Search NASA⌕ Search

SEARCH · Search NASA

Results for “Earthquake Prediction”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

Toward Robust and Routine Determination of Mw for Small Earthquakes: Application to the 2020 Mw 5.7 Magna, Utah, Seismic Sequence

To better characterize seismic hazard, particularly, for induced seismicity, there is an increasing interest in methods to estimate moment magnitude (M w ) for small earthquakes. M w is generally preferred over other magnitude types, but, it is difficult to estimate M w for earthquakes with local magnitude (M L ) <3-3.5, using conventional moment tensor (MT) inversion. The 2020 M ww 5.7 Magna, Utah, seismic sequence provides an opportunity to illustrate and evaluate the value of spectral methods for this purpose. Starting with a high-quality seismic catalog of 2103 earthquakes (M L <5.6), we estimate M w using two independent spectral methods—one based on direct waves, yielding M w,direct , and the other based on coda waves, yielding M w,coda . For the direct-wave method, we present a non-parametric (NP) inversion scheme that solves for apparent geometrical spreading, G(R), and site effects (S), similar to other NP procedures that have been used to calibrate regional M L scales. The NP inversion is constrained using M ws derived from MTs for nine events in the Magna sequence. We recover statistically robust and physically reasonable G(R) and S and compute M w,direct for 635 Magna earthquakes down to M L 0.7. For the coda-wave method, we consider two separate calibration schemes involving previous MT solutions and compute M w,coda for 311 earthquakes down to M L 1.0. For 280 of the events that were processed with both methods—M w,direct and M w,coda —are strongly correlated (r = 0.98), with a mean difference of only 0.05. We compare M w,direct and M w,coda with M L and find reasonably good agreement for M L <3.6 with the theoretically predicted relationship of M w =(2/3)M L +C, in which C is a regional constant. Our results imply that seismic network operators can use spectral-based M w estimates to replace M L estimates for events with M L ≥1.0, and possibly smaller. The main requirement is the existence of a small number of MT solutions for calibration purposes.

58 GEOSCIENCES↗

Geodetic Measurement of Deformation East of the San Andreas Fault in Central California

Triangulation and trilateration data from two geodetic networks located between the western edge of the Great Valley and the San Andreas fault have been used to calculate shear strain rates in the Diablo Range and to estimate the slip rate along the Calaveras and Paicines faults in Central California. Within the Diablo Range the average shear strain rate was determined for the time period between 1962 and 1982 to be 0.15 + or - 0.08 microrad/yr, with the orientation of the most compressive strain at N 16 deg E + or - 14 deg. The orientation of the principal compressive strain predicted from the azimuth of the major structures in the region is N 25 deg E. It is inferred that the measured strain is due to compression across the folds of this area: the average shear straining corresponds to a relative shortening rate of 4.5 + or - 2.4 mm/yr. From an examination of wellbore breakout orientations and the azimuths of P-axes from earthquake focal mechanisms the inferred orientation of maximum compressive stress was found to be similar to the direction of maximum compressive strain implied by the trend of local fold structures. Results do not support the hypothesis of uniform fault-normal compression within the Coast Ranges. From trilateration measurements made between 1972 and 1987 on lines that are within 10 km of the San Andreas fault, a slip rate of 10 to 12 mm/yr was calculated for the Calaveras-Paicines fault south of Hollister. The slip rate of the Paicines fault decreases to 4 mm/yr near Bitter.

Sauber, Jeanne M.↗

Ionospheric Signature of Surface Mine Blasts from Global Positioning System Measurements

Sources such as atmospheric or buried explosions and shallow earthquakes are known to produce infrasonic pressure waves in the atmosphere. Because of the coupling between neutral particles and electrons at ionospheric altitudes, these acoustic and gravity waves induce variations of the ionospheric electron density. The Global Positioning System (GPS) provides a way of directly measuring the total electron content in the ionosphere and, therefore, of detecting such perturbations in the upper atmosphere. In July and August 1996, three large surface mine blasts (1.5 Kt each) were detonated at the Black Thunder coal mine in eastern Wyoming. As part of a seismic and acoustic monitoring- experiment, we deployed five dual-frequency GPS receivers at distances ranging from 50 to 200 km from the mine and were able to detect the ionospheric perturbation caused by the blasts. The perturbation starts 10 to 15 min after the blast, lasts for about 30 min, and propagates with an apparent horizontal velocity of 1200 meters per second. Its amplitude reaches 3 x 10 (exp 14) el per square meters in the 7-3 min period band, a value close to the ionospheric perturbation caused by the M = 6.7 Northridge earthquake. The small signal-to-noise ratio of the perturbation can be improved by slant-stacking the electron content time-series recorded by the different GPS receivers taking into account the horizontal propagation of the perturbation. The energy of the perturbation is concentrated in the 200 to 300 second period band, a result consistent with previous observations and numerical model predictions. The 300 second band probably corresponds to gravity modes and shorter periods to acoustic modes, respectively. Using a 1-D stratified velocity model of the atmosphere we show that linear acoustic ray tracing fits arrival times at all GPS receivers. We interpret the perturbation as a direct acoustic wave caused by the explosion itself. This study shows that even relatively small subsurface events can produce ionospheric perturbations that are above the detection threshold of the GPS technique. By sensing derivative signals, which can be detected over a relatively broad region, it appears that GPS might be particularly useful for source characterization within the first acoustic quiet zone where infrasound would probably be ineffective. This suggests that dual-frequency GPS monitoring could contribute to Comprehensive Nuclear Test Ban Treaty verification.

Calais, Eric↗

A Unique Perspective from Space on our Planet: Science, Technologies and Applications

The study of Planet earth is a very complex problem. It has many non-linear and chaotic systems operating in parallel and have interdependencies. In reality, these systems/phenomena s are not well understood or mathematically modeled because of our lack of knowledge of such intricate processes. However, in order to further the subject of Earth as an integrated system, space provides excellent vantage points to look at these processes in multidimensional framework. For example, we can make strives to understand the global water cycle, carbon cycle, atmospheric chemistry, biomass changes, oceans and solid Earth variations by making multitude of global measurements such as soil moisture, precipitation, tropospheric and stratospheric gases, aerosols, tropospheric winds, ocean salinity, ocean color, vegetation cover, crustal dynamics and many more. Such suites of measurements derive the coupled models so we may predict the changes due to natural and anthropogenic forcing. NASA along with other international space agencies have made tremendous investments in recent years in developing and flying remote sensing space borne sensors to enable these measurements. These science measurements and products are further used to address pressing issues such as coastal zone erosion, air quality, severe weather, water availability and quality, public health, fires, earthquakes, land slides and others for societal benefits. This presentation provides a comprehensive overview of NASA s science investigations, related technologies and satellites/sensors and applications.

Habib, Shaid↗

Methodological guidelines on concrete degradation based on predictive models and the release of MOSAIC for industry use

In light-water reactors (LWRs), the concrete biological shield (CBS) designates the concrete structure directly facing the reactor pressure vessel (RPV). The primary function of the CBS is to protect equipment and personnel from the neutron and gamma radiation exiting the RPV. Most CBSs in operation in the United States also provide structural support to the RPV. Based on a long-term structural analysis, the structural integrity of the CBS to transfer the in-service passive load to the foundation, dynamic loading during an earthquake, and thermal loading during a loss-of-coolant accident (LOCA) must be maintained. Based on test reactor data for accelerated conditions, the mechanical properties of irradiated concrete are affected when exposed to neutron fluence higher than ≈ 10 19 n.cm -2 (E > 0.1 MeV). At 80 years of operation, the fluence estimates at the surface of the CBS range between 1×10 19 and 7×10 19 n.cm -2 (E > 0.1 MeV): the fluence value depends mostly on the design. Although fluence attenuates through the CBS by virtue of the shielding properties of concrete, about 5% to 10% of the CBS wall depth is affected by high fluence. The main degradation mechanism is the so-called radiation-induced volumetric expansion (RIVE) caused by the amorphization of aggregate-forming minerals. RIVE causes large deformation of up to 18% in pure quartz, and it also reduces the structural properties of concrete. The structural effects of long-term exposure to fast neutron irradiation in LWRs was studied in the report entitled “Assessment of the Effect of the Irradiation-Induced Degradation on the In-Service Structural Performance of the Concrete Biological Shields” (M3LW-23OR0403013). This report illustrates that (1) irradiation-induced damage expands further than the region subject to a cumulative fluence of 10 19 n.cm -2 (E > 0.1 MeV) to reach the steel reinforcement location, and (2) the irradiation-induced damage region shows no substantial residual bearing capacity and should not be accounted for in the integrity assessment of the CBS.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A new method for monitoring global volcanic activity

The ERTS Data Collection System makes it feasible for the first time to monitor the level of activity at widely separated volcanoes and to relay these data rapidly to one central office for analysis. While prediction of specific eruptions is still an evasive goal, early warning of a reawakening of quiescent volcanoes is now a distinct possibility. A prototypical global volcano surveillance system was established under the ERTS program. Instruments were installed in cooperation with local scientists on 15 volcanoes in Alaska, Hawaii, Washington, California, Iceland, Guatemala, El Salvador and Nicaragua. The sensors include 19 seismic event counters that count four different sizes of earthquakes and six biaxial borehole tiltmeters that measure ground tilt with a resolution of 1 microradian. Only seismic and tilt data are collected because these have been shown in the past to indicate most reliably the level of volcano activity at many different volcanoes. Furthermore, these parameters can be measured relatively easily with new instrumentation.

Ward, P. L.↗

Fracture Mechanics—Theory, Modeling and Applications

The field of fracture mechanics was developed during the throes of World War II, and since then, it has been a very active area of research. This is a very energetic and vibrant field because fracture processes are relevant for a vast range of engineering applications spanning different temporal and length scales. Depending on the application, material fracture and fragmentation may be either a desirable feature (for example, for the purpose of hydraulic fracturing operations), or something that is to be avoided at all costs (for example, in key components of mechanical systems). In some other instances, fractures are already present and must be accommodated through novel design (for example, in the case of earthquake ruptures occurring in the Earth’s crust). Because of this wide spectra of motivation, there is a continuous need for the fracture mechanics research community to gain more insight on how fractures are created, evolve, and interact with themselves and with material microstructures. In addition, there are still many remaining questions about how fracture propagation, growth, and interaction impact overall material behavior, and how to develop accurate models to predict this behavior.

36 MATERIALS SCIENCE↗

Regional infrasonic observations from surface explosions – influence of atmospheric variations and realistic terrain

SUMMARY A pair of 1-ton, conventional surface explosions were conducted at the Nevada National Security Site in the fall of 2020 producing seismoacoustic signatures observable hundreds of kilometres from the source location. Regional infrasonic observations include tropospheric ducting at large distances to the south, a wide stratospheric waveguide with signals observed more than 700 km to the east, and anomalous arrivals in the stratospheric shadow zone. Notable differences in propagation between the events are identified despite the explosions being conducted just two days apart due to a sharp temporal shift in the tropospheric winds as well as structural changes in the stratospheric winds. Propagation simulations of the two events have been completed using a combination of ray tracing and parabolic equation (PE) methods. Simulations have been conducted to quantify the impact of the temporal variations in the atmosphere as well as the influence of terrain on propagation. Temporal variations in reflection locations are found to produce notable changes in downrange propagation due to spatially varying terrain features. Finite frequency effects modelled by the PE are found to predict ensonification not included in corresponding 2D ray tracing simulations. Notable variations in predicted signal amplitude are found due to focusing by along-path and cross-path terrain gradients; though, the later of these is only modelled using fully 3D ray tracing analysis.

58 GEOSCIENCES↗

Structural modeling and dynamic analysis of condensate storage tanks in nuclear power plants

Condensate storage tanks (CSTs) in nuclear power plants (NPPs) are classified as critical equipment capable of surviving strong shaking in a design basis earthquake to assure the ability to subsequently provide cooling water. Structural modeling and dynamic analysis of CSTs are complicated due to fluid-structure interaction (FSI) and coupling issues, which could have significant effects on seismic response. The capability of a number of approximate models to capture seismic response is investigated using dynamic analysis results from detailed finite element models. Modal analyses and time history analyses are carried out using both 2D and 3D models to predict the dynamic behavior of CSTs as a function of ground motion intensity. Although 2D simplified models can be used to quickly evaluate the dynamic response of CSTs when there is substantial margin to failure, a detailed 3D model is required when it is necessary to examine a limit state associated with the failure mode of the tank. The findings show good agreement between the natural frequencies of convective modes determined from the 2D and 3D CST models. The difference between the frequencies of impulsive modes were found to be equal to or less than 25%.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

WUS324: Multiscale Full Waveform Inversion Approaching Convergence Improves Waveform Fits While Imaging Seismic Structure of the Western United States

Abstract We report a new model of radially anisotropic crustal and upper mantle structure of the western United States (WUS324) obtained from full waveform inversion of earthquake data. We ran three multiscale inversion stages beyond model WUS256 (Rodgers et al., 2022, https://doi.org/10.1029/2022jb024549 ) allowing them to approach convergence to fit a larger data set to a shorter minimum period of 16 s. WUS324 is based on 324 total iterations from its starting model, significantly more (16 times) than previous studies. Waveform misfit reductions are 66%–70% for both the inversion data and an independent validation data set providing confidence in the predictive power of the model. WUS324 provides much better fits and reveals shear wavespeed, v S , structure of this large region with more detail than previous waveform tomography models. We show representative images demonstrating the resolution of diverse seismic structure across this highly heterogeneous region including oceanic lithosphere, subducting slabs and continental magmatism.

58 GEOSCIENCES↗

ANN-based ground motion model for Turkey using stochastic simulation of earthquakes

SUMMARY Turkey is characterized by a high level of seismic activity attributed to its complex tectonic structure. The country has a dense network to record earthquake ground motions; however, to study previous earthquakes and to account for potential future ones, ground motion simulations are required. Ground motion simulation techniques offer an alternative means of generating region-specific time-series data for locations with limited seismic networks or regions with seismic data gaps, facilitating the study of potential catastrophic earthquakes. In this research, a local ground motion model (GMM) for Turkey is developed using region-specific simulated records, thus constructing a homogeneous data set. The simulations employ the stochastic finite-fault approach and utilize validated input-model parameters in distinct regions, namely Afyon, Erzincan, Duzce, Istanbul and Van. To overcome the limitations of linear regression-based models, artificial neural network is used to establish the form of equations and coefficients. The predictive input parameters encompass fault mechanism (FM), focal depth (FD), moment magnitude (Mw), Joyner and Boore distance (RJB) and average shear wave velocity in the top 30 m (Vs30). The data set comprises 7359 records with Mw ranging between 5.0 and 7.5 and RJB ranging from 0 to 272 km. The results are presented in terms of spectral ordinates within the period range of 0.03–2.0 s, as well as peak ground acceleration and peak ground velocity. The quantification of the GMM uncertainty is achieved through the analysis of residuals, enabling insights into inter- and intra-event uncertainties. The simulation results and the effectiveness of the model are verified by comparing the predicted values of ground motion parameters with the observed values recorded during previous events in the region. The results demonstrate the efficacy of the proposed model in simulating physical phenomena.

Karimzadeh, Shaghayegh (ORCID:0000000337531676)↗

On the measurement of S diff splitting caused by lowermost mantle anisotropy

Seismic anisotropy has been detected at many depths of the Earth, including its upper layers, the lowermost mantle and the inner core. While upper mantle seismic anisotropy is relatively straightforward to resolve, lowermost mantle anisotropy has proven to be more complicated to measure. Due to their long, horizontal ray paths along the core–mantle boundary (CMB), S waves diffracted along the CMB (S diff ) are potentially strongly influenced by lowermost mantle anisotropy. S diff waves can be recorded over a large epicentral distance range and thus sample the lowermost mantle everywhere around the globe. S diff therefore represents a promising phase for studying lowermost mantle anisotropy; however, previous studies have pointed out some difficulties with the interpretation of differential SH diff –SV diff traveltimes in terms of seismic anisotropy. Here, we provide a new, comprehensive assessment of the usability of S diff waves to infer lowermost mantle anisotropy. Using both axisymmetric and fully 3-D global wavefield simulations, we show that there are cases in which S diff can reliably detect and characterize deep mantle anisotropy when measuring traditional splitting parameters (as opposed to differential traveltimes). First, we analyze isotropic effects on S diff polarizations, including the influence of realistic velocity structure (such as 3-D velocity heterogeneity and ultra-low velocity zones), the character of the lowermost mantle velocity gradient, mantle attenuation structure, and Earth’s Coriolis force. Secondly, we evaluate effects of seismic anisotropy in both the upper and the lowermost mantle on SH diff waves. In particular, we investigate how SH diff waves are split by seismic anisotropy in the upper mantle near the source and how this anisotropic signature propagates to the receiver for a variety of lowermost mantle models. We demonstrate that, in particular and predictable cases, anisotropy leads to S diff splitting that can be clearly distinguished from other waveform effects. Here, these results enable us to lay out a strategy for the analysis of S diff splitting due to anisotropy at the base of the mantle, which includes steps to help avoid potential pitfalls, with attention paid to the initial polarization of S diff and the influence of source-side anisotropy. We demonstrate our S diff splitting method using three earthquakes that occurred beneath the Celebes Sea, measured at many transportable array stations at a suitable epicentral distance. We resolve consistent and well-constrained S diff splitting parameters due to lowermost mantle anisotropy beneath the northeastern Pacific Ocean.

54 ENVIRONMENTAL SCIENCES↗

Reverse Time Migration of Explosion-generated Infrasound and Ground-Coupled Airwaves

Accurately locating sources of seismic and infrasonic energy is integral to global monitoring of earthquakes and explosions. Infrasound arrivals times can be used to calculate the origins of events that generate acoustic energy. Picking times of emergent infrasound arrivals, however, can be difficult and prone to uncertainty. Reverse time migration (RTM) is a waveform based location method that does not rely on picked arrival times. Here we use RTM to locate a known chemical explosion that generated acoustic and acoustic-to-seismic signals on 26 and 108 receivers, respectively. All location predictions are less than 24 km from the known location with time errors of less than three minutes. We find strong overall agreement between our results and those of existing RTM and arrival time based methods. Our initial results suggest that RTM is a promising method of event location using acoustic arrivals recorded on both infrasound and seismic instrumentation.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Excitation study of the Lageos-derived Chandler wobble

Euler (1765) has deduced that any nonspherical rigid body which is rotating about some axis that is not its principal moment of inertia axis will experience a wobble as it rotates. The earth's wobble predicted by Euler was actually detected by Chandler (1891). The present paper is concerned with this wobble which is now known as the Chandler wobble. The Chandler wobble has now been under observation for more than 80 years. During part of this time, the amplitude of the wobble has actually been seen to grow. It follows that there must be some mechanisms operating to maintain (or excite) the Chandler wobble preventing it from decaying. Possible excitation mechanisms considered include earthquakes and meteorological variations. In this paper, an analysis is conducted of Lageos polar motion data for the period 1977-1983 to find out what can be learned from these data about the excitation mechanisms.

Gross, R. S.↗

Industrial Productivity

NASTRAN is an offshoot of the computer-design technique used in construction of airplanes and spacecraft. [n this technique engineers create a mathematical model of the aeronautical or space vehicle and "fly" it on the ground by means of computer simulation. The technique enables them to study performance and structural behavior of a number of different designs before settling on the final configuration and proceeding with construction. From this base of aerospace experience, NASA-Goddard developed the NASTRAN general purpose computer program, which offers an exceptionally wide range of analytic capability with regard to structures. NASTRAN has been applied to autos, trucks, railroad cars, ships, nuclear power reactors, steam turbines, bridges, and office buildings. NASA-Langley provides program maintenance services regarded as vital by many NASTRAN users. NASTRAN is essentially a predictive tool. It takes an electronic look at a computerire$.dedgn and reports how the structure will react under a great many different conditions. It can, for example, note areas where high stress levels will occur-potential failure points that need strengthening. Conversely, it can identify over-designed areas where weight and material might be saved safely. NASTRAN can tell how pipes stand up under strong fluid flow, how metals are affected by high temperatures, how a building will fare in an earthquake or how powerful winds will cause a bridge to oscillate. NASTRAN analysis is quick and inexpensive. It minimizes trial-and-error in the design process and makes possible better, safe, lighter structures affording large-scale savings in development time and materials. Some examples of the broad utility NASTRAN is finding among industrial firms are shown on these pages.

Source record↗

SMART Subsea Cables for Observing the Earth and Ocean, Mitigating Environmental Hazards, and Supporting the Blue Economy

The Joint Task Force, Science Monitoring And Reliable Telecommunications (JTF SMART) Subsea Cables, is working to integrate environmental sensors for ocean bottom temperature, pressure, and seismic acceleration into submarine telecommunications cables. The purpose of SMART Cables is to support climate and ocean observation, sea level monitoring, observations of Earth structure, and tsunami and earthquake early warning and disaster risk reduction, including hazard quantification. Recent advances include regional SMART pilot systems that are the first steps to trans-ocean and global implementation. Examples of pilots include: InSEA wet demonstration project off Sicily at the European Multidisciplinary Seafloor and water column Observatory Western Ionian Facility; New Caledonia and Vanuatu; French Polynesia Natitua South system connecting Tahiti to Tubaui to the south; Indonesia starting with short pilot systems working toward systems for the Sumatra-Java megathrust zone; and the CAM-2 ring system connecting Lisbon, Azores, and Madeira. This paper describes observing system simulations for these and other regions. Funding reflects a blend of government, development bank, philanthropic foundation, and commercial contributions. In addition to notable scientific and societal benefits, the telecommunications enterprise’s mission of global connectivity will benefit directly, as environmental awareness improves both the integrity of individual cable systems as well as the resilience of the overall global communications network. SMART cables support the outcomes of a predicted, safe, and transparent ocean as envisioned by the UN Decade of Ocean Science for Sustainable Development and the Blue Economy. As a continuation of the OceanObs’19 conference and community white paper (Howe et al., 2019, 10.3389/fmars.2019.00424), an overview of the SMART programme and a description of the status of ongoing projects are given.

54 ENVIRONMENTAL SCIENCES↗

Present-day plate motions

A data set comprising 110 spreading rates, 78 transform fault azimuths and 142 earthquake slip vectors was inverted to yield a new instantaneous plate motion model, designated RM2. The mean averaging interval for the relative motion data was reduced to less than 3 My. A detailed comparison of RM2 with angular velocity vectors which best fit the data along individual plate boundaries indicates that RM2 performs close to optimally in most regions, with several notable exceptions. On the other hand, a previous estimate (RM1) failed to satisfy an extensive set of new data collected in the South Atlantic Ocean. It is shown that RM1 incorrectly predicts the plate kinematics in the South Atlantic because the presently available data are inconsistent with the plate geometry assumed in deriving RM1. It is demonstrated that this inconsistency can be remedied by postulating the existence of internal deformation with the Indian plate, although alternate explanations are possible.

Minster, J. B.↗

Comparison of GPS surveys with historical triangulation surveys in the southern California borderland

Global plate models predict about 56 mm/yr of motion between the North American and Pacific plates along the plate boundary in southern California, while geodetic and Holocene geological data suggest only 34 mm/yr on the San Andreas fault. Deformation in the Great Basin does not explain this discrepancy, and it has been suggested that faulting in the offshore of southern California could account for some of the discrepancy. Evidence of deformation in the offshore region of southern California is most abundant in the Santa Barbara Channel. Geological investigations of folding and faulting in this region, as well as earthquake investigations, indicate north-south shortening across the channel on the order of 10 to 20 mm/yr. The most rapid rates occur to the east of the channel in the Ventura Basin. South of the Santa Barbara Channel, though, evidence for deformation is limited to seismicity studies which are sparse. Seismic events are abundant in this area, but their implication for the amount of deformation in the offshore is unclear. GPS measurements made between June 1986 and May 1988 have been used to obtain vector positions for several stations at which historical first order triangulation observations were performed between the late 1800's and the mid 1900's between the coast of southern California and the nearby offshore islands. By comparing the spheroidal angles obtained from the GPS positions with the the previously observed triangulation data, shear strain rates can be calculated for the region using Frank's method. These results seem to suggest that shear strain deformation occurs in the offshore of southern California as a result of north to north-west shortening. That deformation is most active in the Santa Barbara Channel region and least active between Catalina and San Nicholas islands. Just how much of the missing plate motion can be accounted for by this deformation is not known at this time and will have to await further analysis.

Webb, Frank H.↗