“Basin effects” refers to trapped and reverberat- ing earthquake waves in soft sedimentary deposits overlying convex depressions of the basement bedrock, which signiﬁcantly alter frequency con- tent, amplitude, and duration of seismic waves. This has played an important role on shaking du- ration and intensity in past earthquakes such as the Mw8.0 1985 Micho ´acan, Mexico, Mw6.9 1995 Kobe, Japan, and Mw7.8 2015 Gorkha, Nepal. Although the phenomenon has been understood and addressed in the literature, it has not been fully incorporated in seismic hazard analysis, and Ground Motion Prediction Equations (GMPE). In this study, we perform an extensive parametric study on the characteristics of surface ground mo- tion associated with basin effects using ﬁnite ele- ment simulations. We use an elastic medium sub- jected to vertically propagating SV plane waves and utilize idealized basin shapes to examine the effects of basin geometry and material properties. We speciﬁcally study the effects of four dimen- sionless parameters, the width-to-depth (aspect) ratio, the rock-to-soil material contrast, a dimen- sionless frequency that quantiﬁes the depth of the basin relative to the dominant incident wave- length, and a dimensionless distance quantifying distance of the basin edges relative to the dom- inant wavelength. Our results show that basin effects can be reasonably characterized using at least three independent parameters, each of which can signiﬁcantly alter the resultant ground motion. To demonstrate the application of dimensional analysis applied here, we investigate the response of the Kathmandu Valley during the 2015 Mw7.8 Gorkha Earthquake in Nepal using an idealized basin geometry and soil properties. Our results show that a simpliﬁed model can capture notable characteristics of the ground motion associated with basin effects which suggests that such studies 1Department of Mechanical and Civil Engineering California Institute of Technology. Correspondence to: Peyman Ayoubi<ayoubi@caltech.edu >. Copyright 2019 by the authors.can provide useful insights, relevant to the param- eterization of basin effects in GMPEs and design code provisions. 1. Introduction The effects of material, layering, and geometry of the shal- low crust on surface ground motion is referred to as “site effects”. One subcategory of site effects, “basin effects”, refers to the inﬂuence of bowl-shaped loose sedimentary deposits on the amplitude, frequency and duration of earth- quake ground motions, that ultimately affects the structural performance ([ 12], [24]). These changes have played an im- portant role in many past events including the 1985 Mw8.0 Micho ´acan, Mexico, the 1994 Mw6.7 Northridge, USA, the 1995Mw6.9 Kobe, Japan, and the 2015 Mw7.8 Gorkha, Nepal ([28], [37], [27], [4]). Studies on basin effects date back half a century and have produced several analytical/semi-analytical and numerical idealized models. The out-of-plane (SH wave) problem was studied ﬁrst due to its scalar nature, and, therefore, its simplicity. Among others, seminal was the work by Aki & Larner (1970) [ 2], who devised a method (Aki-Larner method) based on Rayleigh ansatz to calculate the elastic waveﬁeld in a layer over a half-space medium with a pe- riodic irregular interface subjected to harmonic SH wave incidence. The resultant scattered waveﬁeld was presented as a linear combination of plane waves with discrete hori- zontal wavenumber over a frequency range that was deﬁned by the shear wave velocity and depth of the basin. Results revealed strong lateral interference of waves which were absent in the solution of ﬂat layer approximation (FLA, as- suming horizontally stratiﬁed media). Limitations of the model to simulate basin-modiﬁed seismic waveﬁelds in- cluded the Rayleigh ansatz, the small periodic length, and the truncation of wavenumber components. Parallel to Aki & Larner [ 2], Boore (1970) [ 9] studied an irregularly shaped layer over half-space for a transient input motion using the ﬁnite difference method (FDM). They val- idated the method against analytical solutions and showed the capability of it within a certain frequency range. They observed a signiﬁcant Love wave perturbation in the vicinity of the transition zone where both the amplitude and phase A Systematic Analysis of Basin Effects on Surface Ground Motion of the waveﬁeld are affected. Later, Boore et al. (1971) [ 10] compared results from FDM time-domain simulations to the harmonic frequency-domain solution by Aki and Larner for the case of a layer over half-space and a range of basin conﬁgurations. They transformed the FDM solution to the frequency domain and applied an exponential time-domain window to remove boundary effects, and showed that while results were in good agreement for two different basin con- ﬁgurations, the late arrivals of strong reverberations could not be adequately captured by the FLA due to the lateral interference caused by non-planar basin shape. Shortly after, Trifunac (1971) [ 43], and Wong & Trifunac (1974) [ 47] used the wave expansion method to devise a semi-analytical solution for semi-cylindrical and semi- elliptical basins, respectively. In both cases, they considered out of plane harmonic wave incidence and concluded that other than a few cases, the FLA cannot reliably predict the 2D response of basins to seismic wave incidence that is governed by complex 2D wave interference. Moreover, they found that increasing the frequency of incident wave would complicate the wave interference in the basins, a phe- nomenon that can also occur due to the change in incident angle. Studies on the more complex SV-P (in-plane) problems be- came more prevalent the following decade. Among others, Bard & Bouchon (1980) [ 6] studied the problem of in-plane basin response using a modiﬁed Aki-Larner method for co- sine basins subjected to P and SV incident motions. They considered two cases of low and high-velocity contrasts, and two basin geometries, a narrow (to investigate the en- trapment of waves) and a wide (to investigate the surface wave generation). For wide basins with high-velocity con- trast, they observed a clear generation of Rayleigh waves and showed that higher Rayleigh modes were excited by SV incident wave because of the lower value of shear wave ve- locity. Moreover, they concluded that the general waveﬁeld pattern is similar in both P and SV incidence cases, with the maximum ampliﬁcation corresponding to the direct wave arrival for P-waves, and the Rayleigh wave generation for S-waves. Later, Dravinski (1982) [ 18] examined the scattering of elastic waves by an alluvial valley of elliptical shape sub- jected to harmonic in-plane (P, SV , and Rayleigh) and out- of-plane (SH) incident motions using the boundary integral (BI) method. Boundary methods are attractive due to the lower dimensionality of the problem, compared to FDM, but they are only efﬁcient for conﬁgurations with smooth mate- rial transitions (no sharp contrasts). They observed that the effects of incident motion frequency and basin depth were interdependent, and concluded that at the low-frequency regime, the SH incident waveﬁeld is less sensitive to basin depth compared to P and SV waves. In addition, for the caseof Rayleigh wave incidence (as would be the case e.g. for a basin located next to a surface topographic), they showed a comparable surface displacement ampliﬁcation to the case of P and SV waves incidence. Dravinski & Mossessian (1987) [ 19] later studied single and multiple semi-elliptical dipping layers with weakly anelastic material using the in- direct boundary integral equation (IBIE) for harmonic P, SV , and Rayleigh incident waves. They observed that the surface displacement strongly depends on the angle of in- cidence and the distance from the basin edge for a single layer basin. Adding a second, stiffer layer below strongly affected the surface ampliﬁcation pattern and magnitude, but adding yet a stiffer third layer below didn’t cause any additional signiﬁcant changes. They concluded that shear wave velocity contrast and basin geometry are the dominant governing parameters in basin ampliﬁcation. TheMw8.1 1985 Micho `acan, Mexico earthquake was a turning point in recognizing the signiﬁcance of basin effects. Despite the large distance ( 350km) from the epicenter, Mexico City experienced disproportionately large ampli- ﬁcation and very long shaking duration. A large number of studies were prompted in the wake of the event, and were mostly focused on idealized 2D models of the basin ([7], [13], [28]). The ensemble of studies attributed the ob- served ampliﬁcation to basin-edge effects and reverberation of earthquake waves in the sedimentary deposits. The con- sensus was not as strong for the observed ground motion duration, and some studies attributed it to 3D effects [ 14] not accounted for in 2D models. It was recently shown that the long duration could be attributed to longer period waves reverberating in the deeper sediments of the basin not previously accounted for [15]. Following the 1985 Mexico City Earthquake, 3D models were brought forth to study basin effects in a more realistic setting by simultaneously solving the in-plane and out-of- plane components ([ 40], [35]). Examples include the work by Hiroke et al (1990) [ 26], who used an extended Aki- Larner method to study 3D irregularly layered subsurface structures and observed three dominant 3D effects, namely localization, rapid growth, and strong spatial variability of surface waves. Comparison to 2D simulations conﬁrmed that the true amplitude and duration of surface motion can- not be fully reproduced by idealized 2D models. Pitarka et al (1998) [ 38] used FDM near-fault ground motion simu- lations with kinematic source models of the 1995 Mw6.9 Hyogo-ken Nanbu (Kobe) earthquake, and showed that the constructive interference between source and basin was the main reason for the catastrophic consequences of the event. In the last twenty years, boundary methods (for example [28]) and FDM (for example [ 45]) have been increasingly replaced by the more computationally efﬁcient and highly accurate spectral and pseudo-spectral methods ([ 29], [17], A Systematic Analysis of Basin Effects on Surface Ground Motion [25]) for regional-scale simulations of basin effects. No- tably among others, Komatitsch and Vilotte [ 30] and Fac- cioli et al. [ 21] were the ﬁrst to adopt the spectral element method (SEM) from the ﬂuid dynamics community [ 36]. Their formulation of SEM used the Gauss-Lobatto-Legendre quadrature with Lagrange interpolation instead of lower or- der interpolation functions used in the FEM, which led to a signiﬁcant reduction in computational time. Among others, Stupazzini et al (2009) [ 41] used 3D SEM to study basin effects in the Grenoble valley. In addition to basin ampli- ﬁcation, they also considered source effects and sediment pseudo-nonlinear response, and found that the hypocenter location and directivity play an inﬂuential role in surface ground motion. Moreover, the radiation mechanism and the relative location of the Grenoble valley to the fault strike played a signiﬁcant role in the . However, they concluded that the nonlinear response was not as important as the above-mentioned factors in this case study. In the recent years, focus has shifted to large scale simula- tion case studies ([ 46], [20]) and some idealized parametric analyses of basin-speciﬁc problems ([ 35], [23], [22]). The daunting computational cost and input parameters required to capture basin effects using realistic source models, crustal structures and near-surface effects, however, have hindered the integration of these effects in GMPEs and engineering design practice; instead, the engineering community still relies gravely on 1D site response models that are not appro- priate to capture basin edge physics, when relevant. In this paper we take a different approach: we use dimen- sional analysis to conduct a comprehensive numerical para- metric study of 2D idealized basin geometries and material properties. Our goal is to identify and prioritize parameters that govern basin effects, which could in turn help to param- eterize basin effects in ground motion models (GMM) and engineering design provisions. After veriﬁcation of our nu- merical toolbox, we examine the behavior of semi-elliptical and half-cosine basins by varying the material properties, geometrical conﬁguration, and input motion characteristics. To make the results applicable for general basin conﬁgura- tions, we present them in the dimensionless form. Finally, to test our proposed parameterization, we simulate the re- sponse of the Kathmandu Valley, Nepal during the 2015 Gorkha earthquake. Our simpliﬁed results compare favor- ably to long period observations, suggesting that simple basin geometries could potentially be used to investigate and parameterize key ground motion characteristics associ- ated with basin effects. 2. Fundamental Physics of Basin Effects Basin effects arise from a combination of (a) trapping of seismic waves due to impedance contrast and consecutive reverberations of seismic energy, and (b) focusing effects atthe edges of a basin, frequently referred to as basin-edge ef- fects. Similarly to 1D site response, soil-to-rock impedance contrast plays an important role in the amount of trapped seismic energy in a basin, and thus in the ampliﬁcation and elongation of seismic motion. Figure 1. Schematic representation of reﬂection and transmission of a plane SV wave incident with angle on a plane boundary of two materials One can readily quantify the role of material contrast by solving the wave equation for incidence on a two-material interface (Figure 1). By satisfying traction equilibrium and displacement compatibility conditions at the material inter- face, displacement reﬂection and transmission coefﬁcients can be computed as outlined in detail by Aki and Richards [3]. To show the variation of the reﬂection and transmission coefﬁcients as a function of rock-to-soil shear wave veloc- ity contrast, Figure 2 plots the displacement ampliﬁcation coefﬁcients for the idealized interface problem in Figure 1 subjected to a shear in-plane wave (SV). As can be seen, by increasing the material contrast while keeping all other parameters constant, the amplitude of the reﬂected S-wave increases and the amplitude of transmitted S-wave decreases. In addition, P-waves are generated at the interface due to mode conversion. Such ampliﬁcation and mode conversion effects comprise one aspect of basin effects. Basin-edge effects, on the other hand, result from energy focusing and interference of seismic waves in the wedge-shaped edges of a basin. The constructive interference between direct waves and edge-generated surface waves is schematically depicted in Figure 4: when a vertically propagating plane SV wave incites on a sloped subsurface interface between bedrock and sediment, it generates a set of reﬂected and refracted P and S waves. Focusing on the latter, Figure 4 illustrates the interference of SV direct arrivals, the reﬂections of SV waves from the bedrock-sediment interface, and the trans- versely propagating surface waves. This shows a complex interaction of wave components that frequently exacerbates the intensity of the waveﬁeld in a basin. The combined effects of ampliﬁcation and basin-edge sur- face wave generation are illustrated in Figure 3, in the form A Systematic Analysis of Basin Effects on Surface Ground Motion Figure 2. Variation of displacement reﬂection and transmission coefﬁcients by changing material contrast. This ﬁgure shows the case of incident angle = 5o. Different patterns may be observed for higher angles. With reference to Figure 1, medium 1 is softer material of simulated particle motion on the ground surface of a 20dipping layer subjected to a unit amplitude vertically propagating SV wave of Ricker type. Points 1 to 5 lie on the rock outcrop, while points 6 to 16 lie on the surface of the sedimentary dipping layer. Point 6 is located exactly at the tip of the 20wedge. As can be seen, the basin edge introduces very complex particle motion compared to the frequently assumed horizontally stratiﬁed medium which does not generate any vertical com- ponent. While its effects are evident on the rock outcrop motion in the vicinity of the wedge tip, it predominantly impacts the particle motion inside the dipping layer. We should also note that while the incident motion was purely horizontally polarized, the ground motion has a signiﬁcant vertical component arising from mode conversion, as well as very pronounced spatial variability, both of which are likely to affect distributed systems and long components of infrastructure such as pipelines. 3. Description of Numerical Model The idealized numerical model we used in this study is a 2D basin consisting of two elastic, isotropic, and homo- geneous materials for bedrock and basin. We performed analysis of wave propagation in a basin over halfspace using OpenSees, a FEM code that can solve the wave equation in a heterogeneous medium subjected to initial and boundary conditions using an implicit scheme [ 32]. We discretized the numerical model by requiring 12 quad elements per shortest propagating wavelength to resolve the frequency range of interest based on the dominant frequency of an incoming wave (Figure 5). Free-ﬁeld boundary conditions were placed along the side boundaries, at a distance greater than two times the dom- Figure 3. -Particle motion diagram for a set of stations around the basin edge of 20. Example is shown for material velocity contrast 2, and unit amplitude plane Ricker SV wave with a dominant frequency of 1 Hz. Figure 4. Schematic view of the coupled effect of material contrast and basin edge. P, S and R waves stand for Primary, Shear and Rayleigh waves. 1and 1are S and P wave velocities in the dipping layer, and 2and 2are the ones for bedrock. In this ﬁgure,!= arcsin 1 2sin ,!0= arcsin 1 2sin and 0= arcsin 2 2sin . Other parameters and angles are shown in the ﬁgure. Figure 5. An example of discretized FE domain. The green area shows the basin and the yellow represents the bedrock. The domain is discretized using quad elements. A Systematic Analysis of Basin Effects on Surface Ground Motion inant incident wavelength ( 2, see Figure 10) from basin edges. Free-ﬁeld (FF) boundary condition comprises S- and P-wave absorbing elements (also known as “Lysmer dash- pots” [ 31]), and free-ﬁeld equivalent forces corresponding to 1D wave propagation conditions as shown in Figure 7 [16]. The dashpot coefﬁcients for the tangential and perpendicu- lar directions relative to the lateral boundaries, CsandCp correspondingly, are estimated as follows: Cs=vs (1) Cp=vp (2) whereis the density of the halfspace, and vsandvpare the shear and compressional wave velocities of the halfspace, respectively. Successively, the FF effective forces that rep- resent the stress-ﬁeld for 1D wave propagation conditions were computed as follows: Fx=(Cp(Vm xvff x)ff xx)Ay (3) Fy=(Cs(Vm yvff y)ff xy)Ay (4) whereFxandFyare perpendicular and tangential loads, respectively. Vm xandVm yare nodal velocities in xandy directions computed at each time step during the FE anal- ysis,vff xandvff yare FF velocities in xandydirections andff xxandff xyare the FF stresses in x and y directions, respectively. The last four quantities are calculated using D’Alembert’s method for 1D wave analysis. Ayis the element size in the vertical direction. For incident motion, we used a unit amplitude vertically propagating plane SV wave of Ricker type [ 39] (Figure 6, Eq. 5). This is applied as a shear force at the base of the numerical domain where absorbing boundary conditions (Lysmer dashpots) are prescribed. The force is calculated based on Eq. 6 where Finput andAxare input force and element size at the bottom, respectively. Acc(t) = (122f2 0t2)e2f2 0t2(5) Finput =CsAxZ Acc(t)dt (6) Synthesizing the above, the vertical side boundaries would ideally respond as 1D columns subjected to vertically propa- gating shear waves, had there not been a scattered waveﬁeld (albeit weak in this case) that is leaking from the basin sediments at each reverberation. A schematic view of the numerical domain together with prescribed boundary condi- tions is depicted in Figure 7. (a) (b) Figure 6. Acceleration input time history, a Ricker wavelet in a) time-domain and b) frequency domain Figure 7. Schematic view of the FEM domain and boundary con- ditions. 4. Parametric Analysis In this section, we investigate the variation of surface ground motion with basin geometry, material properties, and input motion characteristics by performing a parametric study on two idealized conﬁgurations, Semi-Elliptical (SE) and Half- Cosine (HC). The SE basin is used as a frequently employed idealization that can easily be parameterized. It is suitable to study the physics of wave propagation inside a basin by investigating the effect of dimensionless parameters that will be presented later. The HC basin is used as a more realistic representation of the basin shape while remaining easy to parameterize for geometric and material properties. Eq. 7 gives the mathematical expression of the bedrock-sediment interface depth for an HC basin. Parameters b,D, andaare depicted in Figure 10. 8 >< >:b jxjD=2 b 2[1 +cos((xD=2) a)]D=2jxjD=2 +a 0 jxjD=2 +a(7) The dimensionless parameter space for the problem in hand can be derived using Buckingham’s theorem [ 11]. For a dynamic problem in elastodynamics, three parameters are needed to deﬁne a material. Here, we use vs(shear wave velocity, denoted heretofore to avoid parameters with multiple indices), (Poisson’s ratio) and (density) as representative parameters for each material. In total, we A Systematic Analysis of Basin Effects on Surface Ground Motion study the effects of six parameters, namely 1,1and1of the basin sediments, and 2,2and2of the bedrock. In addition,a,bandD+ 2aare used to deﬁne geometry of a basin. Finally, f0, the dominant frequency of input motion, is used to represent the excitation. Given the ten parame- ters and three characteristic parameters (length ( [L] =b), mass ( [M] =2b3) and time ( [T] =b= 1)) of the problem, Buckingham’s theorem yields 7 dimensionless parameters (17) deﬁned as follows: 1=1; 2=2; 3=a b; 4= 2 1; 5=f0b 1; 6=1 2; 0 7=D+ 2a 1=(D+ 2a)f0 1(8) Note that0 7is derived by multiplying 7= (D+2a)=band 5. In terms of order of magnitude, the dominant dimension- less parameters of our problem are 3,4,5and0 7. To reduce the computational cost, we perform the parametric study only for these four parameters, and later show that the effects of 1,2and6are negligible for the problem in hand. Unless otherwise stated, we assume 1= 0:33, 2= 0:33and6= 1, as per Kawase & Aki [28]. In the following sections, we ﬁrst present two veriﬁcation examples of our numerical model and then examine the contribution of the dimensionless parameters above. For clarity, we refer to 3as Aspect Ratio ( AR), deﬁned as a overb(see Figure 10); to 4as, the dimensionless width of the basin deﬁned as (D+2a)=1, where1is the dominant wavelength in the sediments deﬁned as 1=f0; and to5 as, the dimensionless frequency. To compare the various realizations of the parametric space, we normalize the peak acceleration amplitude on the ground surface by the peak amplitude on rock outcrop referred to as ampliﬁcation factor (AF). In addition, we utilize seismogram synthetics (SS) on the ground surface and vector ﬁeld snapshots to represent the spatiotemporal variation of the waveﬁeld. 4.1. Numerical Model Veriﬁcation We present two veriﬁcation examples of our numerical mod- els: (a) a semi-circular basin from Mossessian & Dravinski (1987) [ 34], and (b) a trapezoidal basin from Kawase & Aki (1989) [ 28]. Models are presented using dimensionless parameters explained earlier. 4.1.1. S EMI-CIRCULAR BASIN : M OSSESSIAN & DRAVINSKI (1987) The ﬁrst is a semi-circular basin, with geometry character- istics and material properties described in Mossessian & Dravinski [ 34] and listed in Table 1. Mossessian & Dravin- ski used the indirect boundary integral method to compute the steady-state basin response and reported the Ampliﬁ- cation Factor (AF) along the surface as the peak groundsurface spectral amplitude normalized by the peak incident spectral amplitude ( Ux=Uinc x). Figure 8 compares results of the Mossessian & Dravinski to results from this study. To compare our synthetic time-domain results with the steady- state basin response of Mossessian and Dravinski (1987) [34], we extracted the steady-state part of the ground surface displacement, applied the Fast Fourier Transform (FFT), and normalized them by the peak spectral amplitude of the inci- dent motion. The comparison depicted in Figure 8 shows a very satisfactory agreement between the two studies. Table 1. Material, geometry and incident motion parameters for semi-circular basin study [34] 1234560 7 0.333 0.333 1 2 0.5 0.66 1 (a) (b) Figure 8. Surface AF in a) horizontal and b) vertical directions for semi-circular basin of Mossessian and Dravinski [34] 4.1.2. T RAPEZOIDAL BASIN : KAWASE & A KI(1989) The second veriﬁcation example is the trapezoidal basin response published by Kawase and Aki (1989) [ 28]. Table 2 shows the parameters we used to simulate this example. Figure 9 shows an excellent agreement of the two studies in the spatiotemporal domain. Table 2. Material, geometry and incident motion parameters for trapezoidal basin study [28] 1234560 7 0.333 0.333 2 2.5 0.25 1 2.5 Results from the two veriﬁcation tests presented here, where we tested the code against two different geometries and material properties, serve as evidence of the capabilities and accuracy of the numerical model. 4.2. Results In this section, we present results of the parametric study for each basin geometry, separately. Table 3 lists the dimen- sionless parameters and the range of values that will be used in the following sections. First we show results from the SE basin, where we elaborate on the underlying physics of basin effects by ﬁrst investi- A Systematic Analysis of Basin Effects on Surface Ground Motion (a) (c) (d)(b) Figure 9. Comparison of ground surface seismogram synthetics in a, b) horizontal and c, d) vertical directions between this study (left) and Kawase & Aki [ 28] (right). The ﬁgures on the right are extracted from Kawase & Aki [28]. Table 3. Parameter space considered in this study 345 0 7 0.5, 1, 2, 41.5, 2, 3.5, 50.125, 0.25, 0.5, 1, 2, 40.25, 0.5, 1, 1.5, 2, 2.6, 3.2, 3.8, 4.4, 5, 8, 12 (a) (b) Figure 10. Schematic view of a) SE and b) HC basins. 2is deﬁned as 2=f0. gating the effects of the aspect ratio AR; followed by the effects of dimensionless frequency, . We also investigate the role of material contrast, 2= 1, and dimensionless width of the basin, . Finally, we study the dimensionless param- eters that we claimed have a lesser impact on the groundsurface motion, namely 1;2and6. For the HC basin shape, a more realistic idealized geometry for studies of basin effects, we next highlight the differences from the SE basin shape, stemming from the shape of basin edges. At the end of the HC section, we also present the effect of material (low-strain) damping on surface ampliﬁcation. We ﬁnally demonstrate the effectiveness of our parameterization by comparing our long-period simpliﬁed simulations to the recorded ground motions at the Kathmandu Valley in Nepal during the M7.8 2015 Gorkha earthquake. 4.2.1. S EMI-ELLIPTICAL BASINS Figure 11 shows the maximum AF of the horizontal com- ponent of ground surface motion from the ensemble of SE basin analyses corresponding to D= 0, a narrow basin expected to be characterized by a complex 2D waveﬁeld due to the short distance of the two basin edges. The effect ofwill be discussed later in the article. Figure 11. Maximum horizontal AF for all SE analyses. Red cir- cles show unexpected results due to constructive wave interference. Results show that for a given AR, the ampliﬁcation factor generally increases with increasing material contrast 2= 1. This is not particularly surprising since high 2= 1implies a higher percentage of energy entrapment in sediments, and lower energy leakage. There are, however, a few results that merit further discussion: the case of AR= 0:5,= 4and 2= 1= 1:5(circled in top left subﬁgure 11) is a deep basin with relatively stiff sediments subjected to high-frequency ground shaking. We observe a very high ampliﬁcation (AF = 2.95) which is close to the maximum AF that we observed from the ensemble of simulations. As shown in Figure 12, this happens due to the synchronous arrival of direct A Systematic Analysis of Basin Effects on Surface Ground Motion waves and edge-induced surface waves at the center of the basin where they constructively interfere. More speciﬁcally, Figure 12 illustrates the waveﬁeld evolution in four stages outlined below: (a) The incident wave hits the deepest part of the basin. One can identify the onset of waveﬁeld distor- tion in the basin. The sediment-rock material contrast plays an important role since it determines the amplitude of the seismic pulse that enters the basin, and regulates the amount of time it takes to reach the basin surface. (b) Vertically inci- dent waves from the base, and laterally propagating surface waves generated at the basin edges travel toward the basin center. (c) Waves interact while waves propagate toward the basin center. (d) Maximum ampliﬁcation occurs when they constructively interfere at the center. (a) (b) (c) (d) Figure 12. Snapshots of the waveﬁeld for an SE basin with AR= 0:5and 2= 1= 1:5, subjected to vertically propagating shear waves of= 4: a) incident wave enters the basin; b,c) body and surface waves travel towards the basin center; d) body and surface waves generate the maximum AF at the basin center. On the opposite end, for a very shallow basin with very soft sediments, the case of AR= 4, 2= 1= 5, and= 0:25 to= 0:5, a similar phenomenon of constructive interfer- ence in the middle of the basin occurs, as shown in Figure 13. On the left, the spatial distribution of ampliﬁcation is showed where the maximum amplitude occurs in the mid- dle, and on the basis of the seismogram synthetics, takes place at dimensionless time t= 5. In addition to high AF, due to material velocity contrast, we clearly recognize the reverberations of trapped energy in the sediments, which in addition to large AF, lead to prolonged motion duration. 4.2.1.1. Effect of Aspect Ratio (AR): AR deﬁnes the average slope of basin edges, which have shown to dominate the response of most basins during seismic events [ 27]. In this subsection, we present results of surface ampliﬁcation for various AR values. The spatial variations of horizontal and vertical ampliﬁcations are portrayed in Figures 14 (low frequency incident motion) and 16 (high frequency incident (a) (b) Figure 13. a) AF and b) SS in horizontal direction for AR= 4, = 0:5and 2= 1= 5. motion) for a set of aspect ratios, velocity contrasts, and dimensionless frequencies. Figure 15 illustrates the SS for the top panel of Figure 14, and helps to explain the observed surface ampliﬁcation. From these ﬁgures, one can observe a large variation asso- ciated with varying the AF in both horizontal and vertical directions. Focusing on Figure 14, it is clear that for this particular setting, AR= 1 has the largest ampliﬁcation in the horizontal direction for both material contrasts due to constructive interference of direct arrival of the incident wave and laterally propagating edge-induced surface waves, as can be seen in Figure 14-a and c. For shallower and deeper basins, the wave interference and consequent peak ampliﬁcation occurs closer to the basin edges. The AF of the vertical component which arises purely from mode conver- sion (recall that our input motion was a vertically propagat- ing horizontally polarized SV wave) is generated primarily from edge-induced (Figure 15-d,f,h) surface waves except forAR= 0:5(Figure 15-b). For the deepest basin, the basin edges are not playing as important role as their shallower counterparts. Figure 16 shows how higher frequency input motion would affect the resultant waveﬁeld while other parameters are the same as Figure 14. Increasing the frequency, in gen- eral, would result in a more localized interaction of basin and incident motion. This is projected in Figure 16 where higher ampliﬁcation at basin corners happen over a shorter distance (see Figure 16-a and c). In addition, as a result of more localized interaction, the spatial variation of sur- face ampliﬁcation is exacerbated (see Figure 14-b and d) which could cause serious damage to long components of infrastructure system due to torsional particle motion. Based on the last three ﬁgures, the three parameters, namely the coupled behavior of basin geometry, material properties, and frequency content of the incident motion govern the surface ground motion in a basin. For the remainder of the article, we shall use AR= 1as a point of comparison and try to investigate other parameters by keeping the aspect ratio constant. A Systematic Analysis of Basin Effects on Surface Ground Motion (a) 2= 1=2 (b) 2= 1=2 (c) 2= 1=3:5 (d) 2= 1=3:5 Figure 14. AF in a,c) horizontal and b,d) vertical directions for SE basin for a range of ARs, = 1, 2= 1= 2 (top panel) and 2= 1= 3:5(bottom panel). 4.2.1.2. Effects of Dimensionless Frequency ( ) and Ma- terial Contrast ( 2= 1):Figures 17 and 18 show the ef- fects of dimensionless frequency ( ) and material contrast ( 2= 1) on the AF of surface ground motion for a basin withAR= 1. Recall that parameter measures the basin response sensitivity to an incoming wave by quantifying the relative size of the basin to the incoming dominant wave- length. The physical meaning of the parameter is depicted in Figure 17, where, for  0:5and 4, the basin is too small or too large compared to the incident wavelength, respectively. In the ﬁrst case, the wave barely “sees” the basin (basin-bedrock medium behaves as a halfspace), and in the second case, the basin responds similarly to a 1D two-layer column. Therefore, = 0:125(wavelength 8 times larger than basin depth) results in a negligible vertical component since the basin is too small for the seismic wave to experience substantial mode conversion. This ﬁgure also illustrates the aforementioned strong spatial variability of surface ground motion for higher frequencies. Moreover, due to the complexity of the waveﬁeld in the basin, no spe- ciﬁcyields a maximum AF across the basin which can be observed in both the horizontal and vertical components and is more pronounced near basin edges. Figure 18 further details the case of AR= 1by showing the effect of material contrast for different , and thus illustrating the coupled ef- fect of parameters of interest. The AF of the vertical ground motion component reaches surprisingly high value. While the incoming wave is a plane SV-wave, the AF vertical com- ponent near the edges is comparable to the horizontal one, and the spatial variability suggests that structures near the edges would experience not only strong transverse and ver- tical shaking but also rotational motion. In addition, higher (a) AR=0:5 (b) AR=0:5 (c) AR=1 (d) AR=1 (e) AR=2 (f) AR=2 (g) AR=4 (h) AR=4 Figure 15. SS forAR= 0:5(top panel),AR= 1 (second from top panel),AR= 2 (second from bottom panel) and AR= 4 (bottom panel) in a, c, e, g) horizontal and b, d, f, h) vertical directions.= 1and 2= 1= 2are assumed. frequency incident motions interact on a local scale with the geometry and material properties of the basin, which affect the ground motion characteristics over shorter dis- tances. The opposite is true for longer wavelengths. For the case of= 0:5, both horizontal and vertical AFs reveal that the incident motion interacts with the basin as a whole, a fact evidenced in the smooth spatial variation of AF across the basin. By looking through this ﬁgure, the localization effect of frequency increment is obvious. For example, by comparing the AF in Figures 18-b and 18-d, one can see that Figure 18-d indicates a more complex ampliﬁcation distribution due to higher frequency content. 4.2.1.3. Effect of Dimensionless Width ( ):So far we have investigated three parameters with D= 0to observe A Systematic Analysis of Basin Effects on Surface Ground Motion (a) 2= 1=2 (b) 2= 1=2 (c) 2= 1=3:5 (d) 2= 1=3:5 Figure 16. AF in a,c) horizontal and b,d) vertical directions for SE basin for a range of ARs, = 4, 2= 1= 2 (top panel) and 2= 1= 3:5(bottom panel). (a) (b) Figure 17. AF in a) horizontal and b) vertical directions for SE- shaped basin with AR=1 and 2= 1= 2 the waveﬁeld in a basin. For this subsection, we focus on edge-induced Rayleigh waves by examining the effects of D > 0. Figure 19 shows the effect of the dimensionless width () on the spatial distribution of surface ampliﬁcation on a SE basin. Note that the minimum value of corre- sponds to its value for D= 0, namely2a 1= 2AR . By increasing, the ampliﬁcation decreases and a separation between two corners appears. This results in a nearly 1D response in the middle of the basin (denoted by a blue star in Figure 19) while the 2D effects dominate as one moves closer to the basin edges. This does not mean that the mid- dle of the basin will experience purely horizontal motion since the Rayleigh wave’s traverse motion will still generate signiﬁcant vertical movement. This phenomenon will be explained in more detail in a later section of this article. 4.2.1.4. Effect of Other Dimensionless Parameters: In this subsection, we examine the effects of three dimension- less parameters we have not investigated yet (see Eq. 8), namely the Poisson’s ratio of the sediments ( 1) and the (a) =0:5 (b) =0:5 (c) =1 =1(d) (e) =4 (f) =4 Figure 18. AF in horizontal (left panel) and vertical (right panel) directions for SE basin with AR=1 and a,b) = 0:5, c,d)= 1, e,f)= 4. Three different s are shown to also show the coupled effect of material contrast and dimensionless frequency. (a) * (b) * Figure 19. Effect of dimensionless width ( = (D+ 2a)=1) for SE basin for a) horizontal and b) vertical components. AR= 1, = 1and 2= 1= 2are assumed bedrock (2), and the ratio of mass density of the sediments to the bedrock (1 2). The range of values we consider is shown in Table 4. Figure 20 shows the effects of Pois- son’s ratio on the surface ampliﬁcation for 2= 1= 2and 2= 1= 3:5,= 1andAR= 1. As can be readily seen, the effects of Poisson‘s ratio are negligible compared to the four main dimensionless parameters we discussed earlier. We should however note here that we expect the effects of Poisson‘s ratio to be more pronounced for nearly incom- A Systematic Analysis of Basin Effects on Surface Ground Motion pressible material behavior ( 0:5or undrained loading conditions). Table 4. Considered parameters for studying effects of 1,2and 6 1(1)1(2)6(1 2) Value0.25, 0.35, 0.450.22 3, 0.8 (a) (b) Figure 20. Effect ofon surface ground motion for two differ- ent 2= 1values, for SE basin with = 1 andAR= 1 in a) horizontal and b) vertical directions Similarly, Figure 21 shows the effects of density contrast (2=1) on the spatial variability of peak ampliﬁcation, for the case of an SE basin with = 1andAR= 1. Results are shown for two velocity contrasts 2= 1= 2and3:5. As can be seen, the effects of density contrast are on the order of 5% in the vicinity of the peak horizontal and vertical ampliﬁcation, which are still considered of secondary im- portance when compared to the four parameters investigated earlier. (a) (b) Figure 21. Effect of1=2on surface ground motion for two dif- ferent 2= 1values, for the case of an SE basin with = 1and AR= 1in a) horizontal and b) vertical directions 4.2.2. H ALF-COSINE BASINS Although SE models have been widely used as idealized basin geometries ([ 43], [18]), their sharp corners do not resemble realistic basin edges. In more realistic scenarios, one would expect landscape evolution processes, such as weathering and alluvial or ﬂuvial deposits, to lead to a more gradual transition from rock to sediments near the basin edges. Given the important role of edges in the focusingand diffraction phenomena that govern basin effects (see Figure 22), we here study a more realistic idealized basin shape adopted from the geomorphology literature and re- ferred as Half-Cosine (HC) (see Figure 10 for a schematic representation). Figure 22. Particle motion comparison for SE and HC basins in the vicinity of basin edge. AR= 1,= 1 and 2= 1= 2 are assumed. Figure 22 compares the particle motion of two basin geome- tries (SE and HC) near the edge with otherwise identical aspect ratios, impedance contrasts, dimensionless width and frequency. The bottom row schematically depicts the geom- etry of the basin edge and the location where the comparison is taking place. As can be seen, the waveﬁeld is affected by the basin edge geometry (and convexity). The particle motion change would be even more pronounced for higher frequency components. Note that the edge geometry caused a horizontal shift in the waveﬁeld, and it seems that each point on the SE basin corresponds to a further point in HC. For example, points 4and4have similar particle motions. For the rest of this section, we focus on the parameters that are directly affected by edge geometry, namely ARand. Althoughand 2= 1have been shown to signiﬁcantly alter the basin’s waveﬁeld, their effects do not differ signiﬁcantly A Systematic Analysis of Basin Effects on Surface Ground Motion for a givenARand; results are thus shown for the case of = 1and 2= 1= 2, similarly to SE geometry. 4.2.2.1. Effect of Aspect Ratio (AR): The effects of AR for HC basins are depicted in Figure 23. The effects of edge convexity manifest in the spatial distribution of AF. As can be seen, by changing the basin geometry, the separation of edges does not happen as fast as it happened in the case of the SE basin (Figure 14) because of gradual variation of the basin-bedrock interface depth over distance. This shows how a more realistic basin geometry could affect the ampliﬁcation variation in a basin, especially for shallower (AR> 1) conﬁgurations that are more prevalent in urban environments. (a) (b) Figure 23. AF for different ARs of HC basins of D= 0,= 1 and 2= 1= 2in a) horizontal and b) vertical directions. 4.2.2.2. Effect of Dimensionless Width ( ):Figure 24 shows the effect of on the surface ground motion in the horizontal and vertical directions. We consider a range of  that capture the response of narrow and wide basins. Results illustrate the fading effect of basin edges on the ampliﬁca- tion factor close to the basin center. This does not mean that the basin middle would behave as a purely 1D column due to Rayleigh waves traverse propagation within the basin which mostly contributes to the vertical component of sur- face ground motion. As can be seen, for separation 5, the corner half-cosines have minimal inﬂuence in shaping the horizontal ampliﬁcation, which is evidenced by a uni- form spatial distribution of AF over the central part of the basin. Results of the midpoint response for an HC basin are next compared, for representative , to the analytical solution of a 1D two-layered linear elastic soil column [ 44] subjected to a vertically propagating SV Ricker wave. Fig- ure 25 compares the acceleration time series, Fourier and response spectra at the basin midpoint calculated from 2D wave propagation simulations for = 3;5;9, and 12to the corresponding response of a horizontally stratiﬁed 1D lay- ered model. As expected, by increasing , the basin center (denoted by a blue star in Figure 24) increasingly responds like a 1D column as the two basin edges separate. However, even for the case of = 12 , edge-induced surface waves traveling horizontally are evident as late arrivals in the mid- point signal, an effect that 1D site response approximations (a) * (b) * Figure 24. Effect of dimensionless width ( ) on the surface am- pliﬁcation in a) horizontal and b) vertical directions. AR= 1, 2= 1= 2and= 1are assumed. . are not able to capture. = 3 = 5 = 9 = 12 Figure 25. Comparison of the 1D analytical solution with the nu- merical results at the basin center. The value is shown on the ﬁgure.AR= 1,= 1and 2= 1= 2are assumed. 4.2.2.3. Effect of Damping: In reality, during large earth- quakes, the soft sedimentary deposit would undergo con- siderable deformation that causes waveﬁeld attenuation. In this article, we have so far studied the waveﬁeld coupling effects of geometry, material contrast and frequency content without the attenuating contribution of material (low-strain) A Systematic Analysis of Basin Effects on Surface Ground Motion damping. Figure 26 shows a comparison between two con- ﬁgurations with AR= 1andAR= 4;= 1, 2= 1= 2 and a range of realistic damping values. Two damping val- ues= 2:5%and5%are considered and the resultant ampliﬁcation curve is compared with no-damping condi- tion. In order to calibrate Rayleigh damping parameters, fmin= 0:15(Hz) andfmax= 3:5(Hz) are used while the dominant frequency of input motion is f0= 1(Hz) and the fundamental frequency of the soil column corresponding to the deepest part of the basin is 1 4b= 0:25(Hz). (a) (b) Figure 26. Effect of damping of surface AF in a) horizontal and b) vertical directions. We assumed two different damping parameters (= 2:5and5:0),= 1, andAR= 1and4. For the range of geometries and damping values studied here, results are affected by low-strain attenuation in the horizontal direction only at the midpoint of the basin (and no more than AF20%, and are practically unaffected in the vertical direction). We should, however, highlight that results are shown only for = 1, and that higher frequency ground motions are expected to be more strongly affected by low-strain damping effects. Finally, waveﬁeld snapshots for an HC basin with AR= 1, 2= 1= 2and= 3are shown in Figure 27. The middle rectangle-like part of the basin behaves similar to a 1D col- umn before the edge generated surface waves arrive, while the corner half-cosines where surface waves originate from amplify the waveﬁeld via focusing. Although the surface wave characteristics differ from the case of the SE-basin due to differences in edge geometry, the same general four-stage waveﬁeld evolution can be observed here as well: (a) body wave arrival, followed by (b-c) surface wave generation at the edges, followed by (d) interaction of body and surface waves in the middle, followed by (e-f) horizontal and ver- tical wave reverberations in the basin and energy leakage towards the halfspace. The characteristic rotational wave pattern at the base of the basin shown in Figure 27-f is re- ferred to as the “breathing zone” [ 33], a region where energy transfer occurs between the scattered P- and S-waveﬁelds. HC basins with large are an appropriate representation of wide shallow basin geometries, similar to the trapezoidal geometry used by Kawase & Aki (1989) [ 28] to study basin effects in Mexico City. In the following section, we use an HC idealized geometry to study basin effects in Kathmandu, (a) (b) (c) (d) (e) (f) Figure 27. Snapshots of total waveﬁeld for HC basin with AR=1, = 5,= 1, and 2= 1= 2. The trapezoidal black line shows the basin boundary. Nepal, that were observed during the 2015 Mw7.8 Gorkha Earthquake. 5. Basin Effects in Kathmandu, Nepal: A simpliﬁed model approximation During the 2015 Mw7.8 Gorkha earthquake [ 4], macroseis- mic observations and recorded evidence strongly showed that basin effects had played an important role on the char- acteristics of strong motion recordings, and the distribution of damage (or lack thereof). To test the extent to which simpliﬁed models can capture complexities of basin effects, we here approximate the Kathmandu basin with a HC ide- alized model. The model was selected to approximate the geometry of the top 0.5 km of basin sediments and is shown in Figure 29 (see Ayoubi et al [ 5] for more detail). The cross-section of the basin corresponds to the red line shown in Figure 28. The strong ground motion stations depicted in the same ﬁgure were installed by Hokkaido University and Tribhuvan University, and they reported the recorded accelerations during the mainshock [ 42]. These records will be used to evaluate the accuracy of the idealized model presented in this study. To estimate the basin response of the idealized model, we use a train of two plane SV Ricker wavelets as shown in Figure 30, to excite a range of resonant modes of the basin. The ”Data” (Figure 30-b) is used that shows the incident excitation derived using de-convolution at depth of b(see Figure 29) from the East-West horizontal component of recorded motion at reference station KTP. In Figure 30- b, we show the low frequency (LF) and high frequency A Systematic Analysis of Basin Effects on Surface Ground Motion 10 km N➤➤ N Image © 2019 DigitalGlobe Image © 2019 DigitalGlobe Image © 2019 DigitalGlobe Image © 2019 CNES / Airbus Image © 2019 CNES / Airbus Image © 2019 CNES / Airbus Image © 2019 Maxar Technologies Image © 2019 Maxar Technologies Image © 2019 Maxar Technologies Figure 28. A plan view of Kathmandu basin. The location of strong ground motion stations is shown by their name. The red line shows the cross section that was used by Ayoubi et al (2018) [ 5] and is used in this study. Figure 29. HC basin used in this study. Dashed line shows the realistic geometry of the basin which was used to ﬁnd the corre- sponding simpliﬁed version in the current study. (HF) components of input motion which we sum to produce the idealized incident plane wave (Sum Incident Motion in the Figure 30). The time series of each wavelet and the combined input shaking are shown in Figure 30-a. We also assume that the basin is made of an elastic isotropic material with properties listed in Table 5. The bedrock properties were adopted from Wei et al (2018) [ 46], and the basin shear wave velocity was calculated using 1D velocity proﬁles published by Bijuckchehn et al (2017) [ 8] beneath the strong motion stations shown in Figure 28. The proﬁles are shown in Figure 31, along with the average proﬁle that we used to estimate a 1D approximation of the sedimentary structure inside the basin. The latter was used to calculate the weighted average shear wave velocity for the simpliﬁed basin model listed in Table 5. Table 5. Basin and halfspace parameters with reference to dimen- sional analysis of section 4. 1234560 7 0.333 0.244 3.6 6.4 0.312 0.79 11.15 Figures 32 and 33 show the results of the simpliﬁed basin analysis where Figure 32-a and 32-b show the AF of the horizontal, and vertical components on the surface of the basin. Basin edge effects can be readily observed in the (a) (b) Figure 30. Time series and Fourier spectrum of incident motion from Ayoubi et al (2018) [ 5] and the current study. The low frequency (LF) and high frequency (HF) show two Ricker wavelets that are summed to derive the input of the numerical simulation (Sum Incident Motion) Figure 31. Black lines show the 1D velocity proﬁles by Bi- juckchehn et al (2017) [ 8]. Blue line shows the averaged and smoothed velocity. We temporally averaged the “1D basin velocity proﬁle” (blue line) to obtain a single value for the shear wave velocity of the basin (red line). form of localized ground motion ampliﬁcation and strong spatial variability. The complex spatiotemporal variation of the basin waveﬁeld is depicted by seismogram synthetics in Figures 32-c and 32-d. In this example, the incident motion includes two Ricker wavelets, each triggering the basin response at a different length scale. The constructive interference of the two is leading to the complex AF spatial variation of Figures 32-a and 32-b; although this complexity would be further accentuated in the case of a broadband seismic incident motion, the main features of ampliﬁcation that include a strong vertical motion in the basin can be adequately captured using this simpliﬁed combination of Ricker pulses. Figure 33 shows a comparison between the ampliﬁcation factor in the frequency domain for the simpliﬁed basin of this study, and the ground motion records from a strong mo- tion array in Kathmandu that recorded the Mw7.8 Gorkha mainshock [ 42]. As can be seen, the simpliﬁed HC basin model captures some characteristics (low frequency) of the complex ground motion records with acceptable accuracy. A Systematic Analysis of Basin Effects on Surface Ground Motion (a) (b) (c) (d) Figure 32. a) Horizontal AF, b) vertical AF, c) Horizontal SS and d) Vertical SS at basin surface As expected, the simpliﬁed model does not capture higher frequencies (more than 1 Hz in this case) since it lacks detailed stratigraphy information that would manifest in high-frequency effects. We should also highlight that the response at station TVU is governed by basin edge effects due to its proximity to the outskirts of the basin; thus, in absence of detailed geometry representation of the basin edge, the predictive capabilities of the idealized model in Figure 33-a are less clear than in the case of Figures 33-b and -c. (a) (b) (c) Figure 33. Comparison of simple HC basin (“Current Study”), and recorded motion during the mainshock from Takai et al (2016) [42] for a) TVU station b) PTN station and c) THM station6. Conclusions In this article, we performed an extensive parametric study to examine the coupled effects of material properties, in- terface geometry and ground motion characteristics on the ground surface response of sedimentary basins. We ﬁrst investigated a simple dipping layer. The calculated surface motion shows that the coupled effect of material contrast and basin-edge can drastically change the waveﬁeld com- pared to a ﬂat ground with no irregular subsurface, and can produce a substantial vertical motion even when the incident motion is purely horizontal. We then deﬁned two idealized geometries (Semi-Elliptical, SE, and Half-Cosine, HC) and studied their effects for elastic media subjected to vertically propagating SV waves of Ricker type using four dimension- less parameters: aspect ratio ( AR), dimensionless frequency (), material contrast ( 2= 1), and dimensionless width ( ). We ﬁrst studied AR, a key parameter in describing the ge- ometry of basin edges. We observed that the location and magnitude of maximum horizontal ampliﬁcation depend on AR; and that for the same AR, SE and HC edge geometries can yield different ampliﬁcation patterns. The parameter  measures the relative size of a basin to the dominant wave- length. For lower values of , an incoming wave treats the basin as a whole (very low motions completely ‘miss‘ the basin), while very high motions interact only locally with the basin edges. By increasing , the spatial varia- tion of ampliﬁcation factor (both horizontal and vertical) enhances, and the AF changes over shorter distances. Our results show that = 0:125had the least impact on the am- pliﬁcation factor, and the response approximated half-space conditions. We next considered material contrast between soil and rock ( 2= 1), a parameter that controls the energy that enters the basin, and regulates the wave speed in each medium. Increasing material contrast generally resulted in a higher ampliﬁcation factor due to the entrapment of earth- quake waves within the basin, and longer duration. Last, we considered the dimensionless width parameter ( ), and showed that it can change the pattern of wave interference by separating the whole basin into two 2D problems (corner half-cosine). We observed that for 5, the basin behaves as two decoupled dipping layers with minimal interactions. Finally, we showed that the edge geometry plays a signiﬁ- cant role in shaping the surface motion and basin waveﬁeld, and recommended a cosine-shaped basin edge for idealized basin simulations. Our results show that dimensionless frequency, material velocity contrast, and aspect ratio are the most inﬂuential among the seven dimensionless parameters we investigated. The dimensionless width ( ) was shown to be less inﬂu- ential compared to the above-mentioned three parameters, which is expected since it stands as a proxy for lateral wave reverberations while the scenarios we examined involved A Systematic Analysis of Basin Effects on Surface Ground Motion vertically propagating incidence. Other dimensionless pa- rameters such as density contrast, Poisson’s ratio or low- strain damping were shown to play a secondary role in this case. This conclusion can be particularly important in de- veloping parameterizations to integrate complex, non-1D phenomena such as basin effects, in data-driven models such as ground motion prediction equations (GMPEs). In the last section of the article, we approximated the shape of Kathmandu basin, Nepal, with an idealized HC 2D basin, and studied its response compared to the 2015 Mw 7.8 Gorkha earthquake observations obtained on the basin ground surface. We presented the ampliﬁcation factor com- puted and recorded on the four strong ground motion sta- tions in the basin and showed that even a simpliﬁed model can reproduce key features of the recordings associated with basin effects. We asserted that a more complex model would be required to study the physics of the phenomenon in more detail by incorporating source effects, 2D or 3D basin ge- ometry models, layering and nonlinear site response. Our ﬁndings show that basin effects can be best captured by proxies of three parameters, , 2= 1andAR. Currently, the most up-to-date GMPEs incorporate basin (really, 1D site) effects through the use of Vs30(average shear wave ve- locity in top 30 meters) and Z1(depth to shear wave velocity 1km=s ), while there is evidence that the two parameters can be correlated within the conﬁnes of similar geologic units [ 1]. Our experience shows that parameters or 2= 1 could help improve GMPE parameterization for both 1D and non-1D conditions, while including a basic measure of basin geometry such as ARshould be investigated as a means of decreasing aleatoric uncertainty associated with site effects in sedimentary basin settings.