase-velocity perturbations w.r.t. PREM predictions between 4-40 mHz Love waves (avgdcbyc_Love.ref) Rayleigh Waves (avgdcbyc_Rayleigh.ref) Reference normal mode datasets Radial Modes - Eigenfrequencies (RADIAL_F.ref), Quality Factors (RADIAL_Q.ref) Spheroidal Fundamental Modes - Eigenfrequencies (SFUND_F.ref), Quality Factors (SFUND_Q.ref) Spheroidal Overtones - Eigenfrequencies (SOVER_F.ref), Quality Factors (SOVER_Q.ref) Toroidal Fundamental Modes - Eigenfrequencies (TFUND_F.ref), Quality Factors (TFUND_Q.ref) Toroidal Overtones - Eigenfrequencies (TOVER_F.ref), Quality Factors (TOVER_Q.ref) REM1D Data Fits and Predictions Fits to reference datasets Radial Modes (FITS_RADIAL.txt) Spheroidal Fundamental Modes, including Rayleigh waves (FITS_SFUND.txt) Spheroidal Overtones (FITS_SOVER.txt) Toroidal Fundamental Modes, including Love waves (FITS_TFUND.txt) Toroidal Overtones (FITS_TOVER.txt) Normal mode catalogs for periods down to 24 seconds in binary (REM1D_024.rts) and HDF formats (REM1D_024.h5). These calculations use the new reference astronomic-geodetic constants (e.g. revised Gravitational constant G) from Paper I. These can be read using standard HDF5 modules (e.g. h5py) or the open-source AVNI package. Conversion from the binary file was done using the following commands: from avni.data import NM NM.write_modes_hdf('REM1D_024.rts','REM1D_024.h5') Non-linear crustal corrections derived from REM1D overlain with CRUST2.0 heterogeneity for Love (nonlinear_CRUST2_Love.csv) and Rayleigh waves (nonlinear_CRUST2_Rayl.csv). These files contain domega and dc/c that need to be added to the eigenfrequency and dispersion predictions from REM1D, respectively, following equations 13 and 14 in Paper I.地球的平均物理性质（如密度、剪切/体衰减、波速、各向异性）究竟为何？ 天文大地测量数据与全频谱地震数据（约1~3200秒）能否相互协调一致？ 在径向模型中，如何合理阐释（即结合理论与观测）强烈的横向变化（如地壳结构）？ 基于地球的径向结构特征，我们能够对地球内部作出哪些可靠的解读？ 外核是否处于充分混合状态并经历绝热压缩？ 在下地幔中能否观测到含铁矿物的自旋转变？ 地球不同区域的整体成分为何？是否所有区域均为原始地幔岩（pyrolitic）？ 核幔边界顶部是否存在普遍分布的热化学边界层？ 地幔中大规模各向异性的径向分布范围与成因是什么？ 能量耗散最显著的区域位于何处，其主导机制为何？ 球平均的弹性、密度与衰减剖面，反映了非均质地地球内部的整体成分、温度分布与主导演化过程。下文两篇详尽的手稿介绍了新型径向（一维）参考地球模型（REM1D），该模型是对初步参考地球模型（PREM；Dziewonski与Anderson，《物理地球与行星内部》，1981年）的更新。第一篇手稿阐述了新型建模理念与参考数据集，而第二篇手稿则讨论了REM1D的模型特征与地质学解读。我们拓展了全频谱层析成像（Full Spectrum Tomography, FST）技术，该技术是构建参考模型的必要手段，可用于校正多样数据中的横向非均质性与地理偏差。 总结图：REM1D_summary.png 项目官网：rem3d.org 如有反馈或疑问，请联系Raj Moulik：邮箱[e-mail]，个人主页rajmoulik.com 参考文献： 若使用本数据集或软件，请引用以下文献： Moulik P. 与Ekström G. (2025) 《地球径向结构：(I) 模型理念与数据集》，《物理地球与行星内部》，DOI:10.1016/j.pepi.2025.107319 Moulik P. 与Ekström G. (2025) 《地球径向结构：(II) 模型特征与解读》，《物理地球与行星内部》，DOI:10.1016/j.pepi.2025.107320 您也可以引用本Zenodo页面中的数据集与软件（可选）： Moulik P. (2025) 《径向参考地球模型REM1D数据集与软件》，载于《物理地球与行星内部》（v1.0），Zenodo，DOI:10.5281/zenodo.8407693 研究亮点： 模型特征与解读（Graphic_abstract_I.png） 本研究提出了用于表征地球平均物理性质的径向参考地球模型（REM1D）。 上地幔存在各向异性峰值（aS=3.90%）与衰减峰值（Qμ≈60~80，Qκ≈386）。 800 km以浅的地幔成分为原始地幔岩，且存在底部热化学边界层，与该模型结果一致。 下地幔的模量比（μ/κ）与泊松比特征，与含铁矿物的自旋转变现象相符。 外核处于中性稳定状态，充分混合且经历绝热压缩。 建模理念与数据集（Graphic_abstract_II.png） 提出以非均质性的球平均为基础的径向参考模型构建新框架。 参考数据集包含天文大地测量常数、体波/面波数据与地球自由振荡模数据。 对理论局限性、地理偏差与地壳非线性效应进行了量化分析。 调整参数化方案以适配观测数据集与矿物物理学的预期结果。 通过解析核函数与最新先验约束条件，实现了模型的快速收敛。 总结摘要： 模型特征与解读： 本研究提出了新型参考模型，用于表征球平均的弹性、密度与衰减剖面，这些剖面可反映非均质地地球内部的整体成分、温度分布与主导演化过程。本文讨论REM1D的模型特征与地质学解读，而相关的建模理念与参考数据集则在配套手稿中详述。 REM1D中所有物理参数在莫霍界面（Mohorovicic discontinuity）与410 km间断面之间平滑变化，因此摒弃了早期模型中220 km间断面的设定。针对地震定位优化的广泛使用但理论上不完备的各向同性模型，REM1D预测的主要体波震相走时与其偏差在±0.8 s以内，标准化残差ψpb≤0.25 s，二者吻合良好。 显著的径向各向异性仅存在于最浅层地幔（约250 km以浅），在125~150 km深度区间达到剪切波各向异性（aS=3.90%，ξ=1.08）与压缩波各向异性（aP=3.78%，φ=0.93）的峰值，这与变形区域内固有各向异性矿物定向排列形成的组构特征相符。 上地幔（24.4~410 km）是能量耗散最显著的区域，其体衰减品质因数Qκ≈386，剪切衰减品质因数Qμ≈60~80，在力学软弱的软流圈约150~175 km深度达到峰值。 在上地幔及过渡带扩展区域（<800 km），富橄榄石的原始地幔岩成分与REM1D的结构特征总体吻合，且在410 km与650 km间断面处存在物性阶跃变化。 下地幔的特征可与以下现象相协调：(i) 下地幔中部（771~2741 km）的热驱动对流作用，导致分层参数ηB呈现明显的亚绝热特征；(ii) 含铁矿物的自旋转变效应，在约1300~1700 km（压力52~73 GPa）的复杂过渡区域两侧，模量比与泊松比呈现清晰的线性分段特征；(iii) 热边界层的超绝热梯度比近地表区域更陡，最终在2741 km深度超过纵波（vP）与横波（vS）的临界梯度（但密度ρ未出现此现象）；(iv) 地幔底部约500~750 km区域存在化学分层，该分层可抑制热效应的影响。 该热化学边界层的识别标志包括：(i) 下地幔中密度随深度（dρ/dz）逐渐升高且梯度陡峭为正；(ii) 分层参数ηB>1.03，在核幔边界（CMB）附近骤降至1以下；(iii) 体积模量随压力的变化κl=dκ/dp，与均匀成分的状态方程（EoS）预期不符；(iv) 纵波与横波梯度极陡且为负值，在D''区域形成低速带。 外核的纵波与密度变化具有陡峭梯度，其导数性质与充分混合的铁合金经历绝热压缩的中性稳定区域（ηB≈1，N²≈0，κll为负值）相符。 REM1D采用模块化构建方式，易于拓展，其表征的平均物理性质与特征，是地质学解读与三维参考地球模型构建的必要基础。 建模理念与数据集： 本研究提出了径向参考模型的构建框架，该框架整合多样观测与技术手段，以提升对地球整体结构的约束精度。本文阐述了新型建模理念与参考数据集，而参考地球模型REM1D的特征与地质学解读则在配套手稿中讨论。 近年来各类技术的测量精度得到提升，且结果总体一致，本文将其总结为带有不确定度的最优估计值。我们构建的参考数据集包含地球自由振荡模本征频率与品质因数、面波频散曲线、阻抗约束、体波走时曲线以及天文大地测量观测数据。 经典径向参考模型未考虑地壳与地幔非均质性带来的理论效应与观测偏差。我们针对平均弹性、非弹性与密度结构建模中的横向变化问题，解决了三个关键难点： 其一，当前地震射线的覆盖范围偏向北半球结构，导致尤其在下地幔中测得的波速偏高。 其二，在多数波传播的射线理论与有限频公式中，通常假设地震波遇到的非均质性水平波长远大于对应地球自由振荡模的波长。但该近似忽略了全体积敏感性对本征频率与相速度的影响，对于基频球型模（瑞利波，周期T≥220 s）与环型模（勒夫波，周期T≥120 s）而言，该影响超过了数据的不确定度；对于此类长周期波，无法仅通过射线路径的径向变化进行建模。 其三，对于短周期波（T≤100 s），强烈非均质地壳结构带来的非线性效应显著，在构建径向模型时必须加以考虑。 在解决上述非均质性相关问题后，通过引入最新文献的先验约束、考虑物理频散的解析灵敏度核函数，以及由多项式函数与三次B样条组成的灵活参数化方案，可实现平均结构模型的快速收敛。 相较于弹性结构，我们对密度采用更高阶的多项式参数化，从而避免了在外核等潜在充分混合区域出现强非均质性与非绝热性的虚假特征。 针对核区的导数物性（如体积模量随压力的梯度κl=dκ/dp与布伦分层参数（Bullen’s stratification parameter）ηB）进行调整，使其符合矿物物理学的预期，同时不降低对参考数据集的拟合精度。 下地幔采用三次多项式参数化，足以捕捉与含铁矿物自旋转变相关的模量比梯度变化。 径向参考模型的构建需考虑横向非均质性与先验地质信息，才能准确表征非均质地地球的整体平均性质。 数据产品： REM1D模型系数 弹性/密度结构文件（REM1D.elas）、非弹性结构文件（REM1D.anelas），以及包含750个同心层/壳层物性信息的配套卡片文件（REM1D.cards）。这些文件适用于各类地球自由振荡模、面波与天文大地测量计算。同时提供REM1D模型的总结亮点图（REM1D_summary.png）。 上述文件的适配版本，用于体波走时计算（REM1D_TT.elas、REM1D_TT.anelas、REM1D_TT.cards）。该版本将上地壳物性延伸至地表，并移除了海洋效应，仅适用于体波计算。 REM1D在地球内部750个同心层/壳层中计算得到的所有物理参数（VPH、VSH、VPV、VSV、VP、VS、Eta、A、C、N、L、F、Rho、Qμ、Qκ）与导数物性（泊松比、压力、dK/dP、布伦参数、重力加速度），存储于REM1D_layer_properties.txt文件中。这些数值基于上述文件（REM1D.elas、REM1D.anelas）中的模型系数，利用第二篇手稿中的公式在参考周期1秒下计算得到。若需计算其他周期下的弹性物性并考虑物理频散，可遵循第二篇手稿中的公式8，并使用下文提供的Python脚本。 Python脚本 纯Python 3脚本（evaluate_REM1D.py），可在任意深度与周期下计算REM1D的物理参数并考虑物理频散。该脚本需与系数文件（REM1D.elas、REM1D.anelas）置于同一目录下。以下为部分命令行示例： 帮助信息：evaluate_REM1D.py -h 使用格式：evaluate_REM1D.py [-h] [-m MODEL] [-T PERIOD] [-p 参数 [参数 ...]] [-b 边界标识] -d 深度_千米 [深度_千米 ...] 该脚本默认在参考周期1秒下计算REM1D物理参数，例如： - 计算150 km深度处的所有参数：evaluate_REM1D.py -d 150 可选参数： -h, --help 显示帮助信息并退出 -m MODEL, --model MODEL 参考周期下定义的径向参考地球模型（默认：1秒） -T PERIOD, --period PERIOD 参考周期（默认：1秒） -p 参数 [参数 ...], --parameter 参数 [参数 ...] 物理参数，可指定多个，例如rho vpv vsv qkappa qmu vph vsh eta -b BOUNDARY, --boundary BOUNDARY 若查询深度为内部间断面，+表示计算间断面上方的数值，-表示计算间断面下方的数值。若查询深度存在重复值，则忽略该参数，默认按+处理。 -d DEPTH_IN_KM [DEPTH_IN_KM ...], --depth_in_km DEPTH_IN_KM [DEPTH_IN_KM ...] 查询深度（单位：km），可指定多个，例如24.4 75 150 225 300 410 530 650 650 820 1320 1820 2320 2550 2791 2891。若深度重复，则默认查询间断面上方与下方的数值。 示例： 1. 计算150 km深度处的所有参数：evaluate_REM1D.py -d 150 2. 计算100 km深度处的密度：evaluate_REM1D.py -d 100 -p rho 3. 结合第二篇手稿中的公式8，计算150 km深度、200秒周期下的所有参数并考虑物理频散：evaluate_REM1D.py -d 150 -T 200 4. 计算100、150、650、1500与2891 km深度处的所有参数。注意：若需查询内部间断面上下方的数值，需重复输入该间断面深度；若未重复，则脚本默认仅返回间断面上方的数值：evaluate_REM1D.py -d 100 150 650 650 1500 2891 2891 5. 明确计算650 km间断面下方的所有参数：evaluate_REM1D.py -d 650 -b - 参考地球自由振荡模/面波数据集 相对于PREM预测结果的相速度扰动参考数据集，周期范围4~40 mHz： 勒夫波数据集（avgdcbyc_Love.ref） 瑞利波数据集（avgdcbyc_Rayleigh.ref） 参考地球自由振荡模数据集： 径向模——本征频率（RADIAL_F.ref）、品质因数（RADIAL_Q.ref） 基频球型模——本征频率（SFUND_F.ref）、品质因数（SFUND_Q.ref） 球型泛音模——本征频率（SOVER_F.ref）、品质因数（SOVER_Q.ref） 基频环型模——本征频率（TFUND_F.ref）、品质因数（TFUND_Q.ref） 环型泛音模——本征频率（TOVER_F.ref）、品质因数（TOVER_Q.ref） REM1D数据拟合与预测结果 参考数据集拟合结果： 径向模拟合结果（FITS_RADIAL.txt） 基频球型模（含瑞利波）拟合结果（FITS_SFUND.txt） 球型泛音模拟合结果（FITS_SOVER.txt） 基频环型模（含勒夫波）拟合结果（FITS_TFUND.txt） 环型泛音模拟合结果（FITS_TOVER.txt） 周期低至24秒的地球自由振荡模目录，提供二进制格式（REM1D_024.rts）与HDF格式（REM1D_024.h5）。该计算采用第一篇手稿中提出的新型天文大地测量常数（如修正后的引力常数G）。可通过标准HDF5模块（如h5py）或开源AVNI包读取该目录。二进制文件格式转换可使用以下命令： from avni.data import NM NM.write_modes_hdf('REM1D_024.rts','REM1D_024.h5') 基于REM1D与CRUST2.0非均质性叠加得到的非线性地壳校正数据，适用于勒夫波（nonlinear_CRUST2_Love.csv）与瑞利波（nonlinear_CRUST2_Rayl.csv）。这些文件包含dω与dc/c，需分别按照第一篇手稿中的公式13与14，添加至REM1D预测的本征频率与频散结果中。